Alabama Course of Study

Collect and analyze data and interpret results.

Classify objects into given categories of 10 or fewer; count the number of objects in each category and sort the categories by count.

Categorize data on Venn diagrams, pictographs, and "yes-no" charts using real objects, symbolic representations, or pictorial representations.

Count forward orally from 0 to 100 by ones and by tens. Count backward orally from 10 to 0 by ones.

Count to 100 by ones beginning with any given number between 0 and 99.

Write numerals from 0 to 20.

Represent 0 to 20 using concrete objects when given a written numeral from 0 to 20 (with 0 representing a count of no objects).

Connect counting to cardinality using a variety of concrete objects.

Say the number names in consecutive order when counting objects.

Indicate that the last number name said tells the number of objects counted in a set.

Indicate that the number of objects in a set is the same regardless of their arrangement or the order in which they were counted.

Explain that each successive number name refers to a quantity that is one larger.

Count to answer "how many?" questions.

Count using no more than 20 concrete objects arranged in a line, a rectangular array, or a circle.

Count using no more than 10 concrete objects in a scattered configuration.

Draw the number of objects that matches a given numeral from 0 to 20.

Orally identify whether the number of objects in one group is greater/more than, less/fewer than, or equal/the same as the number of objects in another group, in groups containing up to 10 objects, by using matching, counting, or other strategies.

Compare two numbers between 0 and 10 presented as written numerals (without using inequality symbols).

Identify and describe measurable attributes (length, weight, height) of a single object using vocabulary such as long/short, heavy/light, or tall/short.

Represent addition and subtraction up to 10 with concrete objects, fingers, pennies, mental images, drawings, claps or other sounds, acting out situations, verbal explanations, expressions, or equations.

Solve addition and subtraction word problems, and add and subtract within 10, by using concrete objects or drawings to represent the problem.

Decompose numbers less than or equal to 10 into pairs of smaller numbers in more than one way, by using concrete objects or drawings, and record each decomposition by a drawing or equation.

For any number from 0 to 10, find the number that makes 10 when added to the given number, by using concrete objects or drawings, and record the answer with a drawing or equation.

Understand simple patterns.

Duplicate and extend simple patterns using concrete objects.

Compose and decompose numbers from 11 to 19 by using concrete objects or drawings to demonstrate understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Collect and analyze data and interpret results.

Organize, represent, and interpret data with up to three categories.

Ask and answer questions about the total number of data points in organized data.

Summarize data on Venn diagrams, pictographs, and "yes-no" charts using real objects, symbolic representations, or pictorial representations.

Determine "how many" in each category using up to three categories of data.

Determine "how many more" or "how many less" are in one category than in another using data organized into two or three categories.

Build and draw shapes which have defining attributes.

Distinguish between defining attributes and non-defining attributes.

Partition circles and rectangles into two and four equal shares and describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.

Describe "the whole" as two of or four of the shares of circles and rectangles partitioned into two or four equal shares.

Explain that decomposing into more equal shares creates smaller shares of circles and rectangles.

Identify pennies and dimes by name and value.

Extend the number sequence from 0 to 120.

Count forward and backward by ones, starting at any number less than 120.

Read numerals from 0 to 120.

Write numerals from 0 to 120.

Represent a number of objects from 0 to 120 with a written numeral.

Explain that the two digits of a two-digit number represent amounts of tens and ones.

Identify a bundle of ten ones as a "ten."

Compare pairs of two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words "is greater than," "is equal to," and "is less than."

Add within 100, using concrete models or drawings and strategies based on place value.

Add a two-digit number and a one-digit number.

Add a two-digit number and a multiple of 10.

Demonstrate that in adding two-digit numbers, tens are added to tens, ones are added to ones, and sometimes it is necessary to compose a ten.

Relate the strategy for adding a two-digit number and a one-digit number to a written method and explain the reasoning used.

Use addition and subtraction to solve word problems within 20 by using concrete objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Add to with change unknown to solve word problems within 20.

Take from with change unknown to solve word problems within 20.

Put together/take apart with addend unknown to solve word problems within 20.

Compare quantities, with difference unknown, bigger unknown, and smaller unknown while solving word problems within 20.

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 by using concrete objects, drawings, or equations with a symbol for the unknown number to represent the problem.

Explain subtraction as an unknown-addend problem.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by counting on.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by making ten.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by decomposing a number leading to a ten.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by using the relationship between addition and subtraction.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by creating equivalent but easier or known sums.

Explain that the equal sign means "the same as." Determine whether equations involving addition and subtraction are true or false.

Understand simple patterns.

Reproduce, extend, and create patterns and sequences of numbers using a variety of materials.

Collect and analyze data and interpret results.

Measure lengths of several objects to the nearest whole unit.

Create a line plot where the horizontal scale is marked off in whole-number units to show the lengths of several measured objects.

Create a picture graph and bar graph to represent data with up to four categories.

Using information presented in a bar graph, solve simple "put-together," "take-apart," and "compare" problems.

Using Venn diagrams, pictographs, and "yes-no" charts, analyze data to predict an outcome.

Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Recognize and draw shapes having specified attributes.

Partition circles and rectangles into two, three, or four equal shares. Describe the shares using such terms as halves, thirds, half of, or a third of, and describe the whole as two halves, three thirds, or four fourths.

Explain that equal shares of identical wholes need not have the same shape.

Measure the length of an object by selecting and using standard units of measurement shown on rulers, yardsticks, meter sticks, or measuring tapes.

Measure objects with two different units, and describe how the two measurements relate to each other and the size of the unit chosen.

Create a number line diagram using whole numbers and use it to represent whole-number sums and differences within 100.

Express an understanding of common terms such as, but not limited to, quarter past, half past, and quarter to.

Solve problems with money.

Identify nickels and quarters by name and value.

Find the value of a collection of quarters, dimes, nickels, and pennies.

Solve word problems by adding and subtracting within one dollar, using the $ and ¢ symbols appropriately (not including decimal notation).

Explain that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

Explain the following three-digit numbers as special cases: 100 can be thought of as a bundle of ten tens, called a "hundred," and the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words "is greater than," "is equal to," and "is less than."

Use a variety of strategies to add up to four two-digit numbers.

Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.

Explain that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem.

Fluently add and subtract within 20 using mental strategies such as counting on, making ten, decomposing a number leading to ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums.

State automatically all sums of two one-digit numbers.

Use concrete objects to determine whether a group of up to 20 objects is even or odd.

Write an equation to express an even number as a sum of two equal addends.

Using concrete and pictorial representations and repeated addition, determine the total number of objects in a rectangular array with up to 5 rows and up to 5 columns.

Understand simple patterns.

Reproduce, extend, create, and describe patterns and sequences using a variety of materials.

For a given or collected set of data, create a scaled (one-to-many) picture graph and scaled bar graph to represent a data set with several categories.

Determine a simple probability from a context that includes a picture.

Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled graphs.

Recognize and describe polygons (up to 8 sides), triangles, and quadrilaterals (rhombuses, rectangles, and squares) based on the number of sides and the presence or absence of square corners.

Draw examples of quadrilaterals that are and are not rhombuses, rectangles, and squares.

Tell and write time to the nearest minute; measure time intervals in minutes (within 90 minutes.)

Solve real-world problems involving addition and subtraction of time intervals in minutes by representing the problem on a number line diagram.

Use the four operations to solve one-step word problems involving masses or volumes given in the same metric units.

Estimate and measure liquid volumes and masses of objects using liters (l), grams (g), and kilograms (kg).

Find the area of a rectangle with whole number side lengths by tiling without gaps or overlays and counting unit squares.

Relate area to the operations of multiplication using real-world problems, concrete materials, mathematical reasoning, and the distributive property.

Decompose rectilinear figures into smaller rectangles to find the area, using concrete materials.

Construct rectangles with the same perimeter and different areas or the same area and different perimeters.

Solve real-world problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length of rectangles.

Use various strategies to add and subtract fluently within 1000.

Use concrete materials and pictorial models based on place value and properties of operations to find the product of a one-digit whole number by a multiple of ten (from 10 to 90).

Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

Represent a unit fraction (1/b) on a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts as specified by the denominator.

Represent a fraction (a/b) on a number line by marking off a lengths of size (1/b) from zero.

Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.

Illustrate the product of two whole numbers as equal groups by identifying the number of groups and the number in each group and represent as a written expression.

Illustrate and interpret the quotient of two whole numbers as the number of objects in each group or the number of groups when the whole is partitioned into equal shares.

Solve word situations using multiplication and division within 100 involving equal groups, arrays, and measurement quantities; represent the situation using models, drawings, and equations with a symbol for the unknown number.

Develop and apply properties of operations as strategies to multiply and divide.

Use the relationship between multiplication and division to represent division as an equation with an unknown factor.

Use strategies based on properties and patterns of multiplication to demonstrate fluency with multiplication and division within 100.

Fluently determine all products obtained by multiplying two one-digit numbers.

State automatically all products of two one-digit numbers by the end of third grade.

Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding.

Draw and identify lines and angles, and identify shapes by properties of their lines and angles.

Identify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size.

Describe right triangles as a category, and identify right triangles.

Define a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.

Identify line-symmetric figures and draw lines of symmetry.

Select and use an appropriate unit of measurement for a given attribute (length, mass, liquid volume, time) within one system of units: metric - km, m, cm; kg, g, l, ml; customary - lb, oz; time - hr, min, sec.

Within one system of units, express measurements of a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

Use the four operations to solve measurement word problems with distance, intervals of time, liquid volume, mass of objects, and money.

Solve measurement problems involving simple fractions or decimals.

Solve measurement problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Identify an angle as a geometric shape formed wherever two rays share a common endpoint.

Decompose an angle into non-overlapping parts to demonstrate that the angle measure of the whole is the sum of the angle measures of the parts.

Solve addition and subtraction problems on a diagram to find unknown angles in real-world or mathematical problems.

Using models and quantitative reasoning, explain that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right.

Read and write multi-digit whole numbers using standard form, word form, and expanded form.

Use place value understanding to compare two multi-digit numbers using >, =, and < symbols.

Use place value strategies to fluently add and subtract multi-digit whole numbers and connect strategies to the standard algorithm.

Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.

Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

Using area and length fraction models, explain why one fraction is equivalent to another, taking into account that the number and size of the parts differ even though the two fractions themselves are the same size.

Apply principles of fraction equivalence to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, ½, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions.

Explain that comparison of two fractions is valid only when the two fractions refer to the same whole.

Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

Model and explain how a non-unit fraction can be represented by a whole number times the unit fraction.

Extend previous understanding of multiplication to multiply a whole number times any fraction less than one.

Solve word problems involving multiplying a whole number times a fraction using visual fraction models and equations to represent the problem.

Express, model, and explain the equivalence between fractions with denominators of 10 and 100.

Use fraction equivalency to add two fractions with denominators of 10 and 100.

Use models and decimal notation to represent fractions with denominators of 10 and 100.

Use visual models and reasoning to compare two decimals to hundredths (referring to the same whole), recording comparisons using symbols >, =, or <, and justifying the conclusions.

Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

For whole numbers in the range 1 to 100, find all factor pairs, identifying a number as a multiple of each of its factors.

Determine whether a whole number in the range 1 to 100 is a multiple of a given one-digit number.

Determine whether a whole number in the range 1 to 100 is prime or composite.

Generate and analyze a number or shape pattern that follows a given rule.

Interpret data in graphs (picture, bar, and line plots) to solve problems using numbers and operations.

Create a line plot to display a data set of measurements in fractions of a unit (12,14,18).

Solve problems involving addition and subtraction of fractions using information presented in line plots.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

Add, subtract, multiply, and divide fractions to solve problems involving information presented in line plots.

Classify triangles according to side length (isosceles, equilateral, scalene) and angle measure (acute, obtuse, right, equiangular).

Classify quadrilaterals in a hierarchy based on properties.

Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Identify volume as an attribute of solid figures, and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised (non-standard) units.

Pack a solid figure without gaps or overlaps using n unit cubes to demonstrate volume as n cubic units.

Use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.

Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left.

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, using whole-number exponents to denote powers of 10.

Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10, using whole-number exponents to denote powers of 10.

Use place value understanding to round decimals to thousandths.

Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or the relationships between addition/subtraction and multiplication/division; relate the strategy to a written method, and explain the reasoning used.

Use concrete models and drawings to solve problems with decimals to hundredths.

Solve problems in a real-world context with decimals to hundredths.

Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Model and interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b)

Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers

Use a visual fraction model (area model, set model, or linear model) to show (a/b) × q and create a story context for this equation to interpret the product as a parts of a partition of q into b equal parts.

Use a visual fraction model (area model, set model, or linear model) to show (a/b) × (c/d) and create a story context for this equation to interpret the product.

Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths to show that the area is the same as would be found by multiplying the side lengths.

Interpret multiplication as scaling (resizing).

Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and relate the principle of fraction equivalence.

Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number and relate the principle of fraction equivalence.

Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.

Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.

Write, explain, and evaluate simple numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving parentheses, brackets, or braces, using commutative, associative, and distributive properties.

Generate two numerical patterns using two given rules and complete an input/output table for the data.

Use data from an input/output table to identify apparent relationships between corresponding terms.

Form ordered pairs from values in an input/output table.

Graph ordered pairs from an input/output table on a coordinate plane.

Write, evaluate, and compare expressions involving whole number exponents.

Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

Interpret a variable as an unknown value for any number in a specified set, depending on the context.

Write expressions to represent verbal statements and real-world scenarios.

Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.

Determine whether two expressions are equivalent and justify the reasoning.

Use equations and inequalities to represent and solve real-world or mathematical problems.

Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.

Interpret the solution of an equation in the context of the problem.

Write and solve inequalities in the form of x>c, x<c, x≥ c, or x ≤ c to represent a constraint or condition in a real-world or mathematical problem.

Interpret the solution of an inequality in the context of a problem.

Represent the solutions of inequalities on a number line and explain that the solution set may contain infinitely many solutions.

Identify and analyze relationships between independent and dependent variables.

Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.

Use tables, graphs, and equations to represent the relationship between independent and dependent variables.

Use real-world and mathematical problems to analyze data and demonstrate an understanding of statistical variability and measures of center.

Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.

Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.

Determine which measure of center best represents a real-world data set.

Interpret the measures of center and variability in the context of a problem.

Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.

Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).

Use graphical representations of real-world data to describe the context from which they were collected.

Graph polygons in the coordinate plane to solve real-world and mathematical problems.

Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems.

Determine missing vertices of a rectangle with the same x-coordinate or the same y-coordinate when graphed in the coordinate plane.

Use coordinates to find the length of a side between points having the same x-coordinate or the same y-coordinate.

Calculate perimeter and area of a polygon graphed in the coordinate plane (limiting to polygons in which consecutive vertices have the same x-coordinate or the same y-coordinate).

Solve real-world and mathematical problems to determine area, surface area, and volume.

Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.

Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.

Interpret and compute quotients of fractions using visual models and equations to represent problems.

Use quotients of fractions to analyze and solve problems.

Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.

Add, subtract, multiply, and divide decimals using a standard algorithm.

Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

Use factors and multiples to determine prime factorization.

Apply knowledge of the number system to represent and use rational numbers in a variety of forms.

Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.

Locate integers and other rational numbers on a horizontal or vertical line diagram.

Define opposites as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

Find the position of pairs of integers and other rational numbers on the coordinate plane.

Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

Identify (a,b) and (a,-b) as reflections across the x-axis.

Identify (a,b) and (-a,b) as reflections across the y-axis.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts

Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.

Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

Use unit rates to represent and describe ratio relationships.

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Generate expressions in equivalent forms based on context and explain how the quantities are related.

Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

Solve word problems leading to inequalities of the form px + q > r or px + q where p, q, and r are specific rational numbers. Graph the solution set of the inequality, and interpret it in the context of the problem.

Examine a sample of a population to generalize information about the population.

Differentiate between a sample and a population.

Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

Determine whether conclusions and generalizations can be made about a population based on a sample.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and making predictions or conclusions about the population.

Informally explain situations in which statistical bias may exist.

Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.

Investigate probability models.

Use a number from 0 to 1 to represent the probability of a chance event occurring, explaining that larger numbers indicate greater likelihood of the event occurring, while a number near zero indicates an unlikely event.

Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.

Collect and use data to predict probabilities of events.

Compare probabilities from a model to observed frequencies, explaining possible sources of discrepancy.

Approximate the probability of an event using data generated by a simulation (experimental probability) and compare it to the theoretical probability.

Observe the relative frequency of an event over the long run, using simulation or technology, and use those results to predict approximate relative frequency.

Find probabilities of simple and compound events through experimentation or simulation and by analyzing the sample space, representing the probabilities as percents, decimals, or fractions.

Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams, and determine the probability of an event by finding the fraction of outcomes in the sample space for which the compound event occurred.

Represent events described in everyday language in terms of outcomes in the sample space which composed the event.

Construct and describe geometric figures, analyzing relationships among them.

Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume.

Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

Informally derive the formula for area of a circle.

Solve area and circumference problems in real-world and mathematical situations involving circles.

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.

Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.

Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

Explain subtraction of rational numbers as addition of additive inverses.

Use a number line to demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a non-zero divisor) as a rational number.

Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.

Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.

Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.

Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.

Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease.

Generate expressions in equivalent forms based on context and explain how the quantities are related.

Apply concepts of rational and integer exponents

Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

Use square root and cube root symbols to represent solutions to equations.

Evaluate square roots of perfect squares (less than or equal to 225) and cube roots of perfect cubes (less than or equal to 1000).

Explain that the square root of a non-perfect square is irrational.

Express and compare very large or very small numbers in scientific notation.

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used, expressing answers in scientific notation.

Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

Interpret scientific notation that has been generated by technology.

Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

Use variables to represent quantities in a real-world or mathematical problem and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

Solve word problems leading to inequalities of the form px + q > r or px + q , where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Create equations in two variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear functions.

Represent constraints by equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear.

Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem.

Explain, evaluate, and compare functions.

Identify the effect on the graph of replacing f(x) by f(x) + k, k · f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and explain the effects on the graph using technology, where appropriate. Limit to linear functions.

Construct a function to model the linear relationship between two variables.

Interpret the rate of change (slope) and initial value of the linear function from a description of a relationship from two points in a table or graph.

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Limit to linear equations.

Find approximate solutions by graphing the functions, making tables of values, or finding successive approximations, using technology where appropriate.

Examine a sample of a population to generalize information about the population.

Differentiate between a sample and a population.

Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

Determine whether conclusions and generalizations can be made about a population based on a sample.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and make predictions or conclusions about the population.

Informally explain situations in which statistical bias may exist.

Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.

Investigate probability models.

Use a number between 0 and 1 to represent the probability of a chance event occurring, explaining that larger numbers indicate greater likelihood of the event occurring, while a number near zero indicates an unlikely event.

Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.

Collect and use data to predict probabilities of events.

Compare probabilities from a model to observe frequencies, explaining possible sources of discrepancy.

Approximate the probability of an event by using data generated by a simulation (experimental probability) and compare it to theoretical probability.

Observe the relative frequency of an event over the long run, using simulation or technology, and use those results to predict approximate relative frequency.

Find probabilities of simple and compound events through experimentation or simulation and by analyzing the sample space, representing the probabilities as percents, decimals, or fractions.

Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams, and determine the probability of an event by finding the fraction of outcomes in the sample space for which the compound event occurred.

Represent events described in everyday language in terms of outcomes in the sample space which composed the event.

Construct and describe geometrical figures, analyzing relationships among them.

Construct geometric shapes (freehand, using a ruler and a protractor, and using technology) given measurement constraints with an emphasis on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

Informally derive the formula for area of a circle.

Solve area and circumference problems in real-world and mathematical situations involving circles.

Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.

Use informal arguments to establish that the sum of the interior angles of a triangle is 180 degrees.

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.

Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions.

Use formulas to calculate the volumes of three-dimensional figures to solve real-world problems.

Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship.

Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

Apply and extend prior knowledge of addition, subtraction, multiplication, and division to operations with rational numbers.

Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.

Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

Explain subtraction of rational numbers as addition of additive inverses.

Use a number line to demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a non-zero divisor) as a rational number.

Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.

Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.

Understand that the real number system is composed of rational and irrational numbers.

Define the real number system as composed of rational and irrational numbers.

Explain that every number has a decimal expansion; for rational numbers, the decimal expansion repeats in a pattern or terminates.

Convert a decimal expansion that repeats in a pattern into a rational number.

Locate rational approximations of irrational numbers on a number line, compare their sizes, and estimate the values of irrational numbers.

Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.

Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease.

Analyze the relationship between proportional and non-proportional situations.

Graph proportional relationships.

Interpret the unit rate of a proportional relationship, describing the constant of proportionality as the slope of the graph which goes through the origin and has the equation y = mx where m is the slope.

Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts.

Compare proportional and non-proportional linear relationships represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) to solve real-world problems.

Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

Use square root and cube root symbols to represent solutions to equations.

Evaluate square roots of perfect squares (less than or equal to 225) and cube roots of perfect cubes (less than or equal to 1000).

Explain that the square root of a non-perfect square is irrational.

Estimate and compare very large or very small numbers in scientific notation.

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

Interpret scientific notation that has been generated by technology.

Analyze the relationship between proportional and non-proportional situations.

Determine whether a relationship between two variables is proportional or non-proportional.

Graph proportional relationships.

Interpret the unit rate of a proportional relationship, describing the constant of proportionality as the slope of the graph which goes through the origin and has the equation y = mx where m is the slope.

Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts.

Compare proportional and non-proportional linear relationships represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) to solve real-world problems.

Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem.

Solve systems of two linear equations in two variables by graphing and substitution.

Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems.

Explain, evaluate, and compare functions.

Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs.

Evaluate functions defined by a rule or an equation, given values for the independent variable.

Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.

Distinguish between linear and non-linear functions.

Construct a function to model a linear relationship between two variables.

Interpret the rate of change (slope) and initial value of the linear function from a description of a relationship or from two points in a table or graph.

Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph.

Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line.

Use a linear model of a real-world situation to solve problems and make predictions.

Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

Analyze parallel lines cut by a transversal.

Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.

Use informal arguments to establish that the sum of the interior angles of a triangle is 180 degrees.

Informally justify the Pythagorean Theorem and its converse.

Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications.

Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions.

Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.

Understand that the real number system is composed of rational and irrational numbers.

Define the real number system as composed of rational and irrational numbers.

Explain that every number has a decimal expansion; for rational numbers, the decimal expansion repeats or terminates.

Convert a decimal expansion that repeats into a rational number.

