Georgia's K-12 Mathematics Standards

Identify, describe, and compare basic shapes encountered in the environment, and form two-dimensional shapes and three-d...

Identify, sort, classify, analyze, and compare two- dimensional shapes and three-dimensional figures, in different sizes...

Describe the relative location of an object using positional words.

Use basic shapes to represent specific shapes found in the environment by creating models and drawings.

Use two or more basic shapes to form larger shapes.

Observe, describe, and compare the physical and measurable attributes of objects and analyze graphical displays of data ...

Directly compare, describe, and order common objects, using measurable attributes (length, height, width, or weight) and...

Classify and sort up to ten objects into categories by an attribute; count the number of objects in each category and so...

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve p...

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Demonstrate and explain the relationship between numbers and quantities up to 20; connect counting to cardinality (the l...

Count up to 20 objects in a variety of structured arrangements and up to 10 objects in a scattered arrangement.

When counting objects, explain that the last number counted represents the total quantity in a set (cardinality), regard...

Given a number from 1-20, identify the number that is one more or one less.

Identify pennies, nickels, and dimes and know their name and value.

Use count sequences within 100 to count forward and backward in sequence.

Count forward to 100 by tens and ones and backward from 20 by ones.

Count forward beginning from any number within 100 and count backward from any number within 20.

Use place value understanding to compose and decompose numbers from 11–19.

Describe numbers from 11 to 19 by composing (putting together) and decomposing (breaking apart) the numbers into ten one...

Identify, write, represent, and compare numbers up to 20.

Identify written numerals 0- 20 and represent a number of objects with a written numeral 0-20 (with 0 representing a cou...

Compare two sets of up to 10 objects and identify whether the number of objects in one group is more or less than the ot...

Explain the concepts of addition, subtraction, and equality and use these concepts to solve real-life problems within 10...

Compose (put together) and decompose (break apart) numbers up to 10 using objects and drawings.

Represent addition and subtraction within 10 from a given authentic situation using a variety of representations and str...

Use a variety of strategies to solve addition and subtraction problems within 10.

Fluently add and subtract within 5 using a variety of strategies to solve practical, mathematical problems.

Explain, extend, and create repeating patterns with a repetition, not exceeding 4 and describe patterns involving the pa...

Create, extend, and describe repeating patterns with numbers and shapes, and explain the rationale for the pattern.

Describe patterns involving the passage of time using words and phrases related to actual events.

Compose shapes, analyze the attributes of shapes, and relate their parts to the whole.

Identify common two-dimensional shapes and three-dimensional figures, sort and classify them by their attributes and bui...

Compose two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter-circles) and three-dimensional...

Partition circles and rectangles into two and four equal shares.

Use appropriate tools to measure, order, and compare intervals of length and time, as well as denominations of money to ...

Estimate, measure, and record lengths of objects using non-standard units, and compare and order up to three objects usi...

Tell and write time in hours and half-hours using analog and digital clocks, and measure elapsed time to the hour on the...

Identify the value of quarters and compare the values of pennies, nickels, dimes, and quarters.

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to compare...

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Extend the count sequence to 120. Read, write, and represent numerical values to 120 and compare numerical values to 100...

Count within 120, forward and backward, starting at any number. In this range, read and write numerals and represent a n...

Explain that the two digits of a 2-digit number represent the amounts of tens and ones.

Compare and order whole numbers up to 100 using concrete models, drawings, and the symbols >, =, and <.

Explain the relationship between addition and subtraction and apply the properties of operations to solve real-life addi...

Use a variety of strategies to solve addition and subtraction problems within 20.

Use pictures, drawings, and equations to develop strategies for addition and subtraction within 20 by exploring strings ...

Recognize the inverse relationship between subtraction and addition within 20 and use this inverse relationship to solve...

Fluently add and subtract within 10 using a variety of strategies.

Use the meaning of the equal sign to determine whether equations involving addition and subtraction are true or false.

Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers.

Apply properties of operations as strategies to solve addition and subtraction problem situations within 20.

Use concrete models, the base ten structure, and properties of operations to add and subtract within 100.

Use a variety of strategies to solve applicable, mathematical addition and subtraction problems with one- and two-digit ...