Locate rational approximations of irrational numbers on a number line, compare their sizes, and estimate the values of the irrational numbers.

Expressions can be rewritten in equivalent forms by using algebraic properties, including properties of addition, multiplication, and exponentiation, to make different characteristics or features visible.

Interpret linear, quadratic, and exponential expressions in terms of a context by viewing one or more of their parts as a single entity.

Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph.

Solve systems of two linear equations in two variables by graphing and substitution.

Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems.

Finding solutions to an equation, inequality, or system of equations or inequalities requires the checking of candidate solutions, whether generated analytically or graphically, to ensure that solutions are found and that those found are not extraneous.

Explain why extraneous solutions to an equation involving absolute values may arise and how to check to be sure that a candidate solution satisfies an equation.

The structure of an equation or inequality (including, but not limited to, one-variable linear and quadratic equations, inequalities, and systems of linear equations in two variables) can be purposefully analyzed (with and without technology) to determine an efficient strategy to find a solution, if one exists, and then to justify the solution.

Select an appropriate method to solve a quadratic equation in one variable.

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Explain how the quadratic formula is derived from this form.

Solve quadratic equations by inspection (such as x² = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.

Select an appropriate method to solve a system of two linear equations in two variables.

Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.

Expressions, equations, and inequalities can be used to analyze and make predictions, both within mathematics and as mathematics is applied in different contexts – in particular, contexts that arise in relation to linear, quadratic, and exponential situations.

Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions.

Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.

Represent constraints by equations and/or inequalities, and solve systems of equations and/or inequalities, interpreting solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.

Functions shift the emphasis from a point-by-point relationship between two variables (input/output) to considering an entire set of ordered pairs (where each first element is paired with exactly one second element) as an entity with its own features and characteristics.

Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range.

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions.

Compare and contrast relations and functions represented by equations, graphs, or tables that show related values; determine whether a relation is a function. Identify that a function f is a special kind of relation defined by the equation y = f(x).

Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions.

Use arithmetic operations to combine different types of standard functions to write and evaluate functions.

Use function composition to combine different types of standard functions to write and evaluate functions.

Graphs can be used to obtain exact or approximate solutions of equations, inequalities, and systems of equations and inequalities – including systems of linear equations in two variables and systems of linear and quadratic equations (given or obtained by using technology).

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).

Find the approximate solutions of an equation graphically, using tables of values, or finding successive approximations, using technology where appropriate.

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes, using technology where appropriate.

Solve systems consisting of linear and/or quadratic equations in two variables graphically, using technology where appropriate.

Functions can be described by using a variety of representations: mapping diagrams, function notation (e.g., f(x) = x²), recursive definitions, tables, and graphs.

Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Include linear, quadratic, exponential, absolute value, and linear piecewise.

Distinguish between linear and non-linear functions.

Define sequences as functions, including recursive definitions, whose domain is a subset of the integers.

Write explicit and recursive formulas for arithmetic and geometric sequences and connect them to linear and exponential functions.

Functions that are members of the same family have distinguishing attributes (structure) common to all functions within that family.

Identify the effect on the graph of replacing f(x) by f(x) + k, k·f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and explain the effects on the graph, using technology as appropriate. Extend from linear to quadratic, exponential, absolute value, and linear piecewise functions.

Show that linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals.

Define linear functions to represent situations in which one quantity changes at a constant rate per unit interval relative to another.

Define exponential functions to represent situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Use graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

Functions can be represented graphically and key features of the graphs, including zeros, intercepts, and, when relevant, rate of change and maximum/minimum values, can be associated with and interpreted in terms of the equivalent symbolic representation.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and general piecewise functions.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Limit to linear, quadratic, exponential, and absolute value functions.

Graph piecewise-defined functions, including step functions and absolute value functions.

Graph exponential functions, showing intercepts and end behavior.

Functions model a wide variety of real situations and can help students understand the processes of making and changing assumptions, assigning variables, and finding solutions to contextual problems.

Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions.

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, describing patterns in terms of positive, negative, or no association, linear and non-linear association, clustering, and outliers.

Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line.

Use a linear model of a real-world situation to solve problems and make predictions.

Data arise from a context and come in two types: quantitative (continuous or discrete) and categorical. Technology can be used to "clean" and organize data, including very large data sets, into a useful and manageable structure – a first step in any analysis of data.

Distinguish between quantitative and categorical data and between the techniques that may be used for analyzing data of these two types.

The association between two categorical variables is typically represented by using two-way tables and segmented bar graphs.

Analyze the possible association between two categorical variables.

Summarize categorical data for two categories in two-way frequency tables and represent using segmented bar graphs.

Interpret relative frequencies in the context of categorical data (including joint, marginal, and conditional relative frequencies).

Identify possible associations and trends in categorical data.

Data analysis techniques can be used to develop models of contextual situations and to generate and evaluate possible solutions to real problems involving those contexts.

Generate a two-way categorical table in order to find and evaluate solutions to real-world problems.

Aggregate data from several groups to find an overall association between two categorical variables.

Recognize and explore situations where the association between two categorical variables is reversed when a third variable is considered (Simpson's Paradox).

Mathematical and statistical reasoning about data can be used to evaluate conclusions and assess risks.

Use mathematical and statistical reasoning with bivariate categorical data in order to draw conclusions and assess risk.

Making and defending informed, data-based decisions is a characteristic of a quantitatively literate person.

Design and carry out an investigation to determine whether there appears to be an association between two categorical variables, and write a persuasive argument based on the results of the investigation.

Two events are independent if the occurrence of one event does not affect the probability of the other event. Determining whether two events are independent can be used for finding and understanding probabilities.

Explain whether two events, A and B, are independent, using two-way tables or tree diagrams.

Conditional probabilities – that is, those probabilities that are "conditioned" by some known information – can be computed from data organized in contingency tables. Conditions or assumptions may affect the computation of a probability.

Compute the conditional probability of event A given event B, using two-way tables or tree diagrams.

Explain why the conditional probability of A given B is the fraction of B's outcomes that also belong to A, and interpret the answer in context.

Informally justify the Pythagorean Theorem and its converse.

Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications.

Together, irrational numbers and rational numbers complete the real number system, representing all points on the number line, while there exist numbers beyond the real numbers called complex numbers.

Define the imaginary number i such that i² = -1.

Expressions can be rewritten in equivalent forms by using algebraic properties, including properties of addition, multiplication, and exponentiation, to make different characteristics or features visible.

Interpret linear, quadratic, and exponential expressions in terms of a context by viewing one or more of their parts as a single entity.

Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.

Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.

Finding solutions to an equation, inequality, or system of equations or inequalities requires the checking of candidate solutions, whether generated analytically or graphically, to ensure that solutions are found and that those found are not extraneous.

Explain why extraneous solutions to an equation involving absolute values may arise and how to check to be sure that a candidate solution satisfies an equation.

The structure of an equation or inequality (including, but not limited to, one-variable linear and quadratic equations, inequalities, and systems of linear equations in two variables) can be purposefully analyzed (with and without technology) to determine an efficient strategy to find a solution, if one exists, and then to justify the solution.

Select an appropriate method to solve a quadratic equation in one variable.

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Explain how the quadratic formula is derived from this form.

Solve quadratic equations by inspection (such as x² = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.

Select an appropriate method to solve a system of two linear equations in two variables.

Solve a system of two equations in two variables by using linear combinations; contrast situations in which use of linear combinations is more efficient with those in which substitution is more efficient.

Contrast solutions to a system of two linear equations in two variables produced by algebraic methods with graphical and tabular methods.

Expressions, equations, and inequalities can be used to analyze and make predictions, both within mathematics and as mathematics is applied in different contexts – in particular, contexts that arise in relation to linear, quadratic, and exponential situations.

Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions.

Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.

Represent constraints by equations and/or inequalities, and solve systems of equations and/or inequalities, interpreting solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.

Functions shift the emphasis from a point-by-point relationship between two variables (input/output) to considering an entire set of ordered pairs (where each first element is paired with exactly one second element) as an entity with its own features and characteristics.

Given a relation defined by an equation in two variables, identify the graph of the relation as the set of all its solutions plotted in the coordinate plane.

Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range.

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions.

Compare and contrast relations and functions represented by equations, graphs, or tables that show related values; determine whether a relation is a function. Explain that a function f is a special kind of relation defined by the equation y = f(x).

Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions.

Use arithmetic operations to combine different types of standard functions to write and evaluate functions.

Use function composition to combine different types of standard functions to write and evaluate functions.

Graphs can be used to obtain exact or approximate solutions of equations, inequalities, and systems of equations and inequalities – including systems of linear equations in two variables and systems of linear and quadratic equations (given or obtained by using technology).

Solve systems consisting of linear and/or quadratic equations in two variables graphically, using technology where appropriate.

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).

Find the approximate solutions of an equation graphically, using tables of values, or finding successive approximations, using technology where appropriate. Note: Include cases where f(x) is a linear, quadratic, exponential, or absolute value function and g(x) is constant or linear.

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes, using technology where appropriate.

Functions can be described by using a variety of representations: mapping diagrams, function notation (e.g., f(x) = x²), recursive definitions, tables, and graphs.

Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Extend from linear to quadratic, exponential, absolute value, and general piecewise.

Define sequences as functions, including recursive definitions, whose domain is a subset of the integers.

Write explicit and recursive formulas for arithmetic and geometric sequences and connect them to linear and exponential functions.

Functions that are members of the same family have distinguishing attributes (structure) common to all functions within that family.

Identify the effect on the graph of replacing f(x) by f(x) + k, k·f(x), f(f·x), for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear piecewise functions.

Show that linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals.

Define linear functions to represent situations in which one quantity changes at a constant rate per unit interval relative to another.

Define exponential functions to represent situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Use graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

Interpret the parameters of functions in terms of a context. Extend from linear functions, written in the form mx + b, to exponential functions, written in the form abx. Functions can be represented graphically and key features of the graphs, including zeros, intercepts, and, when relevant, rate of change and maximum/minimum values, can be associated with and interpreted in terms of the equivalent symbolic representation.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and linear piecewise functions.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Limit to linear, quadratic, exponential, and absolute value functions.

Graph piecewise-defined functions, including step functions and absolute value functions.

Graph exponential functions, showing intercepts and end behavior.

Functions model a wide variety of real situations and can help students understand the processes of making and changing assumptions, assigning variables, and finding solutions to contextual problems.

Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions.

Mathematical and statistical reasoning about data can be used to evaluate conclusions and assess risks.

Use mathematical and statistical reasoning with bivariate categorical data in order to draw conclusions and assess risk.

Making and defending informed, data-based decisions is a characteristic of a quantitatively literate person.

Design and carry out an investigation to determine whether there appears to be an association between two categorical variables, and write a persuasive argument based on the results of the investigation.

Data arise from a context and come in two types: quantitative (continuous or discrete) and categorical. Technology can be used to "clean" and organize data, including very large data sets, into a useful and manageable structure—a first step in any analysis of data.

Distinguish between quantitative and categorical data and between the techniques that may be used for analyzing data of these two types.

The association between two categorical variables is typically represented by using two-way tables and segmented bar graphs.

Analyze the possible association between two categorical variables.

Summarize categorical data for two categories in two-way frequency tables and represent using segmented bar graphs.

Interpret relative frequencies in the context of categorical data (including joint, marginal, and conditional relative frequencies).

Identify possible associations and trends in categorical data.

Data analysis techniques can be used to develop models of contextual situations and to generate and evaluate possible solutions to real problems involving those contexts.

Generate a two-way categorical table in order to find and evaluate solutions to real-world problems.

Aggregate data from several groups to find an overall association between two categorical variables.

Recognize and explore situations where the association between two categorical variables is reversed when a third variable is considered (Simpson's Paradox).

Two events are independent if the occurrence of one event does not affect the probability of the other event. Determining whether two events are independent can be used for finding and understanding probabilities.

Explain whether two events, A and B, are independent, using two-way tables or tree diagrams.

Conditional probabilities – that is, those probabilities that are "conditioned" by some known information – can be computed from data organized in contingency tables. Conditions or assumptions may affect the computation of a probability.

Compute the conditional probability of event A given event B, using two-way tables or tree diagrams.

Explain why the conditional probability of A given B is the fraction of B's outcomes that also belong to A, and interpret the answer in context.

Together, irrational numbers and rational numbers complete the real number system, representing all points on the number line, while there exist numbers beyond the real numbers called complex numbers.

Define the imaginary number i such that i² = -1.

Expressions can be rewritten in equivalent forms by using algebraic properties, including properties of addition, multiplication, and exponentiation, to make different characteristics or features visible.

Factor polynomials using common factoring techniques, and use the factored form of a polynomial to reveal the zeros of the function it defines.

Finding solutions to an equation, inequality, or system of equations or inequalities requires the checking of candidate solutions, whether generated analytically or graphically, to ensure that solutions are found and that those found are not extraneous.

Explain why extraneous solutions to an equation may arise and how to check to be sure that a candidate solution satisfies an equation. Extend to radical equations.

The structure of an equation or inequality (including, but not limited to, one-variable linear and quadratic equations, inequalities, and systems of linear equations in two variables) can be purposefully analyzed (with and without technology) to determine an efficient strategy to find a solution, if one exists, and then to justify the solution.

For exponential models, express as a logarithm the solution to abct = d, where a, c, and d are real numbers and the base b is 2 or 10; evaluate the logarithm using technology to solve an exponential equation.

Expressions, equations, and inequalities can be used to analyze and make predictions, both within mathematics and as mathematics is applied in different contexts—in particular, contexts that arise in relation to linear, quadratic, and exponential situations.

Create equations and inequalities in one variable and use them to solve problems. Extend to equations arising from polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions.

Solve simple equations involving exponential, radical, logarithmic, and trigonometric functions using inverse functions.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales and use them to make predictions. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Graphs can be used to obtain exact or approximate solutions of equations, inequalities, and systems of equations and inequalities—including systems of linear equations in two variables and systems of linear and quadratic equations (given or obtained by using technology).

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).

Find the approximate solutions of an equation graphically, using tables of values, or finding successive approximations, using technology where appropriate. Extend to cases where f(x) and/or g(x) are polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions.

Functions can be described by using a variety of representations: mapping diagrams, function notation (e.g., f(x) = x²), recursive definitions, tables, and graphs.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Extend to polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions.

Functions that are members of the same family have distinguishing attributes (structure) common to all functions within that family.

Identify the effect on the graph of replacing f(x) by f(x) + k, k·f(x), f(k·x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Functions can be represented graphically, and key features of the graphs, including zeros, intercepts, and, when relevant, rate of change and maximum/minimum values, can be associated with and interpreted in terms of the equivalent symbolic representation.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Graph sine and cosine functions expressed symbolically, showing period, midline, and amplitude.

Graph logarithmic functions expressed symbolically, showing intercepts and end behavior.

Graph reciprocal functions expressed symbolically, identifying horizontal and vertical asymptotes.

Graph square root and cube root functions expressed symbolically.

Compare the graphs of inverse functions and the relationships between their key features, including but not limited to quadratic, square root, exponential, and logarithmic functions.

Functions model a wide variety of real situations and can help students understand the processes of making and changing assumptions, assigning variables, and finding solutions to contextual problems.

Use the mathematical modeling cycle to solve real-world problems involving polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions, from the simplification of the problem through the solving of the simplified problem, the interpretation of its solution, and the checking of the solution's feasibility.

Mathematical and statistical reasoning about data can be used to evaluate conclusions and assess risks.

Use mathematical and statistical reasoning about normal distributions to draw conclusions and assess risk; limit to informal arguments.

Making and defending informed data-based decisions is a characteristic of a quantitatively literate person.

Design and carry out an experiment or survey to answer a question of interest, and write an informal persuasive argument based on the results.

Distributions of quantitative data (continuous or discrete) in one variable should be described in the context of the data with respect to what is typical (the shape, with appropriate measures of center and variability, including standard deviation) and what is not (outliers), and these characteristics can be used to compare two or more subgroups with respect to a variable.

From a normal distribution, use technology to find the mean and standard deviation and estimate population percentages by applying the empirical rule.

Use technology to determine if a given set of data is normal by applying the empirical rule.

Estimate areas under a normal curve to solve problems in context, using calculators, spreadsheets, and tables as appropriate.

Study designs are of three main types: sample survey, experiment, and observational study.

Describe the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

The role of randomization is different in randomly selecting samples and in randomly assigning subjects to experimental treatment groups.

Distinguish between a statistic and a parameter and use statistical processes to make inferences about population parameters based on statistics from random samples from that population.

Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding a population versus regarding cause and effect.

The scope and validity of statistical inferences are dependent on the role of randomization in the study design.

Explain the consequences, due to uncontrolled variables, of non-randomized assignment of subjects to groups in experiments.

Bias, such as sampling, response, or nonresponse bias, may occur in surveys, yielding results that are not representative of the population of interest.

Evaluate where bias, including sampling, response, or nonresponse bias, may occur in surveys, and whether results are representative of the population of interest.

The larger the sample size, the less the expected variability in the sampling distribution of a sample statistic.

Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic.

Simulate a sampling distribution of sample means from a population with a known distribution, observing the effect of the sample size on the variability.

Demonstrate that the standard deviation of each simulated sampling distribution is the known standard deviation of the population divided by the square root of the sample size.

The sampling distribution of a sample statistic formed from repeated samples for a given sample size drawn from a population can be used to identify typical behavior for that statistic. Examining several such sampling distributions leads to estimating a set of plausible values for the population parameter, using the margin of error as a measure that describes the sampling variability.

Produce a sampling distribution by repeatedly selecting samples of the same size from a given population or from a population simulated by bootstrapping (resampling with replacement from an observed sample). Do initial examples by hand, then use technology to generate a large number of samples.

Verify that a sampling distribution is centered at the population mean and approximately normal if the sample size is large enough.

Verify that 95% of sample means are within two standard deviations of the sampling distribution from the population mean.

Create and interpret a 95% confidence interval based on an observed mean from a sampling distribution.

Use data from a randomized experiment to compare two treatments; limit to informal use of simulations to decide if an observed difference in the responses of the two treatment groups is unlikely to have occurred due to randomization alone, thus implying that the difference between the treatment groups is meaningful.

When an object is the image of a known object under a similarity transformation, a length, area, or volume on the image can be computed by using proportional relationships.

Define the radian measure of an angle as the constant of proportionality of the length of an arc it intercepts to the radius of the circle; in particular, it is the length of the arc intercepted on the unit circle.

Recognizing congruence, similarity, symmetry, measurement opportunities, and other geometric ideas, including right triangle trigonometry in real-world contexts, provides a means of building understanding of these concepts and is a powerful tool for solving problems related to the physical world in which we live.

Choose trigonometric functions (sine and cosine) to model periodic phenomena with specified amplitude, frequency, and midline.

Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to calculate trigonometric ratios.

Derive and apply the formula A = ½·ab·sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side, extending the domain of sine to include right and obtuse angles.

Derive and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles. Extend the domain of sine and cosine to include right and obtuse angles.

Together, irrational numbers and rational numbers complete the real number system, representing all points on the number line, while there exist numbers beyond the real numbers called complex numbers.

Identify numbers written in the form a + bi, where a and b are real numbers and i² = –1, as complex numbers.

Add, subtract, and multiply complex numbers using the commutative, associative, and distributive properties.

Matrices are a useful way to represent information.

Describe the roles that zero and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real numbers.

Find the additive and multiplicative inverses of square matrices, using technology as appropriate.

Explain the role of the determinant in determining if a square matrix has a multiplicative inverse.

Complex counting problems can be solved efficiently using a variety of techniques.

Use multiple representations and methods for counting objects and developing more efficient counting techniques. Note: Representations and methods may include tree diagrams, lists, manipulatives, overcounting methods, recursive patterns, and explicit formulas.

Develop and use the Fundamental Counting Principle for counting independent and dependent events.

Use various counting models (including tree diagrams and lists) to identify the distinguishing factors of a context in which the Fundamental Counting Principle can be applied.

Using application-based problems, develop formulas for permutations, combinations, and combinations with repetition and compare student-derived formulas to standard representations of the formulas.

Identify differences between applications of combinations and permutations.

Using application-based problems, calculate the number of permutations of a set with n elements. Calculate the number of permutations of r elements taken from a set of n elements.

Using application-based problems, calculate the number of subsets of size r that can be chosen from a set of n elements, explaining this number as the number of combinations "n choose r."

Using application-based problems, calculate the number of combinations with repetitions of r elements from a set of n elements as "(n + r – 1) choose r."

Use various counting techniques to determine probabilities of events.

Use the Pigeonhole Principle to solve counting problems.

Various methods for determining a winner in a voting system can result in paradoxes or other issues of fairness.

Analyze advantages and disadvantages of different types of ballot voting systems.

Identify impacts of using a preferential ballot voting system and compare it to single candidate voting and other voting systems.

Analyze the impact of legal and cultural features of political systems on the mathematical aspects of elections.

Apply a variety of methods for determining a winner using a preferential ballot voting system, including plurality, majority, run-off with majority, sequential run-off with majority, Borda count, pairwise comparison, Condorcet, and approval voting.

Identify issues of fairness for different methods of determining a winner using a preferential voting ballot and other voting systems and identify paradoxes that can result.

Use methods of weighted voting and identify issues of fairness related to weighted voting.

Distinguish between weight and power in voting.

Methods used to solve non-trivial problems of division of objects often reveal issues of fairness.

Explain and apply mathematical aspects of fair division, with respect to classic problems of apportionment, cake cutting, and estate division. Include applications in other contexts and modern situations.

Identify and apply historic methods of apportionment for voting districts including Hamilton, Jefferson, Adams, Webster, and Huntington-Hill. Identify issues of fairness and paradoxes that may result from methods.

Use spreadsheets to examine apportionment methods in large problems.

Effective systems for sending and receiving information include components that impact accuracy, efficiency, and security.

Critically analyze issues related to information processing including accuracy, efficiency, and security.

Apply ciphers (encryption and decryption algorithms) and cryptosystems for encrypting and decrypting including symmetric-key or public-key systems.

Use modular arithmetic to apply RSA (Rivest-Shamir-Adleman) public-key cryptosystems.

Use matrices and their inverses to encode and decode messages.

Apply error-detecting codes and error-correcting codes to determine accuracy of information processing.

Apply methods of data compression.

The validity of a statement or argument can be determined using the models and language of first order logic.

Represent logic statements in words, with symbols, and in truth tables, including conditional, biconditional, converse, inverse, contrapositive, and quantified statements.

Represent logic operations such as and, or, not, nor, and x or (exclusive or) in words, with symbols, and in truth tables.

Use truth tables to solve application-based logic problems and determine the truth value of simple and compound statements including negations and implications.

Determine whether statements are equivalent and construct equivalent statements.

Determine whether a logical argument is valid or invalid, using laws of logic such as the law of syllogism and the law of detachment.

Determine whether a logical argument is a tautology or a contradiction.

Prove a statement indirectly by proving the contrapositive of the statement.

Complex problems can be modeled using vertex and edge graphs and characteristics of the different structures are used to find solutions.

Use vertex and edge graphs to model mathematical situations involving networks.

Identify properties of simple graphs, complete graphs, bipartite graphs, complete bipartite graphs, and trees.

Solve problems involving networks through investigation and application of existence and nonexistence of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits.

Develop optimal solutions of application-based problems using existing and student-created algorithms.

Give an argument for graph properties.

Apply algorithms relating to minimum weight spanning trees, networks, flows, and Steiner trees.

Use shortest path techniques to find optimal shipping routes.

Show that every connected graph has a minimal spanning tree.

Use Kruskal's Algorithm and Prim's Algorithm to determine the minimal spanning tree of a weighted graph.

Use vertex-coloring, edge-coloring, and matching techniques to solve application-based problems involving conflict.

Determine the minimum time to complete a project using algorithms to schedule tasks in order, including critical path analysis, the list-processing algorithm, and student-created algorithms.

Use the adjacency matrix of a graph to determine the number of walks of length n in a graph.

Recursion is a method of problem solving where a given relation or routine operation is repeatedly applied.

Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

Determine characteristics of sequences, including the Fibonacci Sequence, the triangular numbers, and pentagonal numbers.

Use the recursive process and difference equations to create fractals, population growth models, sequences, and series.

Use mathematical induction to prove statements involving the positive integers.

Develop and apply connections between Pascal's Triangle and combinations.

The structure of an equation or inequality (including, but not limited to, one-variable linear and quadratic equations, inequalities, and systems of linear equations in two variables) can be purposefully analyzed (with and without technology) to determine an efficient strategy to find a solution, if one exists, and then to justify the solution.

Find the coordinates of the vertices of a polygon determined by a set of lines, given their equations, by setting their function rules equal and solving, or by using their graphs.

Expressions, equations, and inequalities can be used to analyze and make predictions, both within mathematics and as mathematics is applied in different contexts – in particular, contexts that arise in relation to linear, quadratic, and exponential situations.

Graphs can be used to obtain exact or approximate solutions of equations, inequalities, and systems of equations and inequalities—including systems of linear equations in two variables and systems of linear and quadratic equations (given or obtained by using technology).

Verify that the graph of a linear equation in two variables is the set of all its solutions plotted in the coordinate plane, which forms a line.

Derive the equation of a circle of given center and radius using the Pythagorean Theorem.

Given the endpoints of the diameter of a circle, use the midpoint formula to find its center and then use the Pythagorean Theorem to find its equation.

Derive the distance formula from the Pythagorean Theorem.

Mathematical and statistical reasoning about data can be used to evaluate conclusions and assess risks.

Use mathematical and statistical reasoning with quantitative data, both univariate data (set of values) and bivariate data (set of pairs of values) that suggest a linear association, in order to draw conclusions and assess risk.

Data arise from a context and come in two types: quantitative (continuous or discrete) and categorical. Technology can be used to "clean" and organize data, including very large data sets, into a useful and manageable structure – a first step in any analysis of data

Use technology to organize data, including very large data sets, into a useful and manageable structure.

Distributions of quantitative data (continuous or discrete) in one variable should be described in the context of the data with respect to what is typical (the shape, with appropriate measures of center and variability, including standard deviation) and what is not (outliers), and these characteristics can be used to compare two or more subgroups with respect to a variable.

Represent the distribution of univariate quantitative data with plots on the real number line, choosing a format (dot plot, histogram, or box plot) most appropriate to the data set, and represent the distribution of bivariate quantitative data with a scatter plot. Extend from simple cases by hand to more complex cases involving large data sets using technology.

Explain how standard deviation develops from mean absolute deviation.

Calculate the standard deviation for a data set, using technology where appropriate.

Interpret differences in shape, center, and spread in the context of data sets, accounting for possible effects of extreme data points (outliers) on mean and standard deviation.

Scatter plots, including plots over time, can reveal patterns, trends, clusters, and gaps that are useful in analyzing the association between two contextual variables.

Find a linear function for a scatter plot that suggests a linear association and informally assess its fit by plotting and analyzing residuals, including the squares of the residuals, in order to improve its fit.

Use technology to find the least-squares line of best fit for two quantitative variables.

Analyzing the association between two quantitative variables should involve statistical procedures, such as examining (with technology) the sum of squared deviations in fitting a linear model, analyzing residuals for patterns, generating a least-squares regression line and finding a correlation coefficient, and differentiating between correlation and causation.

Data analysis techniques can be used to develop models of contextual situations and to generate and evaluate possible solutions to real problems involving those contexts.

Evaluate possible solutions to real-life problems by developing linear models of contextual situations and using them to predict unknown values.

Use the linear model to solve problems in the context of the given data.

Areas and volumes of figures can be computed by determining how the figure might be obtained from simpler figures by dissection and recombination.

Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

Apply geometric concepts to find missing dimensions to solve surface area or volume problems.

Constructing approximations of measurements with different tools, including technology, can support an understanding of measurement.

Given the coordinates of the vertices of a polygon, compute its perimeter and area using a variety of methods, including the distance formula and dynamic geometry software, and evaluate the accuracy of the results.

When an object is the image of a known object under a similarity transformation, a length, area, or volume on the image can be computed by using proportional relationships.

Derive and apply the relationships between the lengths, perimeters, areas, and volumes of similar figures in relation to their scale factor.

Derive and apply the formula for the length of an arc and the formula for the area of a sector.

Applying geometric transformations to figures provides opportunities for describing the attributes of the figures preserved by the transformation and for describing symmetries by examining when a figure can be mapped onto itself.

Represent transformations and compositions of transformations in the plane (coordinate and otherwise) using tools such as tracing paper and geometry software.

Describe transformations and compositions of transformations as functions that take points in the plane as inputs and give other points as outputs, using informal and formal notation.

Compare transformations which preserve distance and angle measure to those that do not.

Explore rotations, reflections, and translations using graph paper, tracing paper, and geometry software.

Given a geometric figure and a rotation, reflection, or translation, draw the image of the transformed figure using graph paper, tracing paper, or geometry software.

Specify a sequence of rotations, reflections, or translations that will carry a given figure onto another.

Draw figures with different types of symmetries and describe their attributes.

Showing that two figures are congruent involves showing that there is a rigid motion (translation, rotation, reflection, or glide reflection) or, equivalently, a sequence of rigid motions that maps one figure to the other.

Define congruence of two figures in terms of rigid motions (a sequence of translations, rotations, and reflections); show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other.

Verify criteria for showing triangles are congruent using a sequence of rigid motions that map one triangle to another.

Verify that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Verify that two triangles are congruent if (but not only if) the following groups of corresponding parts are congruent: angle-side-angle (ASA), side-angle-side (SAS), side-side-side (SSS), and angle-angle-side (AAS).

Showing that two figures are similar involves finding a similarity transformation (dilation or composite of a dilation with a rigid motion) or, equivalently, a sequence of similarity transformations that maps one figure onto the other.

Verify that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

Verify that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Given two figures, determine whether they are similar by identifying a similarity transformation (sequence of rigid motions and dilations) that maps one figure to the other.

Verify criteria for showing triangles are similar using a similarity transformation (sequence of rigid motions and dilations) that maps one triangle to another.

Verify that two triangles are similar if and only if corresponding pairs of sides are proportional and corresponding pairs of angles are congruent.

Verify that two triangles are similar if (but not only if) two pairs of corresponding angles are congruent (AA), the corresponding sides are proportional (SSS), or two pairs of corresponding sides are proportional and the pair of included angles is congruent (SAS).

Using technology to construct and explore figures with constraints provides an opportunity to explore the independence and dependence of assumptions and conjectures.

Find patterns and relationships in figures including lines, triangles, quadrilaterals, and circles, using technology and other tools.

Construct figures, using technology and other tools, in order to make and test conjectures about their properties.

Identify different sets of properties necessary to define and construct figures.

Proof is the means by which we demonstrate whether a statement is true or false mathematically, and proofs can be communicated in a variety of ways (e.g., two-column, paragraph).

Develop and use precise definitions of figures such as angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Justify whether conjectures are true or false in order to prove theorems and then apply those theorems in solving problems, communicating proofs in a variety of ways, including flow chart, two-column, and paragraph formats.

Investigate, prove, and apply theorems about lines and angles, including but not limited to: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; the points on the perpendicular bisector of a line segment are those equidistant from the segment's endpoints.

Investigate, prove, and apply theorems about triangles, including but not limited to: the sum of the measures of the interior angles of a triangle is 180˚; the base angles of isosceles triangles are congruent; the segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length; a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem using triangle similarity.

Investigate, prove, and apply theorems about parallelograms and other quadrilaterals, including but not limited to both necessary and sufficient conditions for parallelograms and other quadrilaterals, as well as relationships among kinds of quadrilaterals.

Proofs of theorems can sometimes be made with transformations, coordinates, or algebra; all approaches can be useful, and in some cases one may provide a more accessible or understandable argument than another.

Recognizing congruence, similarity, symmetry, measurement opportunities, and other geometric ideas, including right triangle trigonometry, in real-world contexts provides a means of building understanding of these concepts and is a powerful tool for solving problems related to the physical world in which we live.

Use congruence and similarity criteria for triangles to solve problems in real-world contexts.

Discover and apply relationships in similar right triangles.

Derive and apply the constant ratios of the sides in special right triangles (45˚-45˚-90˚ and 30˚-60˚-90˚).

Use similarity to explore and define basic trigonometric ratios, including sine ratio, cosine ratio, and tangent ratio.

Demonstrate the converse of the Pythagorean Theorem.

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems, including finding areas of regular polygons.

Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems.

Investigate and apply relationships among inscribed angles, radii, and chords, including but not limited to: the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Experiencing the mathematical modeling cycle in problems involving geometric concepts, from the simplification of the real problem through the solving of the simplified problem, the interpretation of its solution, and the checking of the solution's feasibility, introduces geometric techniques, tools, and points of view that are valuable to problem-solving.

Use the mathematical modeling cycle involving geometric methods to solve design problems.

Together, irrational numbers and rational numbers complete the real number system, representing all points on the number line, while there exist numbers beyond the real numbers called complex numbers.

Extend understanding of irrational and rational numbers by rewriting expressions involving radicals, including addition, subtraction, multiplication, and division, in order to recognize geometric patterns.

Quantitative reasoning includes and mathematical modeling requires attention to units of measurement.

Use units as a way to understand problems and to guide the solution of multi-step problems.

Choose and interpret units consistently in formulas.

Choose and interpret the scale and the origin in graphs and data displays.

Two- and three-dimensional representations, coordinates systems, geometric transformations, and scale models are useful tools in planning, designing, and constructing solutions to real-world problems.

Use the Mathematical Modeling Cycle to solve real-world problems involving the design of three-dimensional objects.

Construct a two-dimensional visual representation of a three-dimensional object or structure.

Determine the level of precision and the appropriate tools for taking the measurements in constructing a two-dimensional visual representation of a three-dimensional object or structure.

Create an elevation drawing to represent a given solid structure, using technology where appropriate.

Determine which measurements cannot be taken directly and must be calculated based on other measurements when constructing a two-dimensional visual representation of a three-dimensional object or structure.

Determine an appropriate means to visually represent an object or structure, such as drawings on paper or graphics on computer screens.

Plot coordinates on a three-dimensional Cartesian coordinate system and use relationships between coordinates to solve design problems.

Describe the features of a three-dimensional Cartesian coordinate system and use them to graph points.

Graph a point in space as the vertex of a right prism drawn in the appropriate octant with edges along the x, y, and z axes.

Find the distance between two objects in space given the coordinates of each.

Find the midpoint between two objects in space given the coordinates of each.

Use technology and other tools to explore the results of simple transformations using three-dimensional coordinates, including translations in the x, y, and/or z directions; rotations of 90º, 180º, or 270º about the x, y, and z axes; reflections over the xy, yz, and xy planes; and dilations from the origin.

Create a scale model of a complex three-dimensional structure based on observed measurements and indirect measurements, using translations, reflections, rotations, and dilations of its components.

Functions can be used to represent general trends in conditions that change over time and to predict future conditions based on present observations.

Use elements of the Mathematical Modeling Cycle to make predictions based on measurements that change over time, including motion, growth, decay, and cycling.

Use regression with statistical graphing technology to determine an equation that best fits a set of bivariate data, including nonlinear patterns.

Create a scatter plot with a sufficient number of data points to predict a pattern.

Describe the overall relationship between two quantitative variables (increase, decrease, linearity, concavity, extrema, inflection) or pattern of change.

Make a prediction based upon patterns.

Create a linear representation of non-linear data and interpret solutions, using technology and the process of linearization with logarithms.

Statistical studies allow a conclusion to be drawn about a population that is too large to survey completely or about cause and effect in an experiment.

Use the Statistical Problem Solving Cycle to answer real-world questions.

Construct a probability distribution based on empirical observations of a variable.

Estimate the probability of each value for a random variable based on empirical observations or simulations, using technology.

Represent a probability distribution by a relative frequency histogram and/or a cumulative relative frequency graph.

Find the mean, standard deviation, median, and interquartile range of a probability distribution and make long-term predictions about future possibilities. Determine which measures are most appropriate based upon the shape of the distribution.

Construct a sampling distribution for a random event or random sample.

Use the binomial theorem to construct the sampling distribution for the number of successes in a binary event or the number of positive responses to a yes/no question in a random sample.

Use the normal approximation of a proportion from a random event or sample when conditions are met.

Use the central limit theorem to construct a normal sampling distribution for the sample mean when conditions are met.

Find the long-term probability of a given range of outcomes from a random event or random sample.

Perform inference procedures based on the results of samples and experiments.

Use a point estimator and margin of error to construct a confidence interval for a proportion or mean.

Interpret a confidence interval in context and use it to make strategic decisions.

Perform a significance test for null and alternative hypotheses.

Interpret the significance level of a test in the context of error probabilities, and use the results to make strategic decisions.

Critique the validity of reported conclusions from statistical studies in terms of bias and random error probabilities.

Conduct a randomized study on a topic of student interest (sample or experiment) and draw conclusions based upon the results.

Mathematical models involving growth and decay are useful in solving real-world problems involving borrowing and investing; spreadsheets are a frequently-used and powerful tool to assist with modeling financial situations.

Use elements of the Mathematical Modeling Cycle to solve real-world problems involving finances.

Organize and display financial information using arithmetic sequences to represent simple interest and straight-line depreciation.

Organize and display financial information using geometric sequences to represent compound interest and proportional depreciation, including periodic (yearly, monthly, weekly) and continuous compounding.

Explain the relationship between annual percentage yield (APY) and annual percentage rate (APR) as values for r in the formulas A=P(1+r)ᵗ and A=Peʳᵗ.

Compare simple and compound interest, and straight-line and proportional depreciation.

Investigate growth and reduction of credit card debt using spreadsheets, including variables such as beginning balance, payment structures, credits, interest rates, new purchases, finance charges, and fees.

Compare and contrast housing finance options including renting, leasing to purchase, purchasing with a mortgage, and purchasing with cash.

Research and evaluate various mortgage products available to consumers.

Compare monthly mortgage payments for different terms, interest rates, and down payments.

Analyze the financial consequence of buying a home (mortgage payments vs. potentially increasing resale value) versus investing the money saved when renting, assuming that renting is the less expensive option.

Investigate the advantages and disadvantages of various means of paying for an automobile, including leasing, purchasing by cash, and purchasing by loan.

Mathematical modeling and statistical problem-solving are extensive, cyclical processes that can be used to answer significant real-world problems.

Use the full Mathematical Modeling Cycle or Statistical Problem-Solving Cycle to answer a real-world problem of particular student interest, incorporating standards from across the course.

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems, extending to infinite geometric series.

Derive and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

Add, subtract, multiply, and divide rational expressions.

Explain why rational expressions form a system analogous to the rational numbers, which is closed under addition, subtraction, multiplication, and division by a non-zero rational expression.

Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a clear-cut solution. Construct a viable argument to justify a solution method. Include equations that may involve linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric functions, and their inverses.

Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise.

Compare and contrast families of functions and their representations algebraically, graphically, numerically, and verbally in terms of their key features. Families of functions include but are not limited to linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, trigonometric, and their inverses.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Extend from polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions.

Find the difference quotient f(x + △x) - f(x)/△x of a function and use it to evaluate the average rate of change at a point.

Explore how the average rate of change of a function over an interval (presented symbolically or as a table) can be used to approximate the instantaneous rate of change at a point as the interval decreases.

Graph functions expressed symbolically and show key features of the graph, by hand and using technology. Use the equation of functions to identify key features in order to generate a graph.

Graph trigonometric functions and their inverses, showing period, midline, amplitude, and phase shift.

Compose functions. Extend to polynomial, trigonometric, radical, and rational functions.

Given that a function has an inverse, write an expression for the inverse of the function.

Use the inverse relationship between exponents and logarithms to solve problems involving logarithms and exponents. Extend from logarithms with base 2 and 10 to a base of e.

Identify the effect on the graph of replacing f(x) by f(x) + k, k·f(x), f(k·x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Extend the analysis to include all trigonometric, rational, and general piecewise-defined functions with and without technology.

Graph conic sections from second-degree equations, extending from circles and parabolas to ellipses and hyperbolas, using technology to discover patterns.

Graph conic sections given their standard form.

Identify the conic section that will be formed, given its equation in general form.

Recognize attributes of trigonometric functions and solve problems involving trigonometry.

Solve application-based problems involving parametric and polar equations.

Graph parametric and polar equations.

Convert parametric and polar equations to rectangular form.

Demonstrate that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

Use trigonometric identities to solve problems.

Use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to derive the other forms of the identity.

Use the angle sum formulas for sine, cosine, and tangent to derive the double angle formulas.

Use the Pythagorean and double angle identities to prove other simple identities.

Define the constant e in a variety of contexts.

Explore the behavior of the function y=eˣ and its applications.

Explore the behavior of ln(x), the logarithmic function with base e, and its applications.

Analyze possible zeros for a polynomial function over the complex numbers by applying the Fundamental Theorem of Algebra, using a graph of the function, or factoring with algebraic identities.

Understand limits of functions.

Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity.

Apply limits of functions at specific values and at infinity in problems involving convergence and divergence.

Explain that vector quantities have both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.

Find the scalar (dot) product of two vectors as the sum of the products of corresponding components and explain its relationship to the cosine of the angle formed by two vectors.

Explain vector subtraction, v – w, as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

Utilize active listening skills during discussion and conversation in pairs, small groups, or whole-class settings, following agreed-upon rules for participation.

Use knowledge of phoneme-grapheme correspondences and word analysis skills to decode and encode words accurately.

Expand background knowledge and build vocabulary through discussion, reading, and writing.

Use digital and electronic tools appropriately, safely, and ethically for research and writing, both individually and collaboratively.

Utilize the writing process to plan, draft, revise, edit, and publish writings in various genres.

Actively listen and speak using agreed-upon rules for discussion, with guidance and support.

Use speech that is understandable with only grade-appropriate errors.

Use word endings to indicate plurals, possessives, and verb tenses in speech.

Use age-appropriate irregular plurals in conversation.

Listen to others and take turns speaking, carrying on a conversation through multiple exchanges.

Actively engage in teacher-led reading experiences and collaborative discussions with peers to build background knowledge needed to be successful as they learn to read and, later, read to learn.

Actively participate in teacher-led choral and shared reading experiences.

With guidance and support, ask and answer questions to seek help, get information, or clarify information presented orally, through text, or other media.

With guidance and support, present information orally, using complete sentences in correct word order.

Describe people, places, things, and events with relevant details in a story with three to five events.

Uses spatial and temporal concepts correctly.

Restate and follow one- and two-step directions.

Recognize and demonstrate that print conveys meaning.

With prompting and support, explain the roles of the author and illustrator of a text.

Track print, moving left to right and top to bottom on the printed page, returning to the beginning of the next line.

Identify the beginning and end of a sentence by locating the capital letter and end punctuation.

Point to words using one-to-one correspondence, noting that words are separated by spaces.

Distinguish letters from words within sentences.

Compare and contrast letters based upon similarities and differences, including name, shape, sound, and approach strokes for writing.

Demonstrate early phonological awareness to basic phonemic awareness skills in spoken words.

Count the number of words in a spoken sentence.

Recognize alliterative spoken words.

Recognize and produce pairs of rhyming words and distinguish them from non-rhyming pairs using pictures and/or spoken words.

Count, blend, and segment syllables in spoken words, including compound words.

Identify the initial, final, and medial sounds of spoken words.

Blend and segment phonemes in single-syllable spoken words made up of three to four phonemes.

Distinguish between commonly confused cognate consonant sounds, using knowledge of voiced and unvoiced sounds and manner of articulation.

Apply knowledge of phoneme-grapheme correspondences and word-analysis skills to decode and encode (spell) words accurately in both isolation and in decodable, grade-appropriate text.

Produce the most frequent sound(s) for each consonant, including x and q, which have two phonemes (sounds).

Identify the vowel in a closed syllable and produce the short vowel sound for the five major vowels when decoding closed syllables.

Decode consonant-vowel-consonant (CVC) words in isolation and in decodable text.

Identify the vowel in an open syllable and produce the long vowel sound for the five major vowels when decoding open syllables.

With prompting and support, identify the vowel-consonant-e syllable pattern and produce the long vowel sounds for the five major vowels in vowel-consonant-e syllables.

With prompting and support, decode words with suffix -s, using knowledge of unvoiced /s/ and voiced /z/ sounds for letter s.

With prompting and support, produce the most frequent sound for digraphs ck, sh, th, ch, wh, ng, and combination qu, making the connection that a two-letter grapheme can represent one phoneme (sound).

Distinguish between similarly spelled words by identifying the phonemes and graphemes that differ.

Decode grade-appropriate high frequency words that are spelled using predictable, decodable phoneme-grapheme correspondences.

Recognize and name all upper and lower case letters in non-sequential order with accuracy and automaticity.