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoni...

Add and subtract multiples of 10 within 100.

Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns found in real-life s...

Investigate, create, and make predictions about repeating patterns with a core of up to 3 elements resulting from repeat...

Identify, describe, and create growing, shrinking, and repeating patterns based on the repeated addition or subtraction ...

Draw and partition shapes and other objects with specific attributes, and conduct observations of everyday items and str...

Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes...

Identify at least one line of symmetry in everyday objects to describe each object as a whole.

Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the w...

Recognize that equal shares of identical wholes may be different shapes within the same whole.

Estimate and measure the lengths of objects and distance to solve problems found in real-life using standard units of me...

Construct simple measuring instruments using unit models. Compare unit models to rulers.

Estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard ...

Measure to determine how much longer one object is than another and express the length difference in terms of a standard...

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve p...

Represent whole-number sums and differences within a standard unit of measurement on a number line diagram.

Solve real-life problems involving time and money.

Tell and write time from analog and digital clocks to the nearest five minutes, and estimate and measure elapsed time us...

Find the value of a group of coins and determine combinations of coins that equal a given amount that is less than one h...

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Using the place value structure, explore the count sequences to represent, read, write, and compare numerical values to ...

Explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.

Count forward and backward by ones from any number within 1000. Count forward by fives from multiples of 5 within 1000. ...

Represent, compare, and order whole numbers to 1000 with an emphasis on place value and equality. Use >, =, and < symbol...

Apply multiple part-whole strategies, properties of operations and place value understanding to solve real-life, mathema...

Fluently add and subtract within 20 using a variety of mental, part-whole strategies.

Find 10 more or 10 less than a given three-digit number and find 100 more or 100 less than a given three-digit number.

Solve problems involving the addition and subtraction of two-digit numbers using part-whole strategies.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relatio...

Work with equal groups to gain foundations for multiplication through real-life, mathematical problems.

Determine whether a group (up to 20) has an odd or even number of objects. Write an equation to express an even number a...

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; w...

Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns.

Identify, describe, and create a numerical pattern resulting from repeating an operation such as addition and subtractio...

Identify, describe, and create growing patterns and shrinking patterns involving addition and subtraction up to 20.

Identify the attributes of polygons, including parallel segments, perpendicular segments, right angles, and symmetry.

Identify perpendicular line segments, parallel line segments, and right angles, identify these in polygons, and solve pr...

Classify, compare, and contrast polygons, with a focus on quadrilaterals, based on properties. Analyze specific 3-dimens...

Identify lines of symmetry in polygons.

Identify area as a measurable attribute of rectangles and determine the area of a rectangle presented in real-life, math...

Investigate area by covering the space of rectangles presented in realistic situations using multiple copies of the same...

Determine the area of rectangles (or shapes composed of rectangles) presented in relevant problems by tiling and countin...

Discover and explain how area can be found by multiplying the dimensions of a rectangle.

Determine the perimeter of a polygon presented in real-life, mathematical problems.

Determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon. Solve prob...

Investigate and describe how rectangles with the same perimeter can have different areas or how rectangles with the same...

Solve real-life, mathematical problems involving length, liquid volume, mass, and time and analyze graphical displays of...

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve p...

Tell and write time to the nearest minute and estimate time to the nearest fifteen minutes (quarter hour) from the analy...

Solve meaningful problems involving elapsed time, including intervals of time to the hour, half hour, and quarter hour w...

Use rulers to measure lengths in halves and fourths (quarters) of an inch and a whole inch.

Estimate and measure liquid volumes, lengths and masses of objects using customary units. Solve problems involving mass,...

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Use place value reasoning to represent, read, write, and compare numerical values up to 10,000 and round whole numbers u...

Read and write multi-digit whole numbers up to 10,000 to the thousands using base-ten numerals and expanded form.

Use place value reasoning to compare multi-digit numbers up to 10,000, using >, =, and < symbols to record the results o...

Use place value understanding to round whole numbers within up to 1000 to the nearest 10 or 100.

Represent fractions with denominators of 2, 3, 4, 6 and 8 in multiple ways within a framework using visual models.

Describe a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction. Use parts of a who...