Arrange and name letters of the alphabet in sequential order from a to z, with accuracy and automaticity.

With prompting and support, recognize and name digraphs ck, sh, th, ch, wh, ng, and combination qu.

Apply previously-taught phoneme-grapheme correspondences to decodable words with accuracy and automaticity, in and out of context.

Orally read and reread grade-appropriate decodable texts smoothly, accurately, and expressively, at an appropriate rate to support comprehension.

Recognize and read grade-appropriate high frequency words with accuracy and automaticity.

With guidance and support, orally utilize new academic, content-specific, grade-level vocabulary and relate new words to prior knowledge.

Ask and answer questions about unfamiliar words in discussions and/or text.

Describe the relationship between words, including relating them to synonyms and antonyms.

Name and sort pictures of objects into categories based on common attributes while relating vocabulary to prior knowledge and building background knowledge.

Use new and previously-taught vocabulary to produce and expand complete sentences in shared language activities.

Use previously-taught vocabulary words, including nouns, verbs, and adjectives, in speaking and writing.

Use content knowledge built during read-alouds of informational texts by participating in content-specific discussions with peers and/or through drawing or writing.

With prompting and support, manipulate words and/or phrases to create simple sentences, including declarative and interrogative, to help build syntactic awareness and comprehension at the sentence level.

With prompting and support, identify common types of texts and their features, including literary, informational, fairy tale, and poetry.

With prompting and support, identify the topic of texts, using titles, headings, illustrations, and text clues.

Identify and describe the main story elements in a literary text.

With prompting and support, retell a text orally, including main character(s), setting, and important events in logical order.

With prompting and support, use text clues to determine main ideas and make predictions about an ending in a literary text.

With prompting and support, identify the main topic and key details in an informational text.

With prompting and support, ask and answer questions about key details in literary and informational texts.

With prompting and support, self-monitor comprehension of text by pausing to summarize and rereading for clarification, when comprehension is lacking.

With prompting and support, compare and contrast two texts.

Distinguish between literary texts and informational texts.

Compare and contrast the experiences of characters in a literary text.

Compare and contrast two informational texts on the same topic.

Express ideas orally and connect these ideas through drawing and emergent writing.

Print legibly, using proper pencil grip.

Print upper and lower case letters using proper approach strokes, letter formation, and line placement.

With prompting and support, print first and last names using proper letter formation, capitalizing only the first letter of each name.

With prompting and support, use lower case letters in majority of written work, using capitals only when appropriate.

Apply knowledge of grade-appropriate phoneme-grapheme correspondences and spelling rules (or generalizations) to encode words accurately.

Encode at the phoneme level, using the most common grapheme/spelling(s), for a spoken phoneme (sound).

With prompting and support, encode vowel-consonant (VC) and consonant-vowel-consonant (CVC) words, while using some knowledge of basic position-based rules for spelling English words.

With prompting and support, encode grade-appropriate high frequency words that follow regular phoneme-grapheme correspondences.

With prompting and support, encode grade-appropriate high frequency words that follow regular phoneme-grapheme correspondences and patterns in all but one position, pointing out the part of the word that does not follow the regular pattern.

When speaking and writing, follow the rules of standard English grammar, punctuation, capitalization, and grade-appropriate spelling.

With prompting and support, transcribe spoken words to demonstrate that print represents oral language.

With prompting and support, compose a simple sentence, including necessary components to create a complete sentence rather than a fragment.

With prompting and support, identify the role or purpose of a noun and a verb within a sentence and the type of information it conveys.

With prompting and support, write the correct number of words, with proper spacing, for a spoken phrase or sentence.

With prompting and support, begin each sentence with a capital letter.

With prompting and support, capitalize the pronoun I and names of individuals.

With prompting and support, recognize, name, and correctly use end punctuation.

Actively participate in shared and independent writing experiences, for varied purposes and audiences, across different genres.

Actively participate in shared writing experiences to create messages, lists, and labels for a drawing or illustration.

Actively participate in shared writing experiences to create narratives with the events in chronological order and share feelings about the story, using drawing, dictating, and/or writing.

Actively participate in shared writing experiences to create opinion pieces about a topic or text, state the opinion, supply a reason for the opinion, and provide a sense of closure, using drawing, dictating, and/or writing.

Actively participate in shared writing experiences to create explanatory texts or provide factual information about a topic, using drawing, dictating, and/or writing.

With prompting and support, compose writing for varied purposes and audiences, across different genres.

Improve pictorial and written presentations, as needed, by planning, revising, editing, and using suggestions from peers and adults.

Participate in shared research and writing projects to answer a question or describe a topic.

Include information recalled from personal experiences in research and writing projects.

Gather information from provided sources for research and writing projects.

With guidance and support, use a variety of digital tools to produce and publish writing, working both independently and collaboratively with peers.

Engage in collaborative discussions about topics and texts with peers and adults in small and large groups, utilizing agreed-upon rules.

Actively participate in shared reading experiences and collaborative discussions to build background knowledge and learn how oral reading should sound.

Ask and answer questions to seek help, get information, or clarify information to confirm understanding in response to information presented in audible, text, or digital format.

Present information orally using complete sentences and appropriate volume.

Orally describe people, places, things, and events, expressing ideas with relevant details.

Locate a book's title, table of contents, glossary, and the names of author(s) and illustrator(s).

Explain the roles of author(s) and illustrator(s).

Demonstrate basic to advanced phonological and phonemic awareness skills in spoken words.

Count, blend, segment, and delete syllables in spoken words, including polysyllabic words.

Recognize and produce groups of rhyming words and distinguish them from non-rhyming groups of spoken words.

Produce alliterative words.

Blend and segment phonemes in single-syllable spoken words made up of three to five phonemes, including words with consonant blends.

Add, delete, and substitute phonemes at the beginning or end of spoken words made up of three to five phonemes, and produce the resulting word.

Distinguish between commonly-confused vowel sounds and commonly-confused cognate consonant sounds, using knowledge of mouth position, voiced and unvoiced sounds, and manner of articulation.

Identify the sound substitution in words with five to six phonemes.

Apply knowledge of phoneme-grapheme correspondences and word analysis skills to decode and encode words accurately both in isolation and within decodable, grade-appropriate texts.

Produce the most frequent sound(s) for each letter of the alphabet, including x, q, and the long and short sounds of the vowels.

Decode and encode regularly-spelled, one-syllable words with closed syllables, open syllables, and vowel-consonant-e syllables, including words with blends in initial and final position.

Decode words with digraphs, trigraphs, and combinations, including digraphs ck, sh, th, ch, wh, ph, ng, trigraphs tch and dge, and combination qu.

Decode words with a after w read /ä/ and a before l read /â/.

With prompting and support, decode words with the hard and soft sounds of c and g, in context and in isolation

Decode words with vowel y in the final position of one and two syllable words, distinguishing the difference between the long /ī/ sound in one-syllable words and the long /ē/ sound in two-syllable words, and words with vowel y in medial position, producing the short /ĭ/ sound for these words.

Decode regularly spelled one-syllable words with vowel-r syllables, including ar, er, ir, or, and ur.

With prompting and support, decode words with common vowel team syllables, including ai, ay, ee, ea, igh, ie, oa, ou, ow, au, aw, oe, oo, ew, oi, oy, and ue.

With prompting and support, decode words that follow the -ild, -ost, -old, -olt, and -ind patterns.

With prompting and support, decode two-syllable words using knowledge of closed syllables, open syllables, vowel-consonant-e syllables, vowel-r syllables, common vowel team syllables, and consonant-le syllables, including compound words that fit multiple syllable types.

With prompting and support, decode words with silent letter combinations.

With prompting and support, decode words with common prefixes including un-, dis-, in-, re-, pre-, mis-, non-, and ex-.

With prompting and support, decode words with common suffixes, including words with dropped e and y-to-i changes for suffix addition.

Decode contractions with am, is, has, and not.

Decode grade-appropriate high frequency words that are spelled using predictable, decodable phoneme-grapheme correspondences.

Apply previously-taught phoneme-grapheme correspondences to decodable words with accuracy and automaticity, in and out of context.

Read grade-appropriate texts with accuracy and fluency.

Read and reread grade-appropriate decodable text orally with accuracy and expression at an appropriate rate to support comprehension.

Recognize and self-correct decoding and other errors in word recognition and reread for clarification.

Participate in poetry reading, noticing phrasing, rhythm, and rhyme.

Read high-frequency words commonly found in grade-appropriate text.

Utilize new academic, content-specific, grade-level vocabulary, make connections to previously learned words, and relate new words to background knowledge.

Make connections to a word's structure using knowledge of phonology, morphology, and orthography of the word to aid learning.

Ask and answer questions about unfamiliar words and phrases in discussions and/or text.

Identify possessives and plurals and use them as clues to the meaning of text.

Identify meaningful parts of words (morphemes) and use them as clues to the meaning of unknown words, including frequently occurring affixes and inflections -s, -es, -ed, -ing, -er, and -est.

Describe word relationships and nuances in word meanings, including relating them to their opposites and distinguishing shades of meaning in similar or related words.

Use information found within the text to determine the meaning of an unfamiliar or multiple-meaning word or phrase.

Sort and categorize groups of words or pictures based on meaning, and label each category.

Identify and explain adjectives as descriptive words and phrases in all forms of texts, including poems.

Use grade-appropriate academic vocabulary in speaking and writing.

Use content knowledge built during read-alouds of informational and literary texts by participating in content-specific discussions with peers and/or through drawing and writing.

Manipulate words and/or phrases to create simple sentences, including declarative and interrogative, to help build syntactic awareness and comprehension at the sentence level.

Identify common types of texts and their features, including literary, informational, fairy tale, and poetry.

Identify the main topic and key details of literary and informational texts.

Ask and answer questions about key details in literary and informational texts.

Identify and describe the main story elements in a literary text.

Describe the characters and settings, using illustrations and textual evidence from a story.

Retell the plot or sequence of major events in chronological order.

Identify who is telling the story, using evidence from the text.

Use the term narrator to refer to the speaker who is telling the story.

Describe connections between two individuals, events, ideas, or pieces of information, including cause and effect, sequence, and problem and solution, in a literary text.

With prompting and support, use textual evidence to explain the central message or moral of a literary text.

Make predictions using information found within a literary text.

Self-monitor comprehension of text by pausing to summarize or rereading for clarification when comprehension is lacking.

Compare and contrast texts.

Compare and contrast characters, settings, and major events in literary texts.

Describe the connections between individuals, events, ideas, or pieces of information in an informational text.

Point out similarities and differences between two texts on the same topic.

Write legibly, using proper pencil grip.

Print upper and lowercase letters fluently, using proper approach strokes, letter formation, and line placement.

Print first and last names using proper letter formation, capitalization, and punctuation.

Use lower case letters in the majority of written work, using capitals only when appropriate.

Write letters of the English alphabet in alphabetical order from memory.

Apply knowledge of grade-appropriate phoneme-grapheme correspondences and spelling rules (or generalizations) to encode words accurately.

Encode vowel-consonant (VC) and consonant-vowel-consonant (CVC) words, while using some knowledge of basic position-based rules for spelling English words in closed syllables.

Encode consonant-vowel (CV) words using knowledge of open syllable patterns.

Encode words with two-consonant blends in beginning position, including blends that are commonly confused with other spellings, by distinguishing the placement and action of the lips, teeth, and tongue during articulation.

Encode words with consonant digraphs using knowledge that one sound may be spelled with two letters.

Encode words with vowel-consonant-e syllable patterns.

With prompting and support, encode words with the common vowel teams and diphthongs.

With prompting and support, encode words with vowel-r combinations ar, or, er, ir, and ur.

With prompting and support, encode words with final /ch/ sound spelled -ch and -tch.

With prompting and support, encode words with final /f/, /l/, and /s/ sounds in one-syllable base words by doubling the final consonant when it follows a short vowel sound.

Encode words with final /v/ sound, using knowledge that no English word ends with a v.

Encode grade-appropriate high frequency words that follow regular phoneme-grapheme correspondences.

Encode grade-appropriate high frequency words that follow regular phoneme-grapheme correspondences and patterns in all but one position, pointing out the part of the word that does not follow the regular pattern.

Encode words with suffixes -s, -es, -ing, -ed, -er, and -est.

With prompting and support, encode words with common prefixes re-, un-, and mis-.

With prompting and support, encode frequently confused homophones, using knowledge of English and meaning to facilitate learning.

Follow the rules of standard English grammar, punctuation, capitalization, and spelling appropriate to grade level.

Transcribe spoken words to demonstrate that print represents oral language.

Compose a simple sentence, including a subject and a predicate, that expresses a complete thought.

With prompting and support, identify the role or purpose of a noun, verb, and adjective within a sentence and describe the type of the information it conveys.

Write the correct number of words, with proper spacing, for a spoken phrase or sentence.

Begin each sentence with a capital letter.

Capitalize the pronoun I, and names of individuals.

With prompting and support, recognize, name, and correctly use end punctuation, utilizing appropriate academic vocabulary.

Actively participate in shared writing experiences to compose and develop a well-organized paragraph with a topic sentence, details to support, and a concluding sentence.

With prompting and support, write a narrative that recounts two or more appropriately sequenced events using transitions, incorporating relevant details, and providing a sense of closure.

With prompting and support, write an informative or explanatory text about a topic, using facts from a source and providing a sense of closure.

With prompting and support, write an opinion piece about a topic, including at least one supporting reason from a source and providing a sense of closure.

With prompting and support, write simple poems about a chosen subject.

Develop and edit first drafts using appropriate spacing between letters, words, and sentences and left-to-right and top-to-bottom progression.

Improve writing, as needed, by planning, revising, and editing with guidance from peer editors, responding to their questions and suggestions.

Describe ideas, thoughts, and feelings, using adjectives, drawings, or other visual displays to clarify.

Organize a list of words into alphabetical order according to the first and (when necessary) second letters of the words.

Participate in shared research and writing projects to answer a question or describe a topic.

Recall information from experiences to contribute to shared research and writing projects.

Gather information from provided sources.

Use a variety of digital tools to produce and publish writing with guidance and support from adults, working both individually and in collaboration with peers.

Participate in conversations and discussions with groups and peers utilizing agreed-upon rules.

Present information orally using complete sentences, appropriate volume, and clear pronunciation.

Use oral language for different purposes: to inform, to entertain, to persuade, to clarify, and to respond.

Use complex sentence structures when speaking.

Demonstrate oral literacy skills by participating in a variety of oral language activities.

Orally answer who, what, when, where, why, and how questions about a text or conversation, using complete sentences to provide key ideas and details.

Create recordings of stories or poems.

Use visual aids and technology in oral presentations to present key ideas and details about a text or conversation, and add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify thoughts, feelings, and ideas.

Demonstrate standard English usage when speaking.

Use adjectives and adverbs.

Produce and expand complete simple and compound sentences when speaking.

Apply knowledge of voiced and unvoiced sounds and manner of articulation to distinguish between commonly-confused vowel sounds and commonly-confused cognate consonant sounds.

Demonstrate advanced phonemic awareness skills in spoken words.

Add, delete, and substitute phonemes at the beginning, end, or middle of a spoken word made up of up to six phonemes and produce the resulting word.

Delete the initial sound in an initial blend in a one-syllable base word.

With prompting and support, delete the medial and final sounds in blends in one syllable base words.

Apply phoneme chaining that changes only one sound at a time to show addition, deletion, substitution, and resequencing of sounds from one word to the next.

With prompting and support, reverse sounds within a word by saying the last sound first and the first sound last.

Apply knowledge of phoneme-grapheme correspondences, multisyllabic word construction, and syllable division principles to decode and encode (spell) words accurately in isolation and in context.

Decode multisyllabic words with common syllable patterns, including open/closed, vowel-r, vowel-consonant-e, vowel teams, consonant-le, and schwa syllables.

Apply knowledge of multisyllabic word construction and syllable division principles to decode grade-appropriate multisyllabic words.

Decode and encode words with three-consonant blends and blends containing digraphs.

Decode and encode words with consonant digraphs, trigraphs, and combinations.

Decode and encode words with variable vowel teams and vowel diphthongs.

Decode and encode words with vowel-r combinations.

Decode and encode words that follow the -ild, -ost, -old, -olt, and -ind patterns.

Decode and encode words with a after w read /ä/ and a before l read /â/.

Decode and encode words with or after w read /er/.

Decode and encode words with the hard and soft sounds of c and g, in context and in isolation.

Decode and encode words with vowel y in the final position of one and two syllable words, distinguishing the difference between the long /ī/ sound in one-syllable words and the long /ē/ sound in two-syllable words, and words with vowel y in medial position, producing the short /ĭ/ sound for these words.

Decode words with silent letter combinations.

Decode and encode words with prefixes and suffixes, including words with dropped e and y-to-i changes for suffix addition.

Decode and encode grade-appropriate high frequency words that are spelled using predictable, decodable phoneme-grapheme correspondences, including those that contain only one irregularity.

Decode and encode contractions with am, is, has, not, have, would, and will.

Apply previously-taught phoneme-grapheme correspondences to multisyllabic words with accuracy and automaticity, in and out of context.

Read and reread grade-appropriate text accurately, automatically, and with meaningful expression at a rate which supports comprehension.

Read grade-appropriate poetry, noticing phrasing, rhythm, and rhyme.

Read high-frequency words commonly found in grade-appropriate text.

Utilize new academic, content-specific, grade-level vocabulary, making connections to previously learned words and relating new words to background knowledge.

Make connections to a word's structure using knowledge of phonology, morphology, and orthography of the word to aid learning.

Describe word relationships and nuances in word meanings, including relating them to their opposites and distinguishing shades of meaning in similar or related words.

Use knowledge of antonyms and synonyms.

Use knowledge of homophones to determine use of the correct word.

With prompting and support, interpret figurative language.

Analyze meaningful parts of words and phrases in discussions and/or text.

Identify possessives and plurals and use them as clues to the meaning of text.

Identify meaningful parts of words (morphemes) and use them as clues to the meaning of unknown words, including base words, compound words, and frequently occurring affixes and inflections.

Use dictionary definitions and information found within the text to help determine meaning of unfamiliar or multi-meaning words.

Identify new vocabulary and the use of word meanings in text to establish real-life connections.

Use grade-level academic and domain-specific vocabulary to gain meaning from text.

Use grade-level academic and domain-specific vocabulary in writing.

Use content knowledge built during read-alouds and independent reading of informational and literary texts by participating in content-specific discussions with peers and/or through writing.

Identify the main story elements in a literary text.

Explain the plot of a narrative, using textual evidence to list the major events in sequence.

Describe the characters' traits, feelings, and behaviors in a story.

Describe the setting of a narrative, using textual evidence.

Identify the central message or moral of a story.

Identify the theme in myths, fables, and folktales.

Identify the main idea and supporting details of literary and informational texts.

Explain how the supporting details contribute to the main idea.

Recount or summarize key ideas from the text.

Identify and use various text features to locate ideas, facts, or supporting details in both written and digital formats.

Identify and locate captions, bold print, subheadings, indexes, graphs, maps, glossaries, and illustrations.

Explain how specific features can clarify a text or enhance comprehension.

Compare and contrast important details presented by two texts on the same topic or theme.

Compare and contrast different versions of the same story by different authors, from different cultures, or from different points of view.

Compare and contrast story elements of literary texts.

Identify the text structures within literary and informational texts, including cause and effect, problem and solution, and sequence of events.

Establish a purpose before reading literary and informational texts to enhance comprehension.

With prompting and support, identify and interpret various cohesive devices that help link words and sentences to one another within the text as a scaffold to help build comprehension at the sentence and paragraph level.

Read and comprehend literary and informational texts.

State and confirm predictions about a text.

Use background knowledge to make connections to new text.

Draw conclusions based on the text.

Use information from a text to determine the author's purpose in different forms of informational and literary texts.

Identify rhyme schemes in poems or songs.

Read and identify types of poems, including free verse, rhymed verse, haiku, and limerick.

Differentiate between fact and opinion in a text.

Use prior knowledge and information gathered from research to evaluate opinions in texts.

Use textual evidence and gathered research from reliable sources to prove facts.

Demonstrate listening skills and build background knowledge by asking and answering questions about texts read aloud.

Manipulate words and/or phrases to create simple and compound sentences, including coordinating conjunctions for, and, nor, but, or, yet, and so, to help build syntactic awareness and comprehension at the sentence level.

Write legibly.

Write words and sentences fluently using correctly-formed manuscript letters with appropriate size and spacing.

Demonstrate cursive writing strokes, including undercurve, overcurve, downcurve, and slant.

Form uppercase and lowercase letters in cursive.

Apply knowledge of grade-appropriate phoneme-grapheme correspondences, multisyllabic word construction, syllable division principles, and spelling rules (or generalizations) to encode words accurately.

Encode grade-appropriate multisyllabic words using knowledge of syllable types, including open, closed, vowel-consonant-e, vowel teams, vowel-r, and consonant-le.

Apply knowledge of multisyllabic word construction and syllable division principles to encode grade-appropriate words correctly.

Encode words with final /v/ and /j/ sounds using knowledge that no English word ends with a v or j.

Encode one- and two-syllable words with long and short vowel patterns.

Encode words with two- and three-consonant blends, including those containing digraphs.

Encode words with consonant digraphs, trigraphs, and combinations.

Encode words with the common vowel teams, including diphthongs.

Encode words with vowel-r combinations.

Encode words that follow the -ild, -ost, -old, -olt, and -ind patterns.

Encode words with a after w read /ä/ and a before l read /â/.

Encode words with or after w read /er/.

Encode words with hard and soft c and g.

Encode words with vowel y in the final position of one and two syllable words, distinguishing the difference between the long /ī/ sound in one-syllable words and the long /ē/ sound in two-syllable words, and words with vowel y in medial position, producing the short /ĭ/ sound for these words.

Encode words with prefixes and suffixes, including words with dropped e and y-to-i changes for suffix addition.

Encode grade-appropriate high frequency words that are spelled using predictable, decodable phoneme-grapheme correspondences, including those that contain only one irregularity.

Encode contractions with am, is, has, not, have, would, and will, using apostrophes appropriately.

Encode frequently confused homophones accurately, using knowledge of English orthography and meaning to facilitate learning.

Organize a list of words into alphabetical order according to first, second, and third letters.

Write a personal or fictional narrative using a logical sequence of events, including details to describe actions, thoughts, and feelings and providing a sense of closure.

Write informative or explanatory texts, introducing the topic, providing facts and relevant details to develop points, and providing a conclusion.

Write an opinion piece about a topic or text with details to support the opinion, using transitional words and providing a sense of closure.

Write complete sentences demonstrating knowledge of punctuation conventions.

Utilize commas with words in a series in a sentence.

Use apostrophes to form contractions and possessives.

Use punctuation to set off interjections.

Expand sentences using frequently-occurring conjunctions.

With prompting and support, compose and develop a well-organized paragraph with a topic sentence, details to support, and a concluding sentence.

Demonstrate understanding of standard English language conventions when writing.

Identify the role of a noun, verb, adjective, and adverb within a sentence and explain the type of the information it conveys.

Form regular nouns and verbs by adding -s or -es.

Form and use simple present and past verb tenses.

Form plurals by changing -y to -ies.

Form and use frequently-occurring irregular plural nouns and verbs.

Use plural possessives.

Gather and use research to answer questions to complete a research product.

Create topics of interest for a research project.

Create questions to gather information for a research project.

Find information from a variety of sources.

Define plagiarism and explain the importance of using their own words.

Contribute meaningful ideas to discussions with groups and peers utilizing agreed upon rules.

Elaborate on responses in conversations and discussions.

Present information orally using complex sentence structures, appropriate volume, and clear pronunciation.

Use oral language for different purposes: to inform, to entertain, to persuade, to clarify, and to respond.

Apply oral literacy skills by participating in a variety of oral language activities.

Ask and answer questions using complete sentences and grade-level vocabulary.

Express ideas, opinions, and feelings orally in a logical sequence clearly, accurately, and precisely, using appropriate volume, clear pronunciation, and standard English grammar.

Use digital tools to enhance oral presentations, working collaboratively.

Demonstrate advanced phonemic awareness skills in spoken words.

Delete phonemes in initial and final blends of a spoken word.

Substitute phonemes in initial and final blends in a spoken word.

Reverse phonemes in a spoken word.

In a series of words, apply phoneme chaining that changes only one sound at a time to show addition, deletion, substitution and resequencing of sounds from one word to the next.

Use knowledge of syllable and affix substitution and deletion to demonstrate morphological changes.

Apply knowledge of phoneme-grapheme correspondences, multisyllabic word construction, and syllable division principles to decode and encode (spell) words accurately in isolation and in context.

Decode multisyllabic words with common syllable patterns, including open/closed, vowel-r, vowel-consonant-e, vowel teams, consonant-le, and odd or schwa syllables.

Apply knowledge of multisyllabic word construction and syllable division principles to decode grade-appropriate multisyllabic words.

Decode and encode words with three-consonant blends, digraphs, trigraphs, quadrigraph eigh, combinations, diphthongs, and silent letter combinations.

Decode and encode words with graphemes that represent multiple sound-symbol correspondences by applying knowledge of most common to least common frequency.

Decode and encode multisyllabic words using knowledge of stress or accent to pronounce a word correctly, including the schwa sound when appropriate.

Decode and encode words using knowledge of the morphological structure of a word, including prefixes, suffixes, and roots.

Decode and encode contractions with am, is, has, not, have, would, and will.

Decode and encode frequently confused homophones accurately using knowledge of English and meaning to facilitate learning.

Decode and encode words with hard and soft c and g.

Decode and encode grade-appropriate high frequency words that follow regular and irregular phoneme-grapheme correspondences, using knowledge of the specific sound-symbol correspondences that are irregular.

Apply previously-taught phoneme-grapheme correspondences to multisyllabic words with accuracy and automaticity, in and out of context.

Read and reread grade-appropriate text accurately, automatically, and with meaningful expression at a rate which supports comprehension.

Read and reread grade-appropriate poetry, practicing phrasing, rhythm, rhyme, and meaningful expression.

Read high-frequency words commonly found in grade-appropriate text accurately and automatically.

Utilize new academic, content-specific, grade-level vocabulary to make connections to previously learned words and relate new words to background knowledge.

Make connections to a word's structure using knowledge of phonology, morphology, and orthography of the word to aid learning.

Describe word relationships and nuances in word meanings, including relating them to their opposites and distinguishing shades of meaning in similar or related words, including nouns, verbs, and adjectives.

Determine meaning of words using synonyms in context.

Determine meaning of words using antonyms as a clue.

Describe the similarities and differences between related words.

Use knowledge of homophones to determine appropriate use of words.

Interpret figurative language.

Identify relationships and nuances in word meanings to determine real-life connections between words and their use.

Analyze meaningful parts (morphemes) of words and phrases in discussions and/or text.

Identify meaningful parts of words (morphemes) and use them as clues to the meaning of unfamiliar words, including base words, roots, and frequently occurring affixes and inflections.

Apply knowledge of the changes in tense (-ed), number (-s), and degree (-er and -est) signified by inflected endings to determine the meaning of a word.

Identify common and derivational prefixes and suffixes and use them as clues to a word's meaning.

Identify common Latin and Greek roots and use them to determine the meaning of unfamiliar words.

Sort words with shared and varied suffixes by parts of speech.

Use knowledge of grade-level academic and domain-specific vocabulary to gain meaning from text.

Use grade-level academic and domain-specific vocabulary in writing.

Demonstrate content knowledge built during independent reading of informational and literary texts by participating in content-specific discussions with peers and/or through writing.

Determine the explicit or implied main idea and supporting details of a text.

Explain how supporting details contribute to the main idea, using textual evidence.

Recount or summarize the key ideas from the text.

Establish a purpose before reading literary and informational texts to enhance comprehension, including identifying background knowledge and generating questions about the topic or characters.

Identify and interpret various cohesive devices that link words and sentences to one another within the text.

Describe literary elements within a story, including setting, plot, characters, and themes.

Describe in detail the characters' behavior, emotions, and traits and explain how their actions influence events in the story.

Explain how the characters' actions and dialogue contribute to the meaning of the story.

Identify the central message, theme, or moral in a story, including myths, fables, and folktales, and explain the meaning conveyed in the passage.

Compare and contrast the themes, settings, and plots from two texts.

Identify and use text features in informational passages to locate information.

Explain how text features support details in the text.

Explain how illustrations contribute to meaning in a story.

Interpret text features used in written and digital formats.

Identify the text structures within literary and informational texts.

Explain how the structures, including comparison and contrast, sequence of events, problem and solution, and cause and effect, contribute to the meaning of the text, using textual evidence.

Identify statements in informational texts as facts or opinions.

Use prior knowledge and/or details from the text to distinguish fact from opinion.

Use information gathered from research to evaluate opinions.

Use text comparisons (text to text, text to self, and text to world) to make meaning.

Use prior knowledge to determine similarities between texts they are reading and texts they have previously read.

Compare different versions of the same story.

Read prose, poetry, and dramas, identifying the literary devices used by the author to convey meaning.

Identify the narration of a literary text as first person or third person.

Determine the main idea of a text read aloud or information presented in an audible format.

Manipulate words and/or phrases to create compound sentences, including coordinating conjunctions for, and, nor, but, or, yet, or so, and complex sentences to help build syntactic awareness and comprehension at the sentence level.

Write legibly in cursive with connected, correctly-formed letters and appropriate spacing between words.

Apply knowledge of grade-appropriate phoneme-grapheme correspondences, multisyllabic word construction, syllable division rules, and spelling rules (or generalizations) to encode words accurately.

Apply knowledge of multisyllabic word construction and syllable division principles to encode multisyllabic words.

Encode multisyllabic words, using common syllable patterns: open/closed, vowel-r, vowel-consonant-e, vowel teams, consonant-le, and odd or schwa syllables.

Encode words with two and three letter blends and previously taught digraphs, trigraphs, combinations, diphthongs, quadrigraph eigh, vowel y, hard and soft c and g, silent letter combinations, and contractions.

Encode words with less common prefixes, suffixes, and common Latin roots.

Encode frequently confused homophones accurately, using context to determine correct spelling.

Write personal or fictional narratives with a logical plot (sequence of events), characters, transitions, and a sense of closure.

Write informative or explanatory texts about a topic using sources, including an introduction, facts, relevant details with elaboration, and a conclusion.

Write an argument to convince the reader to take an action or adopt a position, using an introduction, logical reasoning supported by evidence from various sources, and a conclusion.

Demonstrate knowledge of the rules of standard English grammar including punctuation, capitalization, sentence formation, and spelling appropriate for third grade.

Use articles a, an, and the correctly.

Identify the role of a noun, verb, adjective, adverb, pronoun, preposition, and conjunction within a sentence and explain the type of the information it conveys.

Form plural nouns, verbs, and possessives, including irregular plural nouns and verbs.

Use simple abbreviations, including days of the week, months of the year, titles, units of metric and customary measurement, street names, and state names.

Compose simple, compound, and complex sentences with correct subject-verb agreement.

Identify and correct sentence fragments and run-on sentences.

Identify the subject and predicate of a sentence.

Compose and develop a well-organized paragraph with a topic sentence, details to support, and a concluding sentence.

Gather and evaluate information about a topic from a variety of sources, including digital sources, and utilize it to create a project, report, or presentation.

Avoid plagiarism by using their own words and utilizing digital sources ethically.

Use grade-level and domain-appropriate vocabulary in writing.

Use specific vocabulary to develop a story.

Use specific vocabulary to explain or inform on a topic.

Use words and phrases in writing for effect and elaboration.

Use transition words and phrases for sentence variety.

Write poetry or prose in response to visual images to interpret their meanings.

Utilize active listening skills during discussion and conversation in pairs, small groups, or whole-class settings, following agreed-upon rules for participation.

Use context clues to determine meanings of unfamiliar spoken or written words.

Use digital and electronic tools appropriately, safely, and ethically when researching and writing, both individually and collaboratively.

Utilize a writing process to plan, draft, revise, edit, and publish writings in various genres.

Identify and explain literary devices in prose and poetry.

Assess the formality of occasions in order to speak or write using appropriate language and tone.

Apply knowledge of grade-appropriate phoneme-grapheme correspondences, syllable types, and morphological structure to read unfamiliar multisyllabic words accurately, both in context and in isolation.

Determine and use the correct syllable type(s) to decode unfamiliar multisyllabic words, including open, closed, vowel-consonant-e, r-controlled, vowel team (including diphthongs), consonant-le, and "leftovers" including odd and schwa syllables.

Apply knowledge of roots, prefixes, and suffixes to decode unfamiliar multisyllabic words.

Apply knowledge of roots, prefixes, and suffixes to encode unfamiliar multisyllabic words.

Demonstrate fluency when reading grade-level text and when responding through writing or speaking.

Read grade-level text orally with appropriate pauses, phrasing, stress, intonation, rate, and integration to support comprehension.

Read words with irregular and regular spelling patterns accurately and automatically.

Write routinely and independently in response to text.

Accurately interpret general academic and domain-specific words and phrases.

Explain how specific word choices shape meaning or tone.

Explain how figurative language contributes to the meaning of text, including simile, metaphor, alliteration, personification, hyperbole, and idioms.

Use the relationships between synonyms, antonyms, and homographs to increase understanding of word meanings.

Use commonly misused words correctly in writing.

Consult reference materials to find the pronunciation of unknown words and phrases.

Use grade-appropriate general academic and domain-specific words and phrases in presentations and discussions.

Demonstrate comprehension of literary and informational text by utilizing its content when discussing or writing in response to the text.

Analyze in depth a character, setting, or event in a story or drama, drawing on specific details in the text.

Identify and explain attitudes and influences of multiple characters within a text.

Explain how the main character changes throughout the story, using explicit evidence from the text.

Make an inference about a character's behavior, the setting, and/or specific events, using explicit details from the story.

Describe how authors use literary devices and text features to convey meaning in prose, poetry, and drama.

Identify clues in the text to recognize implicit meanings.

Apply prior knowledge to textual clues to draw conclusions about the author's meaning.

Make an inference about the meaning of a text and support it with textual evidence.

Identify the narrator's point of view in a literary text and explain how it differs from a character's perspective.

Explain the difference between first person and third person narration, including omniscient and third person limited.

State an opinion of the author's use of narration, supporting reasoning with examples from the text.

Identify the point of view in a narrative and describe how the narrative would be different if told from the perspective of a different character or narrator.

Compare the perspectives of different characters within a text.

Compare and contrast the treatment of similar themes in stories, myths, and traditional literature from different cultures.

Determine and state an implied theme, explicit theme, or life lesson from a myth, story, or other traditional literature.

Analyze a common or shared theme and its development in stories, myths, and/or other traditional literature.

Use details and examples from a text to indicate what the text explicitly states.

Interpret facts from an informational article, using details and examples from the text to explain the interpretation.

List the main questions answered by an informational article.

Categorize statements in an article or other informational text as fact or opinion and give reasons for each choice.

Explain the differences between primary and secondary sources, giving examples from texts.

Explain how relevant details support the implied or explicit main idea of a text.

Determine the central idea or theme of a text.

Explain the difference between implied and explicit details.

Summarize the key supporting details by citing evidence from a text.

Analyze events, procedures, ideas, or concepts in informational texts, including what happened and why, based on specific information in the text.

Cite evidence to explain the author's perspective toward a topic in an informational text.

Evaluate how text features and structures contribute to the meaning of an informational text.

Identify and describe the structures within a text, including description, comparison and contrast, sequence, problem and solution, and cause and effect.

Interpret information from text features in both print and digital formats.

Explain how an author uses reasons and evidence to support particular points and claims in an informational text or argument.

Make text-based inferences to determine possible reasons for an author's stance.

Explain how the form of a poem contributes to its meaning.

Analyze how rhythm and rhyme in poetry contribute to meaning.

Write clear and coherent responses to texts, using explicit or implicit evidence that supports a particular point.

Add audio recordings to presentations, when appropriate, to enhance the development of main ideas or themes.

Synthesize information on a topic in order to write or speak knowledgeably about the subject.

Make complex inferences within and across texts to determine the importance of information.

Use evidence to explain information across texts including different perspectives and/or points of view.

Orally paraphrase portions of a text or information presented in diverse media when collaborating and/or presenting.

Respond in writing to literature and informational text, including stories, dramas, poetry, and cross-curricular texts, both independently and with support, demonstrating grade-level proficiency.

Use research to produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.

Introduce a research topic clearly and group related ideas.

Integrate and cite evidence to present research findings in written form.

Paraphrase portions of texts or information presented in diverse media and formats.

Write fluently and legibly in cursive, using correctly formed letters with appropriate spacing.

Write personal or fictional narratives using a logical plot, transitional words and phrases, sensory details, and dialogue, and providing a sense of closure.

Write informative or explanatory text about a topic using sources, incorporating academic vocabulary, and including an introduction, facts, details with elaboration, and a conclusion.

Write an argument to persuade the reader to take an action or adopt a position, using an introduction, logical reasoning supported by evidence from relevant sources, and linking words to connect their argument to the evidence.

Compose complete sentences with correct subject-verb agreement, punctuation, and usage.

Form and use prepositional phrases and conjunctions.

Recognize and correct sentence fragments and run-on sentences.

Use commas, apostrophes, and quotation marks correctly.

Demonstrate command of the conventions of standard English grammar and usage.

Use relative pronouns who, whose, which, and that, relative adverbs where, when, and how, and irregular possessive nouns.

Compose friendly and formal letters using appropriate elements, including date, greeting, body, and a signature.

Write return address and mailing address in the proper locations on an envelope.

Present an opinion orally, sequencing ideas logically and using relevant facts.

Express appropriate and meaningful responses to questions posed by others.

Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes, and speaking clearly with adequate volume, appropriate pacing, and clear pronunciation.

Articulate ideas, claims, and perspectives in a logical sequence, presenting information, findings, and credible evidence from multiple sources and modalities to enhance listeners' understanding.

Apply phonics and word analysis skills to encode and decode words in grade-level texts.

Use combined knowledge of letter-sound correspondences, appropriate blending, syllabication patterns, morphology, and word attack skills to read unfamiliar multisyllabic, grade-level words accurately in context and in isolation.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases, choosing flexibly from a range of strategies.

Write familiar and unfamiliar multisyllabic, grade-level appropriate words accurately in context and in isolation.

Demonstrate fluency when independently reading, writing, and speaking in response to grade-level literary and informational text, including stories, dramas, poetry, and cross-curricular texts.

Read grade-level text orally with accuracy, automaticity, appropriate prosody or expression, purpose, and understanding, self-correcting and rereading as necessary.

Orally present information and original ideas clearly.

Express ideas clearly and effectively to diverse partners or groups.

Pose and respond to explicit questions in ways that contribute to the discussion and elaborate on the remarks of others.

Verbally summarize information read aloud or presented in diverse media and formats.

Report orally on a topic or text, sequencing ideas logically and supporting main ideas with appropriate facts and relevant details.

Speak clearly at an understandable rate.

Respond directly to specific information shared by others in classroom discussion, using facts to support the ideas being discussed.

Acquire and use grade-level vocabulary, clarifying the meaning of unknown and multiple-meaning words and phrases in text, choosing flexibly from a range of strategies.

Interpret the meaning of words, phrases, and patterns as they are used in texts, including domain-specific and academic vocabulary and figurative language.

Locate similes, metaphors, personification, hyperbole, imagery, alliteration, onomatopoeia, and idioms and interpret their meanings in context.

Explain the meanings of common idioms, adages, and proverbs.

Explain how an author's vocabulary and style influence the tone and mood of a text and support his/her purpose for writing.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases.

Write using grade-appropriate general academic and domain-specific words and phrases accurately, including those that signal contrasting ideas, additional information, and other logical relationships.

Use grade-appropriate general academic and domain-specific words and phrases during presentations and discussion.

Demonstrate comprehension of varied literary and informational texts by utilizing its content when discussing or writing in response to the text.

Demonstrate comprehension of text by asking and responding to questions about literary elements used in the text.

Explain the relationships among events, people, or concepts in informational texts, supported by textual evidence.

Interpret how authors use literary elements throughout a text, including character, setting, conflict, dialogue, and point of view.

Explain how the author's use of character types throughout a narrative helps drive its plot.

Compare and contrast characters, points of view, or events in two or more literary texts.

Determine the implied and/or explicit main idea in literary and informational texts.

Determine and analyze themes of various culturally-diverse literary texts, supporting analysis with textual evidence.

Analyze common themes of diverse texts with support from textual evidence.

Summarize a story or drama, describing how the plot unfolds and how characters respond to challenges or change their thoughts and actions and citing textual evidence.

Determine and evaluate the effectiveness of digital and print text features and structures, including comparison and contrast, problem and solution, and cause and effect.

Identify various text features used in diverse forms of text.

Determine credibility and appropriateness of a research source by distinguishing between fact and the author's opinion in informational text.

Analyze how two or more texts address similar topics in diverse media and formats, including graphics, live and/or recorded performances, and written works.

Explain how visual and multimedia elements contribute to the overall meaning and tone of a text.

Compare and contrast the approaches to theme in several stories within a genre.

Locate information quickly within a text and apply information from multiple sources to analysis of the topics.

Explain how an author uses reasons and evidence to support particular points in a text.

Compare the approaches of several authors of articles about the same or similar topics.

Review the key ideas expressed in a text and draw conclusions, using facts to support them.

Use audio and/or visual sources of information to obtain the answer to a question.

Summarize in writing a variety of texts, stating their implied and/or explicit main ideas.

Use textual evidence to support summarization.

Cite appropriately when summarizing.

Quote literary and informational texts accurately to support conclusions and inferences drawn from them.

Respond in writing to literature and informational text, including stories, dramas, poetry, and cross-curricular texts, independently and with grade-level proficiency.

Write fluently and legibly in cursive, using correctly formed letters with appropriate spacing and placing text elements correctly on the page.

Write personal or fictional narratives incorporating literary elements (characters, plot, setting, conflict), dialogue, strong voice, and clear event sequences.

Write informative or explanatory texts using multiple sources to examine a topic, conveying ideas and information clearly and incorporating a strong organizational structure, relevant details, and elaboration.

Write an argument to persuade the reader to take an action or adopt a position, stating a claim, supporting the claim with relevant evidence from sources, using connectives to link ideas, and presenting a strong conclusion.

Write about research findings independently over short and/or extended periods of time.

Gather information on a topic or question, and share the results through various modes of writing, including projects and presentations.

Locate information in print and digital sources.

Summarize, quote, and paraphrase information in notes and finished work, providing a list of sources.

Integrate information from several texts on the same topic into presentations of research.

Demonstrate command of the conventions of standard English grammar and usage in writing.

Evaluate the usage of pronouns for the proper case.

Identify inappropriate shifts in pronoun number and person.

Use varied pronouns and their antecedents correctly in composing and revising writing.

Use subject-verb agreement correctly when composing and revising writing.

Recognize and correct inappropriate shifts in verb tense, including subject-verb agreement.

Use perfect verb tenses to compose and revise writing.

Use correlative conjunctions correctly when composing and revising writing.

Use commas to separate items in a series, separate introductory elements from the rest of a sentence, set off tag questions, and indicate direct address.

Write using grade-appropriate general academic and domain-specific words and phrases accurately, including those that signal contrasting ideas, additional information, and other logical relationships.

Utilize active listening skills during discussion and conversation in pairs, small groups, or whole-class settings, following agreed-upon rules for participation.

Use context clues to determine meanings of unfamiliar spoken or written words.

Use digital and electronic tools appropriately, safely, and ethically when researching and writing, both individually and collaboratively.

Utilize a writing process to plan, draft, revise, edit, and publish writings in various genres.

Assess the formality of occasions in order to speak or write using appropriate language and tone.

Identify and explain an author's rhetorical choices, including point of view, purpose, anecdotes, and figurative, connotative, and technical word meanings, to develop central and supporting ideas.

Make inferences and draw logical conclusions from the content and structures of informational texts, including comparison and contrast, problem and solution, claims and evidence, cause and effect, description, and sequencing.

Explain how authors use setting, plot, characters, theme, conflict, dialogue, and point of view to contribute to the meaning and purpose of prose and poetry, using textual evidence from the writing.

Describe the use of literary devices in prose and poetry, including simile, metaphor, personification, onomatopoeia, hyperbole, tone, imagery, irony, symbolism, and mood, and indicate how they support interpretations of the text.

Evaluate the development of central and supporting ideas in recorded or live presentations by examining the speaker's rhetorical choices regarding point of view, purpose, anecdotes, and figurative, connotative, and technical word meanings.

Support interpretations of recorded or live presentations by examining the speaker's use of hyperbole, tone, symbolism, imagery, mood, irony, and onomatopoeia.

Produce clear, coherent narrative, argument, and informative/explanatory writing in which the development, organization, style, and tone are relevant to task, purpose, and audience, using an appropriate command of language.

Write narratives incorporating key literary elements, including characters, plot, setting, point of view, resolution of a conflict, dialogue, and sensory details.

Write informative or explanatory texts with an organized structure and a formal style, incorporating a focused point of view, a clear purpose, credible evidence, and technical word meanings.

Write an argument to convince the reader to take an action or adopt a position, stating a claim and supporting the claim with relevant, well-organized evidence from credible sources.

Participate in collaborative discussions using information from a source.

Participate in collaborative discussions about literary devices and elements found in prose and poetry.

Determine subject, occasion, audience, purpose, tone, and credibility of digital sources.

Utilize written, visual, digital, and interactive texts to generate and answer literal, interpretive, and applied questions.

Interpret language to determine subject, occasion, audience, purpose, and credibility of digital sources, with guidance and support.

Create and edit digital products that are appropriate in subject and purpose for a particular audience or occasion.

Enhance oral presentations by introducing ideas in digital formats with specific attention to subject, occasion, audience, and purpose.

Identify the conventions of standard English grammar and usage in published texts.

Identify subject-verb agreement when interrupted by a prepositional phrase, with inverted word order, and with indefinite pronouns as subjects.

Evaluate pronoun usage for number and case.

Identify common errors in pronoun usage.

Identify the conventions of standard English capitalization, punctuation, and spelling in published texts.

Identify commas, parentheses, and dashes that are used to set off nonrestrictive or parenthetical elements in texts from various genres.

Assess a speaker's organizational choices to determine point of view, purpose, and effectiveness.

Identify a speaker's correct usage of language, including subject-verb agreement and pronouns.

Demonstrate command of standard English grammar, usage, and mechanics when writing.

Revise writing for correct mechanics with a focus on commas, apostrophes, quotation marks, colons, and semicolons.

Compose and revise writing by using various pronouns and their antecedents correctly.

Choose language that maintains consistency in style and tone in a variety of formal and/or informal settings.

Summarize ethical guidelines and explain how they govern the process of finding and recording information from primary, secondary, and digital sources, with guidance and support.

Assess the relevance, reliability, and validity of information from printed and/or digital texts.

Use an audio or audio-visual source of information to obtain the answer to a question.

Write about research findings independently over short and/or extended periods of time.

Quote, paraphrase, and summarize information from sources and present findings, following an appropriate citation style, with guidance and support.

Utilize research findings to communicate relevant details, opinions, and ideas about a topic or text in oral presentations.

Answer questions in discussions about their research findings.

Discover word meanings by analyzing word parts, examining connotation and denotation, or using print or digital reference tools.

Discover word meanings through active listening in various contexts.

Use academic vocabulary in writing to communicate effectively.

Use vocabulary to create specific reactions or effects when speaking in various classroom and digital situations.

Evaluate the contributions of informational text elements, including categories, point of view, purpose, and figurative, connotative, and technical word meanings, to develop central and supporting ideas.

Evaluate how effectively an author uses structures of informational texts, including comparison and contrast, problem and solution, cause and effect, and substantiated or unsubstantiated claims and evidence, to achieve a purpose.

Explain how the author's choice of setting, plot, characters, theme, conflict, dialogue, and point of view contribute to and/or enhance the meaning and purpose of prose and poetry, using textual evidence from the writing.

Evaluate literary devices to support interpretations of literary texts using textual evidence, including simile, metaphor, personification, onomatopoeia, hyperbole, imagery, tone, symbolism, irony, and mood.

Evaluate rhetorical strategies used to develop central and supporting ideas in recorded or live presentations, including point of view, purpose, comparison, categories, and word meanings (figurative, connotative, and technical).

Evaluate the speaker's use of hyperbole, tone, symbolism, imagery, mood, irony, and onomatopoeia in a live or recorded presentation.

Produce clear, coherent narrative, argument, and informative/explanatory writing in which the development, organization, style, and tone are relevant to task, purpose, and audience, using an appropriate command of language.

Write narratives to convey a series of events incorporating key literary elements, establishing a clear purpose, using narrative techniques (dialogue, pacing, description, and reflection), and sequencing events coherently (chronological and/or flashback).

Write informative or explanatory texts with an organized structure and a formal style to examine ideas or processes effectively while developing the topic and utilizing appropriate transitions, precise vocabulary, and credible information or data when relevant.

Write an argument to defend a position by introducing and supporting claim(s), acknowledging alternate or opposing claims, and presenting reasons and relevant text evidence from accurate and credible sources.

Participate in collaborative discussions about arguments by evaluating claims, findings, and evidence from a source.

Participate in collaborative discussions about prose and poetry by evaluating the use of literary devices and elements.

Assess subject, occasion, audience, purpose, tone, and credibility of various digital sources.

Compare and contrast the effectiveness of techniques used in a variety of digital sources to generate and answer literal, interpretive, and applied questions and create new understandings.

Determine the intended purposes of techniques used for rhetorical effect in multiple digital sources.

Interpret language through active listening to determine subject, occasion, audience, purpose, tone, and credibility of digital sources.

Create and edit digital products that are appropriate in subject, occasion, audience, purpose, and tone.

Utilize digital tools and/or products to enhance meaning.

Convey ideas in an appropriate digital format with specific attention to subject, occasion, audience, purpose, and tone.

Identify the conventions of standard English grammar and usage in writing.

Identify subject-verb agreement with compound subjects joined by correlative and coordinating conjunctions and with collective nouns when verb form depends on the rest of the sentence.

Identify the usage of simple, compound, complex, and compound-complex statements and questions to signal differing relationships among ideas in a text.

Evaluate the functions of phrases and clauses in general and their function in specific sentences.

Identify the conventions of standard English capitalization, punctuation, and spelling in a variety of texts.

Correct improper usage of commas, apostrophes, quotation marks, colons, and semicolons through peer editing.

Evaluate a speaker's organizational choices to determine point of view, purpose, and effectiveness.

Identify a speaker's formality of language in order to comprehend, interpret, and respond appropriately.

Create written work using standard English grammar, usage, and mechanics.

Revise their own writing using correct mechanics with a focus on commas, apostrophes, quotation marks, colons, and semicolons.

Construct simple, compound, complex, and compound-complex sentences to represent relationships among ideas.

Choose language that expresses ideas precisely and concisely.

Implement ethical guidelines while finding and recording information from a variety of primary, secondary, and digital sources.

Determine the relevance, reliability, and validity of information from nonfiction and fictional printed and/or digital texts.

Use active listening to acquire information and assess its relevance and credibility.

Produce research writings over extended periods with time for research, reflection, and revision and within shorter time frames, with minimal guidance.

Quote, paraphrase, summarize, and present findings, following an appropriate citation style and avoiding plagiarism.

Incorporate research into oral presentations, summarizing and supporting opinions and ideas with relevant details.

Collect information through the research process to answer follow-up questions and participate in discussions about their research findings.

Determine word meaning through the use of word parts, context clues, connotation and denotation, or print or digital reference tools.

Read and evaluate texts from science, social studies, and other academic disciplines to determine how those disciplines treat domain-specific vocabulary and content organization.

Infer word meaning through active listening in various contexts for purposeful, effective communication.

Apply vocabulary in writing to convey and enhance meaning.

Select and utilize effective words and phrases that are suitable for purpose and audience to communicate clearly in a variety of situations.

Analyze how informational and graphic text elements, including allusions, point of view, purpose, comparisons, categories, and figurative, connotative, and technical word meanings, develop central and supporting ideas.

Make complex inferences from the structure and content of a text, including comparison and contrast, problem and solution, cause and effect, and substantiated and unsubstantiated claims and evidence, to draw logical conclusions about the author's perspective.

Analyze how authors use key literary elements, including setting, plot, theme, characters, internal and external conflict, dialogue, and point of view, to contribute to the meaning and purpose of a text, using text evidence as support.

Analyze the use of literary devices, including simile, metaphor, personification, onomatopoeia, hyperbole, imagery, tone, symbolism, irony, mood, and allusion, to support interpretations of literary texts, using textual evidence to support the analysis.

Compare and contrast the perspectives in a variety of fiction, nonfiction, informational, digital, and multimodal texts produced from diverse historical, cultural, and global viewpoints.

Evaluate the development of central and supporting ideas in recorded or live presentations by examining the speaker's rhetorical strategies and choices regarding point of view, purpose, comparisons, analogies, categories, allusions, and figurative, connotative, and technical word meanings.

Critique the speaker's use of hyperbole, tone, symbolism, imagery, mood, irony, and onomatopoeia in a live or recorded presentation.

Produce clear, coherent narrative, argument, and informative/explanatory writing in which the development, organization, style, and tone are relevant to task, purpose, and audience, using an appropriate command of language.

Write narratives that establish a clear purpose, use narrative techniques, and sequence events coherently.

Write informative or explanatory texts to examine and convey complex ideas or processes effectively, by developing the topic with relevant information or data from credible sources and using appropriate transitions and precise vocabulary.

Write an argument to defend a position by introducing and supporting a claim, distinguishing the claim from opposing claims, presenting counterclaims and reasons, and citing accurate, relevant textual evidence from credible sources.

Participate in collaborative discussions about arguments by evaluating claims, findings, reasoning, relevance, and evidence from multiple sources.

Engage in coherent and collaborative discussions about prose and poetry by evaluating the use of literary devices and elements.

Analyze digital texts to determine subject, occasion, audience, purpose, tone, and credibility.

Interpret and evaluate language through active listening to determine subject, occasion, audience, purpose, tone, and credibility of digital sources.

Create and edit digital products that are appropriate in subject, occasion, audience, point of view, purpose, and tone.

Utilize digital tools and/or products to enhance meaning.

Deliver ideas in an appropriate digital format with specific attention to subject, occasion, audience, purpose, and tone.

Examine the use of conventions of standard English grammar and usage in writing.

Identify gerunds, participles, infinitives, and clauses.

Analyze the effects of active and passive voice and shifts in verb tense.

Explain how using simple, compound, complex, or compound-complex statements and questions signals differing relationships among ideas in a text.

Examine the use of conventions of standard English capitalization, punctuation, and spelling in a variety of texts.

Correct improper usage of commas, apostrophes, quotation marks, colons, semicolons, hyphens, and dashes through peer editing.

Analyze a speaker's formality of language in order to comprehend, interpret, and respond appropriately.

Evaluate a speaker's rhetorical and organizational choices in order to determine point of view, purpose, and effectiveness.

Produce writing that shows a command of standard English grammar, usage, and mechanics.

Construct verbals (gerunds, participles, and infinitives) in pieces of writing, including isolated sentences, paragraphs, and essays.

Compose writing using verbs in active and passive voice to establish mood.

Revise their own writing for correct mechanics with a focus on commas, apostrophes, quotation marks, colons, and semicolons.

Construct simple, compound, complex, and compound-complex sentences to signal differing relationships among ideas.

Apply ethical guidelines while finding and recording information from a variety of primary, secondary, and digital sources.

Determine the relevance, reliability, and validity of information from nonfiction and fictional printed and/or digital texts.

Assess the relevance and credibility of orally-presented information to answer a question, solve a problem, or defend a position.

Produce research writings independently over extended periods of time which encompass research, reflection, and revision and over shorter time frames.

Quote, paraphrase, summarize, and present findings, following a recognized citation style and avoiding plagiarism to demonstrate responsible and ethical research practices.

Synthesize and present information during the research process to answer follow-up questions and participate in both informal and formal discussions about research findings with grade-appropriate command of language.

Analyze word meanings through the use of word parts, context clues, connotation and denotation, and print or digital reference tools.

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines to determine how those disciplines treat domain-specific vocabulary and content organization.

Analyze and connect word meanings through active listening in various contexts for purposeful, effective communication .

Integrate effective vocabulary into writing to create specific effects and communicate purposefully.

Utilize appropriate vocabulary in various classroom, digital, and real-world situations to facilitate effective communication .

Read a variety of print and nonprint documents to acquire new information and respond to the needs and demands of society and the workplace.

Read and comprehend a variety of literary texts to develop a literal and figurative understanding as appropriate to the type of text, purpose, and situation.

Utilize active listening skills in formal and informal conversations, following predetermined norms.

Use digital and electronic tools appropriately, safely, and ethically.

Utilize a writing process which includes planning, revising, editing/peer-editing, and rewriting to create a focused, organized, and coherent piece of writing for a specific purpose and audience.

Employ conventions of grammar, mechanics, and usage in order to communicate effectively with a target audience.

Use context clues to determine meanings of unfamiliar spoken or written words.

Read, analyze, and evaluate complex literary and informational texts written from various cultural perspectives, with an emphasis on works originating outside the United States and the British Isles through 1599.

Analyze information from graphic texts to draw conclusions, defend claims, and make decisions.

Analyze how an author's cultural perspective influences style, language, and themes.

Analyze how authors use characterization, connotation, denotation, figurative language, literary elements, and point of view to create and convey meaning in a variety of texts.

Analyze the impact of context and organizational structures on theme, tone, and the meaning of the work as a whole.

Compare and/or contrast the perspectives in a variety of fiction, nonfiction, informational, digital, and multimodal texts produced from diverse historical, cultural, and global points of view, not limited to the grade-level literary focus.

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines to determine how those disciplines treat domain-specific vocabulary and content organization.

Through active listening, evaluate tone, organization, content, and non-verbal cues to determine the purpose and credibility of a speaker.

Compose both short and extended narrative, informative/explanatory, and argumentative writings that are clear and coherent, use an appropriate command of language, and demonstrate development, organization, style, and tone that are relevant to task, purpose, and audience.

Write a memoir, narrative essay, or personal or fictional narrative to convey a series of events, establishing a clear purpose and using narrative techniques.

Write explanations and expositions that incorporate evidence, using transitions and techniques that objectively introduce and develop topics.

Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning, relevant and sufficient evidence, transitions, and a concluding statement or section that follows from the information presented.

Present research findings to a peer audience, either formally or informally, conveying credible, accurate information from multiple sources, including diverse media.

Participate in collaborative discussions involving multiple perspectives, responding and contributing with relevant evidence and commentary.

Interpret digital texts to determine their subject, occasion, audience, purpose, tone, and credibility.

Interpret a digital audio source to determine its subject, occasion, audience, purpose, tone, and credibility.

Create and edit digital texts that are suitable in purpose and tone for their intended audience and occasion.

Create and deliver a collaborative presentation that is suitable in purpose and tone for its intended audience and occasion.

Interpret how an author's grammar and rhetorical style contribute to the meaning in both fiction, including poetry and prose, and nonfiction, including historical, business, informational, and workplace documents.

Classify formality of language in order to comprehend, interpret, and respond appropriately.

Analyze a speaker's rhetorical, aesthetic, and organizational choices in order to determine point of view and purpose.

Apply conventions of language to communicate effectively with a target audience, including punctuation; capitalization; spelling; verb, pronoun, and modifier usage; and effective sentence structure.

Exhibit stylistic consistency in writing.

Adapt speech to purpose and audience in a variety of contexts and tasks, demonstrating command of formal English conventions as indicated or appropriate.

Locate and determine the usefulness of relevant and credible information to answer a question, solve a problem, or defend a position.

Use a variety of search tools and research strategies.

Use audio sources to obtain useful and credible information to answer a question, solve a problem, or defend a position.

Utilize responsible and ethical research practices to write clear, coherent products with a command of language suitable for a particular target audience and purpose.

Integrate information from at least two sources into writing by quoting, paraphrasing, or summarizing and cite sources, following the rules of a particular style guide.

Compose clear, coherent writing that incorporates information from at least one scholarly source and demonstrates a clear position on a topic, answers a research question, or presents a solution to a problem.

Utilize responsible and ethical research practices to present clear, coherent products with a command of language suitable for a particular target audience and purpose.

Read, analyze, and evaluate complex literary and informational texts written from various cultural perspectives, with an emphasis on works originating outside the United States and the British Isles from 1600 to the present.

Analyze and evaluate information from graphic texts to draw conclusions, defend claims, and make decisions.

Analyze how an author's cultural perspective influences style, language, and themes.

Interpret an author's use of characterization, connotation, denotation, figurative language, literary elements, and point of view to create and convey meaning in a variety of texts.

Analyze context and organizational structures to determine theme, tone, and the meaning of the work as a whole.

Compare and/or contrast the perspectives in a variety of fiction, nonfiction, informational, digital, and multimodal texts produced from diverse historical, cultural, and global viewpoints, not limited to the grade-level literary focus.

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines to determine how those disciplines treat domain-specific vocabulary and content organization.

Through active listening, evaluate tone, organization, content, and non-verbal cues to determine the purpose and credibility of a speaker.

Compose both short and extended narrative, informative/explanatory, and argumentative writings that are clear and coherent, use an appropriate command of language, and demonstrate development, organization, style, and tone that are relevant to task, purpose, and audience.

Write a memoir, narrative essay, or personal or fictional narrative to convey a series of events, establishing a clear purpose, using narrative techniques, and sequencing events coherently.

Write explanations and expositions that incorporate relevant evidence, using effective transitions that objectively introduce and develop topics.

Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning, relevant and sufficient evidence, appropriate transitions, and a concluding section that follows from and supports the information presented.

Present research findings to peers, either formally or informally, integrating credible, accurate information from multiple sources, including diverse media.

Participate in collaborative discussions involving multiple perspectives, responding and contributing with relevant evidence and commentary.

Interpret digital texts to determine subject, occasion, audience, purpose, tone, and credibility.

Interpret a digital audio source to determine subject, occasion, audience, purpose, tone, and credibility.

Create and edit collaborative digital texts that are suitable in purpose and tone for their intended audience and occasion.

Create and deliver an individual or collaborative presentation that is suitable in purpose and tone for its intended audience and occasion.

Interpret how an author's grammar and rhetorical style contribute to the meaning in both fiction, including poetry and prose, and nonfiction, including historical, business, informational, and workplace documents.

Classify formality of language in order to comprehend, interpret, and respond appropriately.

Analyze a speaker's rhetorical, aesthetic, and organizational choices in order to determine point of view and purpose.

Apply conventions of language to communicate effectively with a target audience, including punctuation; capitalization; spelling; verb, pronoun, and modifier usage; and effective sentence structure.

Exhibit stylistic consistency in writing.

Adapt speech to purpose and audience in a variety of contexts and tasks, demonstrating command of formal English conventions when indicated or appropriate.

Locate and determine the usefulness of relevant and credible information to answer a question, solve a problem, or defend a position.

Use a variety of search tools and research strategies to locate credible sources.

Use audio sources to obtain useful and credible information to answer a question, solve a problem, or defend a position.

Utilize responsible and ethical research practices to write clear, coherent products with a command of language suitable for a particular target audience and purpose.

Integrate information from at least two kinds of sources into writing, using quotations, paraphrases, and summaries that consistently follow a particular style guide.

Compose clear, coherent writing that incorporates information from at least one scholarly and at least one non-scholarly source and demonstrates a clear position on a topic, answers a research question, or presents a solution to a problem.

Utilize responsible and ethical research practices to present clear, coherent products with a command of language suitable for a target audience and purpose.

Read, analyze, and evaluate complex literary and informational texts written from various points of view and cultural perspectives, with an emphasis on works of American literature.

Synthesize information from two or more graphic texts to draw conclusions, defend claims, and make decisions.

Analyze how an author explicitly exhibits his/her cultural perspective in developing style and meaning.

Analyze how an author uses characterization, figurative language, literary elements, and point of view to create and convey meaning.

Evaluate structural and organizational details in literary, nonfiction/informational, digital, and multimodal texts to determine how genre supports the author's purpose.

Analyze a text's explicit and implicit meanings to make inferences about its theme and determine the author's purpose.

Compare and/or contrast the perspectives in a variety of fiction, nonfiction, informational, digital, and multimodal texts produced from diverse historical, cultural, and global viewpoints, not limited to the grade level literary focus.

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

Follow instructions in technical materials to complete a specific task.

Through active listening, evaluate tone, organization, content, and non-verbal cues to determine the purpose and credibility of a speaker.

Compose and edit both short and extended products in which the development and organization are relevant and suitable to task, purpose, and audience, using an appropriate command of language.

Incorporate narrative techniques in other modes of writing as appropriate.

Write explanations and expositions that examine and convey complex ideas or processes effectively, develop the topic utilizing and citing credible sources of information or data when relevant, use intentional transitions, choose precise vocabulary, and maintain an organized structure.

Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning supported by relevant and sufficient evidence, making rhetorical choices that convey a specific tone or style, including intentional transitions, and providing a logical conclusion that captures the larger implications of the topic or text.

Collaborate on writing tasks in diverse groups, making necessary compromises to accomplish a goal, sharing responsibility for collaborative work, and showing respect for the individual contributions of each group member.

Synthesize multiple sources of information (including diverse media), evaluate the credibility and accuracy of each source, and share information orally.

Participate in collaborative discussions involving multiple cultural and literary perspectives, responding to, contributing to, building upon, and questioning the ideas of others with relevant, appropriate evidence and commentary.

Analyze digital texts and evaluate their effectiveness in terms of subject, occasion, audience, purpose, tone, and credibility.

Analyze elements of audible communications and evaluate their effectiveness in terms of subject, occasion, audience, purpose, tone, and credibility of digital sources.

Use images, sound, animation, and other modes of expression to create or enhance individual or collaborative digital and multimodal texts that are suitable in purpose and tone for their intended audience and occasion.

Create and deliver an oral presentation, created collaboratively from individual contributions, that is suitable in purpose and tone for its intended audience and occasion.

Interpret how an author's grammar and rhetorical style contribute to the meaning in both fiction, including poetry and prose, and nonfiction, including historical, business, informational, and workplace documents .

Analyze the formality of language in a variety of audible sources in order to comprehend, interpret, and respond appropriately.

Analyze a speaker's rhetorical, aesthetic, and organizational choices in order to determine point of view, purpose, and effectiveness.

Apply conventions of standard English grammar, mechanics, and usage, including appropriate formality of language, to communicate effectively with a target audience.

Exhibit stylistic complexity and sophistication in writing.

Deliver a speech suitable for an authentic audience for a specific purpose, demonstrating command of formal English when indicated or appropriate.

Evaluate the credibility of sources in terms of authority, relevance, accuracy, and purpose.

Assess the usefulness of written information to answer a research question, solve a problem, or take a position.

Use a variety of search tools and research strategies to locate credible sources.

Locate and acquire audible information to answer a question, solve a problem, or defend a position, utilizing active listening to assess its usefulness, relevance, and credibility.

Synthesize research results, using responsible, ethical practices to gather information, and write clear, coherent products demonstrating command of language that is suitable for the target audience and purpose.

Integrate ethically-acquired information from at least three sources of varying types, including at least one visual or statistical source, into a research product, using proper quoting, paraphrasing, summarizing, and citation practices that consistently follow rules of a particular style guide.

Compose clear, coherent writing that incorporates information from a variety of scholarly and non-scholarly sources and demonstrates a clear position on a topic, answers a research question, or presents a solution to a problem.

Synthesize research using responsible and ethical practices to create and orally present clear, coherent products demonstrating command of language that is suitable for the target audience and purpose.

Read, analyze, and evaluate complex literary and historical texts written from particular points of view or cultural experiences, with an emphasis on works of literature from the British Isles.

Read, analyze, and evaluate a play by William Shakespeare, including an examination of its contributions to the English language and its influences on other works of literature.

Synthesize information from two or more graphic texts to draw conclusions, defend claims, and make decisions.

Evaluate how an author explicitly exhibits his/her cultural perspective in developing style and meaning.

Evaluate an author's use of characterization, figurative language, literary elements, and point of view to create and convey meaning.

Evaluate structural and organizational details in texts to determine the author's purpose, including cases in which the meaning is ironic or satirical.

Analyze a text's explicit and implicit meanings to make inferences about its theme and determine the author's purpose.

Compare and/or contrast the perspectives in a variety of fiction, nonfiction, informational, digital, and multimodal texts produced from diverse historical, cultural, and global viewpoints, not limited to the grade level literary focus.

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

Follow instructions in technical materials to complete a specific task.

Determine through active listening the purpose, credibility, and effectiveness of a speaker or multiple sources of information by evaluating tone, organization, content, and verbal and non-verbal cues and identifying any fallacious reasoning or distorted evidence.

Compose, edit, and revise both short and extended products in which the development, organization, and style are relevant and suitable to task, purpose, and audience, using an appropriate command of language.

Incorporate narrative techniques into other modes of writing as appropriate.

Write explanations and expositions that examine and convey complex ideas or processes effectively, develop the topic utilizing and citing credible sources of information or data when relevant, use intentional transitions, choose precise vocabulary, and maintain an organized structure and style.

Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence, making intentional rhetorical choices to convey a specific tone or style, including intentional transitions, and providing a logical conclusion that captures the larger implications of the topic or text.

Within diverse and collaborative writing groups, effectively and respectfully demonstrate a willingness to make necessary compromises to accomplish a goal, share responsibility for collaborative work, and consider contributions made by each group member.

Evaluate the credibility and accuracy of sources from diverse media and/or formats and then use multiple suitable sources of information to develop an idea or further a position.

Actively engage in collaborative discussions about topics and texts, expressing their own ideas by respectfully contributing to, building upon, and questioning the ideas of others in pairs, diverse groups, and whole class settings.

Analyze digital texts and evaluate their effectiveness in terms of subject, occasion, audience, purpose, tone, and credibility.

Analyze elements of audible communications and evaluate their effectiveness in terms of subject, occasion, audience, purpose, tone, and credibility of digital sources.

Use images, sound, animation, and other modes of expression to create or enhance individual or collaborative digital and multimodal texts that are suitable in purpose and tone for their intended audience and occasion.

Create and deliver an oral presentation, created collaboratively from individual contributions, that is suitable in purpose and tone for its intended audience and occasion.

Interpret how an author's grammar and rhetorical style contribute to the meaning in both fiction, including poetry and prose, and nonfiction, including historical, business, informational, and workplace documents .

Evaluate the formality of language in a variety of audible sources to comprehend, interpret, and respond appropriately.

Analyze a speaker's rhetorical, aesthetic, and organizational choices in order to determine point of view, purpose, and effectiveness.

Apply conventions of standard English grammar, mechanics, and usage, including appropriate formality of language, to communicate effectively with a target audience.

Exhibit stylistic complexity, sophistication, and consistency in writing.

Deliver a speech suitable for a professional audience of college and/or workforce stakeholders for a specific purpose, demonstrating command of formal English.

Evaluate the credibility of sources in terms of authority, relevance, accuracy, and purpose.

Assess the usefulness of written information to answer a research question, solve a problem, or take a position.

Use a variety of search tools and research strategies to locate and acquire credible, relevant, and useful information.

Locate and acquire audible information to answer a question, solve a problem, or defend a position, utilizing active listening to assess its usefulness, relevance, and credibility.

Synthesize research results, using responsible, ethical practices to gather information, and write clear, coherent products demonstrating command of language that is suitable for the target audience and purpose.

Integrate ethically-acquired information from at least three sources of varying types, including at least one visual or statistical source, into a research product, using proper quoting, paraphrasing, summarizing, and citation practices that consistently follow rules of a particular style guide.

Compose clear, coherent writing that incorporates information from a variety of scholarly and non-scholarly sources and demonstrates a clear position on a topic, answers a research question, or presents a solution to a problem.

Synthesize research using responsible and ethical practices to create and orally present clear, coherent products demonstrating command of language that is suitable for the target audience and purpose.

Plan and carry out investigations to determine the effects of forces of different strengths and directions on the motion of an object, including speed, direction, and distance traveled.

Analyze data from investigations to determine whether a design solution provides sufficient force to change the speed or direction of an object.

Use data from observations to distinguish characteristics of living and nonliving things.

Use observations to determine patterns of what plants and animals (including humans) need to survive, including light, water, and nutrients.

Gather information from observations and media to explain how plants and animals can provide for their needs by changing their environment.

Use models of natural habitats to represent the interdependence among plants and animals native to their community.

Design, construct, and test a device to reduce the effects of sunlight.

Observe, record, and communicate local weather patterns over a period of time.

Obtain, evaluate, and communicate information about using weather forecasts to make plans and prepare for severe weather.

Identify a problem and design possible solutions that lessen the human impact on the local environment.

Carry out investigations to provide evidence that the vibrations of matter can make sound and sound can make matter vibrate.

Plan and carry out investigations to determine how light is affected when it interacts with various types of materials.

Use information from observations to explain how various external features help living things survive, grow, and meet their needs.

Obtain information from text and other media to provide evidence that parents and their offspring engage in patterns of behavior that help the offspring survive.

Make observations to identify the similarities and differences between offspring and their parents.

Observe, describe, and predict patterns of the sun, moon, and stars as they appear in the sky.

Use observations of seasonal sunrise and sunset patterns to describe the relationship between the number of hours of daylight and the time of year.

Plan and carry out investigations to compare, contrast, and classify various solid and liquid materials according to physical properties, including color and texture.

Conduct investigations to determine suitable uses of natural and manufactured materials based on their observable properties, including strength, flexibility, hardness, absorbency, and texture.

Demonstrate and explain how structures made from a small set of pieces can be disassembled and then reassembled as new and different structures.

Provide evidence that some changes in matter caused by heating or cooling can be reversed and some changes are irreversible.

Plan and carry out an investigation, using one variable at a time, to determine how each variable affects plant growth.

Design and construct models to simulate how animals disperse seeds or pollinate plants.

Obtain information to explain that there are many different kinds of living things that exist in habitats on land and in water.

Use models to distinguish between the shapes and kinds of land and water on Earth.

Obtain information to identify where water is found on Earth and determine whether it is a solid or a liquid.

Evaluate multiple solutions designed to slow or prevent wind or water from changing the shape of Earth’s surface.

Conduct investigations to explain the effects of balanced and unbalanced forces exerted on an object, varying the size, number, and direction of the forces.

Observe and measure an object’s motion to provide evidence that a pattern of motion can be used to predict future motion.

Conduct investigations to determine cause and effect relationships between objects not in contact with one another, including magnetic and electrostatic forces.

Apply scientific ideas about magnetic interactions to solve a problem using the engineering design process.

Develop and use models to compare the diverse life cycles of organisms other than humans, including birth, growth, reproduction, and death.

Use data to provide evidence that plants and animals have observable traits inherited from parents and that variations of these traits exist in groups of similar organisms.

Use evidence to support a claim that traits can be influenced by the environment.

Make a claim from evidence that an organism's likelihood of survival depends upon access to sufficient resources in its habitat, including sunlight, air, water, food, and shelter.

Construct explanations of how forming groups helps some organisms survive.

Obtain and communicate information regarding the impact of existing solutions on plant and animal populations when environmental changes occur.

Represent data in tables or graphical displays to reveal typical weather patterns during a particular season.

Obtain and communicate information on the effectiveness of existing solutions designed to reduce the impact of weather-related hazards.

Plan and carry out investigations to answer questions regarding changes in energy when objects collide, and predict reasonable outcomes based on observed patterns.

Plan and carry out investigations to provide evidence that energy is transferred by sound, light, heat, and electric currents.

Construct an explanation using evidence to support the claim that heat can be produced in many ways.

Construct an explanation with evidence supporting the claim that different objects can absorb, reflect, and/or conduct energy.

Design, construct, and test a device that changes energy from one form to another.

Develop and use models to describe amplitude and wavelength patterns and how waves can cause objects to move.

Construct an explanation of how light, sound, and digitized information are transferred by waves.

Make a claim, using evidence, that the functions of both internal and external structures of plants and animals (including humans) support growth, survival, and behavior.

Carry out investigations to support a claim that different animals receive information through their senses, process that information, and respond in various ways.

Develop and use a model to describe how water moves through Earth’s systems by the processes of evaporation, condensation, and precipitation.

Construct explanations of Earth's changes over time through slow and rapid processes, citing evidence found in rock formations and fossils in rock layers.

Plan and carry out investigations to provide evidence of the effects of weathering or the rate of erosion by water, ice, wind, and vegetation, investigating a single form of weathering or erosion at a time.

Analyze and interpret data from maps to describe patterns of Earth’s features on land and in the ocean.

Gather information to describe how the use of energy derived from renewable and nonrenewable resources affects the environment.

Design, test, and evaluate a solution that will protect humans from the effects of natural Earth processes.

Plan and carry out investigations to provide evidence that matter is made of particles too small to be seen.

Analyze data collected through observations and measurements to identify materials based on their properties, including color, hardness, and reflectivity.

Conduct investigations to provide evidence that the total weight of matter is conserved during phase changes when substances are heated, cooled, or mixed.

Analyze data from tests to determine whether a new substance is formed after two or more substances are combined.

Design and conduct a test to modify the speed of an object falling due to gravity.

Support an argument from evidence that plants primarily use air and water to process matter needed for growth.

Use evidence to explain that energy from the sun is present in animals’ food and is used for body repair, growth, motion, and maintenance of body warmth.

Create and use a model to explain the transfer of matter and energy between the environment and organisms within it.

Obtain and communicate information to explain why the sun appears to be larger and brighter than other stars.

Analyze data that reveal patterns of daily changes in length and direction of shadows, day and night, phases of the moon, and seasonal appearance of some stars in the night sky.

Use a model to represent how any two of Earth's systems (atmosphere, biosphere, geosphere, and hydrosphere) interact and support life.

Construct a model to represent the distribution of freshwater and saltwater on Earth.

Obtain and evaluate information to communicate how science-based solutions are being used to protect Earth’s natural resources and its environment.

Design, test, and revise solutions to clean a polluted environment.

Manipulate models to demonstrate the patterns of motion of the sun, Earth, and moon.

Construct an evidence-based explanation of how the relative positions of the sun and Earth result in observable phenomena, including day and night cycles, length of year, and seasons.

Construct an evidence-based explanation of how the relative positions of the sun, moon, and Earth result in observable phenomena, including lunar cycles, eclipses, and tidal cycles.

Evaluate information to compare and contrast past and current views about the structure of the universe and show how these views have changed over time.

Construct an evidence-based explanation of the role of gravity on the movement of natural and manmade objects within galaxies and the solar system.

Analyze and use data to determine scale properties and characteristics of objects in the solar system including sizes, distances, orbital periods, basic composition, and ability to support life.

Obtain, evaluate, and communicate evidence that explains how constructive and destructive processes shape Earth’s surface.

Develop and use models to demonstrate the processes that form rocks and cycle Earth’s materials.

Construct an evidence-based explanation of how rocks are classified as metamorphic, igneous, or sedimentary based on their characteristics and the process of the rock cycle.

Develop and use models to demonstrate types of weathering, effects of agents of erosion and transportation, and the formation of environments of deposition.

Use research-based evidence to propose a scientific explanation of how the distribution of Earth’s resources, including minerals, fossil fuels, and groundwater, results from ongoing geoscience processes.

Construct an evidence-based explanation of how tectonic plate movement impacts Earth’s surface over geological time.

Construct an evidence-based explanation of how Earth's internal energy flows between its surface and its interior.

Construct a scientific explanation of how the movement of lithospheric plates can cause major geologic events and form Earth’s surface features, including convergent, divergent, and transform boundaries; earthquakes; and volcanoes.

Provide evidence of past plate movements, using data regarding the distribution of fossils, rocks, continental shapes, and seafloor structures.

Analyze data from rock strata and the fossil record to construct a chronology of occurrences in Earth’s history.

Construct an evidence-based explanation of how the sun’s energy drives the motion and cycling of water through the hydrosphere.

Plan and carry out an investigation to determine the differences in rates of energy transfer from the sun to air, to land, and to water via conduction, convection, and radiation.

Develop and use a model that illustrates how differences in heat and pressure affect density and the relationship between density and convection.

Use data analysis to monitor and predict weather changes and the impact of weather events, including severe weather.

Obtain, evaluate, and communicate data that describes characteristics of air masses, including temperature, pressure, and humidity.

Construct an explanation of how air pressure, weather fronts, and air masses are related to weather events.

Design solutions to mitigate the impact of severe weather.

Use observations and data from investigations to demonstrate how the sun, air, land, and water affect Earth’s climate.

Develop models demonstrating how unequal heating and the rotation of the Earth cause local and global wind systems and oceanic currents.

Construct explanations of how the tilt and curvature of the Earth cause unequal heating of its surface, resulting in regional climates based on patterns of latitude.

Construct an explanation of how altitude, geothermal activity, and oceanic distribution of heat produce typical regional climate patterns.

Obtain, evaluate, and communicate information concerning the relationships between human activities and natural processes and how those relationships affect Earth’s systems, including human population growth and its impact on the global environment over time.

Define problems and design solutions to monitor and mitigate human impact on the environment.

Develop and use a model to explain the functions of specific cell structures necessary for maintaining a stable environment, including the cell membrane, cell wall, chloroplasts, endoplasmic reticulum, golgi apparatus, mitochondria, nucleus, ribosomes, and vacuoles.

Engage in argument from evidence to support claims of cell theory.

Construct an explanation of how prokaryotic and eukaryotic cells differ in structure and function.

Plan and carry out an investigation to identify and explain features of a cell’s semi-permeable membrane which enable it to control what enters and exits the cell.

Construct an explanation of how photosynthesis and cellular respiration cycle matter and establish the flow of energy into and out of an organism.

Ask questions and construct an explanation of how anaerobic bacteria produce energy in environments with no oxygen.

Construct an explanation of how the process of mitosis maintains complex organisms and ensures new cells with identical genetic information.

Ask questions and communicate information regarding how errors in mitosis may affect cell division.

Obtain, evaluate, and communicate information explaining how cells, tissues, and organs of various systems of the human body work together for specific functions, including the circulatory, digestive, muscular, nervous, respiratory, and skeletal systems.

Construct an explanation of how the cycling of matter between abiotic and biotic parts of ecosystems demonstrates the flow of energy and the conservation of matter, including the carbon, nitrogen, and water cycles.

Analyze and interpret data to predict how environmental conditions, genetic factors, and resource availability will impact the growth of individual organisms and populations of organisms in an ecosystem.

Analyze and interpret data to explain how density-independent and density-dependent limiting factors in an ecosystem can lead to shifts in populations.

Design a solution to maintain biodiversity and ecosystem services in a given scenario.

Obtain, evaluate, and communicate information about characteristic animal behaviors and specialized plant structures and their effect on the probability of successful reproduction.

Develop and use models to demonstrate how genetic variations between parents and offspring result from differences in inherited genes located on chromosomes.

Develop and use models to explain how genes are expressed through the flow of genetic information from DNA to RNA to a functional protein.

Develop and use models to explain that meiosis results in new genetic combinations with increased variation.

Construct an explanation of the advantages and disadvantages of asexual and sexual reproduction.

Construct an explanation from evidence of how genetic variants may result in harmful, beneficial, or neutral effects on the structure and function of an organism.

Obtain, evaluate, and communicate information on the use of technologies that impact the inheritance and appearance of traits in organisms.

Analyze and interpret data from examination of fossils, relict species, and modern organisms to determine patterns of change in anatomical structures over time.

Obtain, evaluate, and communicate evidence comparing patterns in the embryological development of multiple species to identify relationships not evident in the fully formed adult anatomy.

Ask questions to clarify how natural selection over generations may lead to changes in the frequency of specific traits to enhance survival and reproduction of a population.

Plan and carry out investigations to support the claim that pure substances can be described and defined by their properties, including solubility, electrical conductivity, and density.

Develop and manipulate models to explain changes in particle motion, temperature, and state of a pure substance when thermal energy is added to or removed from a system.

Justify a claim, based on evidence from investigations, that pure substances differ from mixtures, including solutions.

Obtain and communicate information from the periodic table, including atomic number, number of electrons and neutrons, average atomic mass, groups, and periods, to illustrate the structure and composition of atoms of different elements.

Analyze and interpret data to differentiate among elements based on their properties and classify the elements as metals, nonmetals, or metalloids.

Obtain, evaluate, and communicate information from the periodic table to make predictions about the reactivity of the main group elements.

Use valence electron configuration to model ionic and covalent bonds.

Observe and analyze data regarding characteristic properties of substances before and after they are combined to determine whether a chemical reaction has occurred.

Analyze data from an investigation to determine whether thermal energy is released or absorbed in a chemical reaction.

Design and test a device that can release or absorb thermal energy by chemical reactions.

Engage in an argument from evidence to support the claim that matter is conserved in a chemical reaction.

Use a model to verify that atoms of reactants are conserved as products in a chemical reaction.

Use data from an investigation to identify factors that affect acceleration.

Develop and use models to illustrate how individual external forces affect the motion of objects.

Use models to demonstrate each of Newton’s laws of motion and explain the effect of net force on objects.

Use mathematical representations to explain how the sum of external forces on an object and the object’s mass affect its acceleration.

Use a model to identify factors affecting the strength of noncontact forces, including magnetic, gravitational, and electrical forces, and demonstrate that fields exist even though the objects are not in contact.

Design and construct an electromagnet and modify the design to change its strength.

Analyze graphical displays of data to describe the relationship of mass and velocity of an object to its kinetic energy (KE).

Use models to construct an explanation of how a system of objects may contain varying amounts of potential energy, including gravitational, elastic, and chemical.

Use models to construct an explanation of how energy is transformed but still conserved.

Develop and use a model to construct an explanation of how electrical energy is transferred and transformed.

Use models of mechanical and electromagnetic waves to qualitatively describe the relationships among wave properties, including amplitude, wavelength, and frequency.

Use models to compare and contrast light and sound wave behaviors, including reflection, refraction, diffraction, and speed, as waves propagate and interact with matter.

Construct an argument from evidence that digital and analog signals encode and transmit information differently.

Engage in evidence-based argument to relate a cell’s function to the structure, function, and diversity of its components.

Obtain and evaluate information to explain the role of DNA and RNA in transcription and translation leading to protein synthesis and cellular function.

Use a model to describe the structure and sequence of DNA, including nucleotide structure, base pairing, and the structure of the helix.

Obtain and evaluate information to explore additional functions and regulatory roles of RNA, DNA, and protein, including their roles in gene expression and cellular differentiation.

Obtain, evaluate, and communicate information regarding how DNA and genetic technology apply to daily life.

Develop and use models to explain how events during the cell cycle lead to the formation of new cells and repair of multicellular organisms, including cell growth, DNA replication, separation of chromosomes, and separation of cell contents.

Construct an explanation of the process of DNA replication during cellular division (S-phase).

Using observations of cell growth, construct an explanation of how the cell cycle leads to differentiation in tissue development.

Engage in argument from evidence to explain the regulation of cellular processes that maintain homeostasis, including active and passive transport.

Use models to illustrate how the structural characteristics of lipids and proteins in the cell membrane regulate cellular processes.

Construct an explanation of how the unique properties of water are vital to maintaining homeostasis in organisms.

Plan and carry out investigations and utilize results to explain the role and cycling of products and reactants involved in the cellular conversion of energy.

Construct an explanation of how the structural characteristics of carbohydrates and lipids store energy.

Use models of the reactants and products of photosynthesis to illustrate the conversion of light energy into stored chemical energy within cells.

Use models of the reactants and products of cellular respiration (both aerobic and anaerobic) to illustrate how chemical energy is stored in the bonds of carbohydrates and lipids and converted to ATP and heat when the bonds are broken.

Develop and use models to illustrate interactions between ecological hierarchy levels, including biosphere, biome, ecosystem, community, population, and organism.

Develop and use models to illustrate the flow of matter and energy between abiotic and biotic factors in ecosystems, including loss of heat, 10% rule, and the conservation of matter.

Construct an evidence-based explanation of how density-dependent and density-independent factors affect population growth.

Obtain, evaluate, and communicate data to explain how the biodiversity of Alabama contributes to ecosystem services in the state.

Engage in argument from evidence to support the claim that characteristics of an ecosystem contribute to its resilience and stability, including ecological succession and recovery from disturbance.

Use probability and statistical models to explain the variation of expressed traits within a population.

Use mathematics and computational thinking to predict patterns of inheritance, including dominance, recessiveness, codominance, and incomplete dominance.

Obtain, evaluate, and communicate information about how the interplay of heritable risk factors, somatic mutations, and environment influences human disease.

Develop and use an evidence-based model to illustrate the formation of reproductive cells through the process of meiosis.

Construct an explanation of how new genetic combinations and variations occur during crossover.

Obtain, evaluate, and communicate information about how errors during meiosis and environmental factors affect the expression of traits.

Analyze and interpret data to support hypotheses of common ancestry and biological evolution illustrated by cladograms and phylogenetic trees.

Evaluate evidence supporting claims that viruses should be placed in a separate category from living things.

Analyze and interpret data pertaining to adaptations resulting from natural and artificial selection to explain the evolution of populations.

Engage in argument from evidence to explain how populations respond to changes in the environment that can lead to speciation or extinction.

Use the periodic table as a model to predict the structure and properties of atoms and elements.

Assess the merits and limitations of historic and modern atomic models pertaining to the presence, position, mass, and charge of subatomic particles.

Develop and use models of an element’s subatomic particles to compare and contrast its atoms, ions, and isotopes.

Analyze and interpret data to identify or describe an element based on its number of protons, its relative abundance of isotopes, its organization and placement of electrons, and its light emission spectrum.

Ask questions to determine the relationship between an element’s physical and chemical properties and its position on the periodic table.

Construct explanations of how periodic trends can be used to predict the properties of elements.

Construct explanations of the formation of intramolecular and intermolecular forces and their effects on atomic and molecular interactions.

Develop and use Lewis dot diagrams to model the formation of covalent and ionic bonds.

Construct an explanation of the change in potential energy that occurs when chemical bonds are formed.

Plan and carry out an investigation to identify specific physical and chemical properties of compounds formed from ionic, covalent, and metallic bonding.

Develop and use models based on valence shell electron pair repulsion (VSEPR) theory to predict the shape of a molecule up to four electron domains around the central atom.

Construct an explanation of the polarity of a molecule based on electronegativity data and molecular geometry.

Analyze and interpret data from the periodic table to derive chemical formulas and names for ionic and covalent compounds.

Analyze and interpret data to compare the strengths of intermolecular forces and to explain how these forces affect physical properties.

Develop and use multiple types of models to represent chemical reactions.

Use qualitative and quantitative reasoning to describe and balance chemical equations to satisfy the law of conservation of matter.

Use qualitative and quantitative reasoning to classify chemical reactions, predict the products of single replacement and double replacement reactions, and represent chemical reactions using ionic equations.

Analyze and interpret temperature and bond energy data to classify a reaction as endothermic or exothermic.

Construct an explanation, using particle diagrams and collision theory, for how particle size, concentration, and temperature affect the rate of a chemical reaction.

Use stoichiometric ratios to support the claim that atoms, and therefore mass, are conserved during chemical reactions.

Quantitatively apply the concepts of the mole and Avogadro’s number to conceptualize and calculate percent composition and empirical or molecular formulas of common compounds.

Use mathematical representations of the mole concept to solve reaction stoichiometry problems, involving mole-to-mole conversions, mass-to-mole conversions, and mass-to-mass conversions.

Use mathematical models to reveal the relationships among the theoretical, actual, and percent yields of chemical reactions.

Qualitatively and quantitatively determine the limiting reactant when given the masses of all reactants.

Use mathematics and computational thinking to perform gas stoichiometry calculations involving mass, volume, and number of moles at standard temperature and pressure (STP).

Obtain, evaluate, and communicate information concerning factors that affect solubility and the properties of solutions.

Use mathematics and computational thinking to express the concentrations of given solutions in terms of molarity and molality.

Develop and use models to illustrate solute-solvent interactions.

Use mathematics and computational thinking to prepare solutions from both solids and concentrated solutions when given a desired molarity and volume.

Analyze and interpret data to explain the effects of temperature on the solubility of solid, liquid, and gaseous solutes in a solvent and the effects of pressure on the solubility of gaseous solutes.

Design and conduct experiments to evaluate the effect of solute concentration on the colligative properties of a solution.

Make qualitative and quantitative claims, based on ion concentration, about the acidic, basic, or neutral characteristics of a solution.

Obtain, evaluate, and communicate information concerning the properties of acids and bases.

Use the periodic table and computational thinking to derive chemical formulas and names of acids and bases.

Use multiple models to predict the relative properties of strong, weak, concentrated, and dilute acids and bases.

Use mathematics to calculate the pH, pOH, [OH- ], and [H3O+ ] of common solutions.

Plan and carry out a strong acid-strong base titration to determine the concentration of an unknown acidic or basic solution.

Plan and carry out investigations to determine how the atomic and molecular motion in chemical and physical processes is related to the kinetic molecular theory.

Qualitatively and quantitatively relate changes in the temperature and pressure of a gas to particle motion and number of collisions.

Express the relationship among pressure, volume, temperature, and the number of moles of a gas quantitatively, conceptually, and graphically.

Use mathematical representations to illustrate how the first two laws of thermodynamics demonstrate energy transfers throughout ecosystems, including food chains, food webs, and trophic levels, at various levels of biological organization.

Obtain, evaluate, and communicate information to model the cycling of matter through the biosphere, atmosphere, hydrosphere, and geosphere, including the flow of carbon, water, nitrogen, phosphorus, and sulfur.

Construct an explanation of how biotic and abiotic factors affect biodiversity and populations in ecosystems.

Support a claim that biodiversity is a natural resource which fosters ecosystem resilience, including the role of keystone, invasive, native, endemic, and indicator species.

Analyze and interpret data collected through geographic research and field investigations to describe Alabama’s biodiversity by region.

Engage in an evidence-based argument to explain how Earth’s systems affect the biosphere and the biosphere affects Earth’s systems over various amounts of time.

Obtain, evaluate, and communicate information regarding how short-term and long-term natural cyclic fluctuations cause ecosystem change.

Obtain, evaluate, and communicate information to describe the use of renewable and nonrenewable energy sources.

Analyze and interpret data on the origins and availability of renewable and nonrenewable forms of energy to predict consumption trends.

Construct an argument based on data about the risks and benefits of using renewable and nonrenewable energy sources in Alabama.

Obtain, evaluate, and communicate information to describe the development, management, and recycling of mineral resources.

Construct or revise a claim based on evidence of the effects of human activities on Earth’s systems, natural resources, and ecosystem services.

Use engineering practices to evaluate and refine a current solution designed to protect natural resources from anthropogenic sources of atmospheric, terrestrial, or aquatic pollution.

Obtain, evaluate, and communicate information based on evidence to explain how key natural resources, natural hazards, and climate variability influence human activity and welfare.

Communicate scientific information about how environmental change may disproportionately impact people in certain socioeconomic groups or geographic locations.

Use mathematics and graphic models to communicate how human activity may affect genetic variation in organism populations, including threatened and endangered species.

Construct an explanation of how human populations undergo growth and decline.

Analyze and interpret data on human population trends in developing and developed countries and in the global population as a whole.

Construct explanations of the types of environmental impacts produced by human populations in each stage of the demographic transition model.

Obtain, evaluate, and communicate information to describe the effects of human population growth on global ecosystems.

Evaluate and communicate information describing the impact of measures used to increase the food supply for the growing human population, including the use of GMOs, monocultures, integrated pest management (IPM), and precision agriculture.

Evaluate and communicate information describing the effects of urbanization on the environment.

Design and defend a sustainability plan to reduce an individual’s ecological footprint, taking into account how market forces and societal demands influence personal choices.

Obtain, evaluate, and communicate information about the connections among mass, gravity, and fusion in the life cycle of stars.

Utilize models to explain the process of stellar evolution from star birth to star death.

Interpret the Hertzsprung-Russell diagram to analyze the properties of stars, including density, magnitude, temperature, rates of fusion, and spectral class.

Obtain, evaluate, and communicate information about how nuclear fusion in stars and supernovas leads to the formation of all other elements.

Analyze and interpret data to quantify the energy produced in stars, using Einstein’s theory of general relativity by applying E=mc2 to show that the small amount of mass produced during hydrogen fusion produces a large amount of energy.

Obtain, evaluate, and communicate information about the structure and motion of components of the universe and solar system.

Use mathematics and computational thinking to predict the motion of natural and man-made objects in the solar system, using Kepler’s laws, Newton’s laws of motion, and Newton’s gravitational laws.

Use mathematics and computational thinking to explain the relationships between the properties of light and distances in the solar system and universe, including the Doppler effect, red shift, light years, and astronomical units.

Analyze spectroscopic data to determine the properties and motion of objects in space.

Investigate and communicate major properties of bodies in the solar system and the zones they inhabit.

Use mathematics to explain how solar intensity and the tilt of the Earth’s axis impact the distribution of sunlight on the Earth’s surface, including zenith angle, solar angle, and surface area.

Research, evaluate, and communicate information about how the findings of early astronomers, including Aristotle, Ptolemy, Copernicus, Galileo, Brahe, Kepler, Newton, and Einstein, challenged the thinking of their time, allowed for academic advancements, and built a foundation for space exploration.

Obtain and evaluate scientific information that explains how the application of new knowledge and technological advances has improved human understanding of the universe.

Construct an evidence-based explanation of the connections among various cosmic phenomena, citing leading scientific theories.

Obtain and communicate information about Alabama's contributions to space exploration.

Obtain, evaluate, and communicate information about the geologic conditions and processes that form different Earth materials.

Plan and carry out investigations to explore the processes that form plutonic (intrusive) and volcanic (extrusive) igneous rocks of differing compositions and textures.

Analyze and interpret data to explain the effects of mechanical and chemical weathering and erosion on Earth’s materials by wind, water, ice, and gravity.

Construct an explanation using evidence from experiments, models, or data of the processes that create and transform igneous, sedimentary, and metamorphic rocks.

Plan and conduct an investigation on water’s effect on surface and subsurface processes.

Obtain and communicate information about significant geologic characteristics in Alabama and the southeastern United States.

Obtain, evaluate, and communicate information about major events in Earth’s history.

Analyze and interpret data to sequence events in Earth’s history, including relative and absolute dating techniques, principles of superposition and crosscutting relationships, igneous intrusions, radiometric dating, and the fossil record.

Construct an explanation based on evidence of how catastrophic and long-term events have impacted life on Earth, including mass extinctions.

Construct explanations from evidence of how the flow of energy through Earth's systems has changed over time.

Obtain, evaluate, and communicate information about important tectonic and geologic events that have occurred in Alabama over geologic time.

Obtain, evaluate, and communicate information about the theory of plate tectonics.

Construct an evidence-based explanation of continental drift, basing conclusions on comparisons of coastlines, fossils, ages of rocks, climate, and magnetic patterns.

Construct an explanation, based on evidence, of tectonic plate movement, types of plate boundaries, and how boundary type relates to specific tectonic features, including mountain ranges, earthquakes, volcanism, volcanic islands, hotspots, mid-ocean ridges, and faults.

Develop and interpret a model of Earth’s internal structure and composition, including inner core, outer core, asthenosphere, lithosphere, mantle, and crust.

Analyze data to interpret seismic activity and assess the risk of volcanic eruptions and earthquakes in Alabama and other areas in the United States.

Obtain, evaluate, and communicate information about the role of energy transfer in wind, precipitation, cloud formation, and front formation.

Obtain and communicate information to explain how water cycles through the atmosphere, including condensation, evaporation, clouds, types of precipitation, relative humidity, and dew point.

Plan and carry out an investigation to determine the differential heating of land and water and explain how these differences create changes in local and global weather.

Construct an explanation of how air masses, source regions, fronts, weather changes associated with frontal passage (including cold, warm, occluded, and stationary fronts), air pressure, air density, temperature, cloud types, and precipitation are related to each other.

Use data to construct an explanation of the role of pressure differences in the development of wind systems.

Analyze and interpret data to create a surface map, including high-pressure and low-pressure systems, isobars, wind barbs, cloud types, precipitation, and fronts.

Obtain and communicate information to explain different climate regions and their impact on patterns of severe weather.

Analyze temperature and precipitation patterns related to factors that influence climate, including proximity to water, topography, elevation, latitude, and orographic effect.

Analyze and interpret data to develop predictions about the formation of meteorological events.

Communicate scientific information to explain the personal, local, and statewide implications of severe weather events in Alabama.

Obtain, evaluate, and communicate information to explain how differences in cellular structure (mitochondria, cytoskeletal structure, endoplasmic reticulum, cell membrane) lead to differences in the function and organization of the four tissue types (epithelial, connective, muscular, and nervous).

Obtain, evaluate, and communicate information to describe how the structures of the integumentary system and its accessory organs contribute to its function.

Construct an explanation of the relationships between the integumentary system and other organ systems, including the body’s mechanisms for maintaining homeostasis.

Develop and use a model to illustrate how the structures of the skeletal system contribute to its function.

Obtain, evaluate, and communicate information describing the growth and development of the skeletal system.

Construct an explanation of the relationships between the skeletal system and other organ systems, including the body’s mechanisms for maintaining homeostasis.

Develop and build a three-dimensional model to illustrate the structures of the muscular system, including muscle locations, origins, and insertions, and explain their roles in movement and support.

Model the cellular physiology of skeletal muscle, including how the cell functions in muscle contraction and relaxation.

Obtain, evaluate, and communicate information to explain muscle fatigue and tone in terms of muscle cell physiology.

Obtain, evaluate, and communicate information explaining the relationship between the structures and functions of the central nervous system and the peripheral nervous system.

Use a model to illustrate the role of action potentials in neural transmission.

Construct an explanation of the role of reflex arcs, the central nervous system, and special senses in the response to stimuli to maintain homeostasis and guide behavior.

Construct an explanation of the role of neurotransmitters in the functions and behavior of the nervous system.

Obtain, evaluate, and summarize scientific findings regarding the biological origin of emotions and memories in distinct regions of the brain.

Construct an explanation of how the interdependence of the nervous and endocrine systems maintains homeostasis.

Obtain, evaluate, and communicate information explaining how hormones secreted by endocrine glands help the body maintain homeostasis through negative and positive feedback loops

Obtain, evaluate, and communicate information describing the role of endocrine axes involving the thyroid and gonads in controlling growth, development, metabolism, and reproduction.

Obtain, evaluate, and communicate information describing the structure of lymph nodes and primary cells of the immune system (neutrophils, lymphocytes, monocytes, macrophages, eosinophils, and basophils) and explaining their role in inflammation and the body’s defense.

Obtain, evaluate, and communicate information explaining how vaccines work to stimulate immunity in the human body.

Construct an explanation of how the lymphatic system interacts with the immune and circulatory systems.

Obtain, evaluate, and communicate information explaining how the structures of the cardiovascular system are related to its functions.

Create a model to show how a pressure gradient moves blood through the circulatory system.

Carry out an investigation exploring the link between blood pressure and heart rate and include the role of baroreceptors and chemoreceptors in the explanation of results.

Construct an explanation of the cardiovascular system’s relationships with other organ systems, including the body’s mechanisms for maintaining homeostasis.

Obtain, evaluate, and communicate information to explain the relationship between the structures and functions of the respiratory system.

Construct an explanation of how the circulatory system works with respiration to transport respiratory gases.

Use a model to illustrate how pressure gradients move air into and out of the lungs.

Construct an explanation of the respiratory system’s relationships with other organ systems, including the body’s mechanisms for maintaining homeostasis.

Obtain, evaluate, and communicate information explaining the relationship between the structures and functions of the digestive system, including absorption and chemical and mechanical digestion.

Construct an explanation of the roles of accessory organs (salivary glands, pancreas, and liver) in digestion.

Construct an explanation of the relationships between the digestive system and other organ systems, including the body’s mechanisms for maintaining homeostasis.

Use a model to illustrate the microanatomy of excretory structures and describe their functions.

Construct an explanation of how the excretory system maintains homeostasis, including blood pressure and pH.

Use models to compare and contrast the internal and external structures of the female and male reproductive systems and their production of gametes.

Construct an explanation of how the endocrine system influences the growth, development, and functions of the reproductive systems in males and females, including the mechanisms of hormonal birth control.

Obtain, evaluate, and communicate ideas about kinematics, including scalar quantities (distance and speed) and vector quantities (position, displacement, velocity, and acceleration).

Analyze data to create and interpret graphs of position, velocity, and acceleration versus time for one-dimensional motion.

Analyze free fall motion using one-dimensional kinematics to determine the acceleration due to gravity (g).

Analyze and interpret data to explain changes in the vector quantities of position, velocity, and acceleration in two-dimensional projectile motion, including projectiles launched horizontally and at an angle.

Use mathematics and computational thinking to solve problems, using kinematics equations in both one- and two-dimensional motion.

Construct explanations of dynamics from evidence, using Newton’s laws of motion.

Evaluate the effects of balanced and unbalanced forces on an object’s motion.

Use mathematical, graphical, and narrative methods to explain the relationships among net force, mass, and acceleration of a single object.

Create free and fixed body diagrams to model all the forces acting on a single object.

Create an explanation of the nature of forces and the interactions among them, including tension, friction, gravitation, and normal forces, using free-body diagrams.

Analyze data to identify the pair of equal and opposite forces between two interacting bodies and relate their magnitudes and directions using Newton’s third law.

Design and carry out experiments to verify that energy and momentum are conserved in closed systems.

Use mathematical and computational thinking to explain the relationships among work, power, and time.

Create mathematical and graphical representations to depict the transformation of energy from one form to another, including kinetic energy, gravitational potential energy, elastic potential energy, and work due to friction.

Use models to illustrate the relationship between the work performed on an object and the object’s total mechanical energy.

Qualitatively and quantitatively evaluate the relationship among the force acting on an object, the time of interaction, and the change in linear momentum (impulse) of the object.

Obtain, evaluate, and interpret data related to collisions (both elastic and inelastic) and their effects on both linear momentum and energy conservation.

Use mathematics and computational thinking to analyze the effects of pressure changes and buoyant forces in fluid systems.

Plan and carry out experiments to determine the density of objects.

Use and solve algebraic formulas to determine the relationships between pressure, force, area, and density.

Design solutions to determine the magnitude and direction of the buoyant force acting on an object and the effects of the buoyant forces on the object's motion.

Use the buoyant force acting on an object and free body diagrams to determine the acceleration of submerged objects.

Develop and use models to analyze the circular motion of objects.

Use mathematics and free-body diagrams to relate the tangential velocity, the radius of orbit, the centripetal acceleration, and force to each other for an object moving in a circle.

Develop and use a model to describe the mathematical relationship between mass, distance, and force as expressed by Newton’s law of universal gravitation.

Obtain, evaluate, and communicate information concerning static and current electricity.

Develop and use a model to describe the mathematical relationship among charge, distance, and force as expressed by Coulomb’s law.

Obtain, evaluate, and communicate information regarding the relationship among voltage, current, and power for direct current circuits.

Create models of series, parallel, and mixed direct current circuits.

Use mathematics and computational thinking to determine the voltage, current, and resistance for an entire circuit and at each resistor or load.

Obtain, evaluate, and communicate information regarding the propagation, properties, and applications of waves.

Use mathematics and computational thinking to describe the relationships among the velocity, frequency, and wavelength of a propagating wave.

Use results of investigations to explain the production and characteristics of sound waves including interferences, the Doppler effect, and standing waves.

Obtain, evaluate, and communicate information to explain the properties and behavior of electromagnetic waves.

Evaluate sources of information concerning the law of conservation of energy to illustrate energy transformations in practical applications and natural systems.

Plan and carry out investigations to explore how mechanical energy is transformed within a system, including kinetic energy, gravitational potential energy, elastic potential energy, and work.

Collect, analyze, and use data to explain how thermal energy is transferred by conduction, convection, and radiation.

Construct explanations to justify the selection of materials for specific applications based on the materials’ specific heat values.

Investigate collisions and other real-world situations to evaluate the effects of impulse on changes in momentum.

Obtain, evaluate, and communicate information to compare and contrast the properties of mechanical and electromagnetic waves as they relate to real-world applications.

Analyze and interpret data to identify and describe the relationships among wavelength, frequency, amplitude, and energy in waves.

Develop models to illustrate reflection, refraction, interference, and diffraction.

Analyze the ways in which different media and their characteristics affect the speed of sound and light waves.

Use models to illustrate the Doppler effect and explain the changes in sound perception associated with it.

Obtain and communicate information from published materials to explain how transmitting and receiving devices use the principles of wave behavior and wave interactions to transmit and capture information and energy.

Construct an explanation of the ways in which modern science uses both magnetic and electric concepts to create usable products.

Construct an argument using evidence to support the claim that field forces exist between objects and act on the objects even when the objects are not in contact.

Plan and carry out investigations to identify the factors that affect the strength of the electric and magnetic forces between objects.

Use mathematics and computational thinking to represent and determine the quantitative relationships between voltage, current, and resistance in series and parallel circuits in terms of Ohm’s law.

Develop and use models to determine the relationships among voltage, current, and resistance at specific loads in series and parallel circuits.

Plan and carry out investigations to determine the relationships between magnetism and electrical charge in common devices.

Analyze and interpret data concerning the advantages and disadvantages of the energy sources used to produce electricity.

Evaluate the effects of using ions or isotopes of elements as a solution to a complex real-world problem, including cost, safety, trade-offs, and environmental impacts.

Obtain, evaluate, and communicate information from the periodic table concerning the structure of an atom and the arrangement of the atom’s protons, neutrons, and electrons.

Predict the properties of an element based on the element’s number of protons and valence electrons.

Analyze and interpret data to predict properties of ionic and covalent compounds.

Use mathematics and computational thinking to determine the charge of an ion and the mass number of an isotope based on the number of subatomic particles.

Analyze and interpret data to explain how radioactive decay changes a radioactive isotope over time and explain how the age of an object can be estimated by the ratio of radioactive isotopes contained within the object’s atoms.

Use mathematics and computational thinking to identify types of radioactive decay based on balanced chemical equations, penetrating power, identity of emitted particles, and charge.

Use models to explain how nuclear fission and fusion reactions can be used as energy sources.

Generate and defend a data-based claim regarding the use of radioactive materials as an energy source.

Analyze and interpret data to justify the selection of a specific material for a practical application, considering a range of constraints.

Carry out investigations and use results to compare and contrast the physical and chemical properties of matter.

Analyze and interpret data to predict changes in the phase of a material based on changes in particle motion, temperature, pressure, or thermal energy.

Use mathematical and computational thinking to determine the quantitative relationships among temperature, pressure, and volume of confined gases.

Utilize multiple types of models to support and verify the claim that matter is conserved during a simple chemical reaction.

Obtain, evaluate, and communicate information to explain how the properties of various types of solutions make them useful in real-world applications.

Plan and carry out investigations to determine how various factors, including temperature, surface area, and stirring, affect the rate at which a solute dissolves in a solvent.

Develop and use particle diagrams to illustrate diluted and concentrated solutions and describe how adjusting amounts of solute and solvent impacts the concentration of a solution.

Analyze and interpret data from experiments to determine whether solutions are acidic, basic, or neutral to predict properties of the solutions.

Plan and carry out investigations concerning neutralization reactions and describe the properties of the reactants and products.