Compare two unit fractions by flexibly using a variety of tools and strategies.

Represent fractions, including fractions greater than one, in multiple ways.

Recognize and generate simple equivalent fractions.

Use part-whole strategies to represent and solve real-life problems involving addition and subtraction with whole number...

Fluently add and subtract within 1000 to solve problems.

Apply part-whole strategies, properties of operations and place value understanding, to solve problems involving additio...

Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole num...

Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.

Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between...

Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and...

Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication a...

Use place value reasoning and properties of operations to multiply one-digit whole numbers by multiples of 10, in the ra...

Solve practical, relevant problems involving multiplication and division within 100 using part-whole strategies, visual ...

Use multiplication and division to solve problems involving whole numbers to 100. Represent these problems using equatio...

Investigate the concepts of angles and angle measurement to estimate and measure angles.

Recognize angles as geometric shapes formed when two rays share a common endpoint. Draw right, acute, and obtuse angles ...

Measure angles in reference to a circle with the center at the common endpoint of two rays. Determine an angle’s measure...

Identify and draw geometric objects, classify polygons based on properties, and solve problems involving area and perime...

Explore, investigate, and draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular lines, p...

Classify, compare, and contrast polygons based on lines of symmetry, the presence or absence of parallel or perpendicula...

Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths.

Measure time and objects that exist in the world to solve real-life, mathematical problems and analyze graphical display...

Use the four operations to solve problems involving elapsed time to the nearest minute, intervals of time, metric measur...

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve p...

Create dot plots to display a distribution of numerical (quantitative) measurement data.

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Recognize patterns within the base ten place value system with quantities presented in real-life situations to compare a...

Read and write multi-digit whole numbers to the hundred-thousands place using base-ten numerals and expanded form.

Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its r...

Use place value reasoning to represent, compare, and order multi-digit numbers, using >, =, and < symbols to record the ...

Use place value understanding to round multi-digit whole numbers.

Using part-whole strategies, solve problems involving addition and subtraction through the hundred-thousands place, as w...

Fluently add and subtract multi-digit numbers to solve practical, mathematical problems using place value understanding,...

Interpret, model, and solve problems involving multiplicative comparison.

Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involvi...

Solve authentic division problems involving up to 4-digit dividends and 1- digit divisors (including whole number quotie...

Solve multi-step problems using addition, subtraction, multiplication, and division involving whole numbers. Use mental ...

Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of ...

Using concrete materials, drawings, and number lines, demonstrate and explain the relationship between equivalent fracti...

Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that c...

Compare two fractions with different numerators and/or different denominators by flexibly using a variety of tools and s...

Represent whole numbers and fractions as the sum of unit fractions.

Represent a fraction as a sum of fractions with the same denominator in more than one way, recording with an equation.

Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Solve real-life problems involving addition, equivalence, comparison of fractions with denominators of 10 and 100, and c...

Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials an...

Represent, read, and write fractions with denominators of 10 or 100 using decimal notation, and decimal numbers to the h...

Compare two decimal numbers to the hundredths place by reasoning about their size. Record the results of comparisons wit...

Generate and analyze patterns, including those involving shapes, input/output diagrams, factors, multiples, prime number...

Generate both number and shape patterns that follow a provided rule.

Use input-output rules, tables, and charts to represent and describe patterns, find relationships, and solve problems.

Find factor pairs in the range 1–100 and find multiples of single-digit numbers up to 100.

Identify composite numbers and prime numbers and explain the relationship with the factor pairs.

Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of rig...

Classify, compare, and contrast polygons based on properties.

Determine, through exploration and investigation, that attributes belonging to a category of two-dimensional figures als...

Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine...

Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times ...

Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to...

Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time.

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve p...

Convert among units within the metric system and then apply these conversions to solve multistep, practical problems.

Convert among units within relative sizes of measurement units within the customary measurement system.

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Use place value understanding to solve real-life, mathematical problems.

Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to ...

Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to d...

Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems.

Fluently multiply multi-digit (up to 3- digit by 2-digit) whole numbers to solve authentic problems.

Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve pra...

Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strat...

Explain the meaning of a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems involvin...

Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a vari...

Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.

Model and solve problems involving multiplication of a fraction and a whole number.

Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number...

Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.

Read, write, and compare decimal numbers to the thousandths place, and round and perform operations with decimal numbers...

Read and write decimal numbers to the thousandths place using base-ten numerals written in standard form and expanded fo...

Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place...

Use place value understanding to round decimal numbers to the hundredths place.

Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategi...

Write, interpret, and evaluate numerical expressions within authentic problems.

Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to ...

Solve relevant problems by creating and analyzing numerical patterns using the given rule(s).

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by co...

Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordi...

Solve relevant problems involving area, surface area, and volume.

Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or dec...

Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these fi...

Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base...

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers.

Fluently add and subtract any combination of fractions to solve problems.

Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. In...

Perform operations with multi-digit decimal numbers fluently using models and student-selected strategies.

Apply operations with whole numbers, fractions and decimals within relevant applications.

Describe and interpret the center of the distribution by the equal share value (mean).

Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of qu...

Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantita...

Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quan...

Relate the choice of measures of center and variability to the shape of the data distribution and the context in which t...

Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data di...

Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to desc...

Identify and compare integers and explain the meaning of zero based on multiple authentic situations.

Order and plot integers on a number line and use distance from zero to discover the connection between integers and thei...

Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; r...

Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare ra...

Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value a...

Distinguish comparisons of absolute value from statements about order.

Solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions wit...

Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantiti...

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, ...

Solve problems involving proportions using a variety of student-selected strategies.

Describe the concept of rates and unit rate in the context of a ratio relationship.

Solve unit rate problems including those involving unit pricing and constant speed.

Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent.

Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyd...

Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant ...

Write and evaluate numerical expressions involving rational bases and whole-number exponents.

Determine greatest common factors and least common multiples using a variety of strategies to make sense of applicable p...

Write and read expressions that represent operations with numbers and variables in realistic situations.

Evaluate expressions when given values for the variables, including expressions that arise in everyday situations.

Apply the properties of operations to identify and generate equivalent expressions.

Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations.

Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether...

Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unkn...

Solve problems by writing and solving equations of the form x + p = q, px = q and x/p = q for cases in which p, q and x ...

Recognize and generate inequalities of the form x > c, x ≥ c, x ≤ c, or x < c to explain situations that have infinitely...

Graph rational numbers as points on the coordinate plane to represent and solve contextual, mathematical problems; draw ...

Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and ot...

Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and dete...

Solve problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute...

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side j...

Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, an...

Measure angles in whole nonstandard units.

Measure angles in whole number degrees using a protractor.

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve e...

Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the fo...

Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.

Solve realistic problems involving surface area of right prisms and cylinders.

Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in the plan...

Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using...

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational number...

Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quant...

Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the...

Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing...

Show and explain p + q as the number located a distance ∣q∣ from p, in the positive or negative direction, depending on ...

Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve auth...

Show and explain subtraction of rational numbers as adding the additive inverse, p − q − p + (−q). Show that the distanc...

Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.

Make sense of multiplication of rational numbers using realistic applications.

Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rat...

Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients...

Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers re...

Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant contextu...

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coeff...

Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in...

Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symboli...

Construct algebraic equations to solve practical problems leading to equations of the form px + q = r and p(x + q) = r, ...

Construct algebraic inequalities to solve problems, leading to inequalities of the form px ± q > r, px ± q < r, px ± q ≤...

Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationshi...

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured...

Predict characteristics of a population by examining the characteristics of a representative sample. Recognize the poten...

Analyze sampling methods and conclude that random sampling produces and supports valid inferences.

Use data from repeated random samples to evaluate how much a sample mean is expected to vary from a population mean. Sim...

Determine the unit rate (constant of proportionality) in tables, graphs (1, r), equations, diagrams, and verbal descript...

Determine whether two quantities presented in authentic problems are in a proportional relationship.

Identify, represent, and use proportional relationships.

Use context to explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, ...

Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from...

Use similar triangles to explain why the slope, m, is the same between any two distinct points on a nonvertical line in ...

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportion...

Use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations.

Using mathematical reasoning, investigate chance processes and develop, evaluate, and use probability models to find pro...

Represent the probability of a chance event as a number between 0 and 1 that expresses the likelihood of the event occur...

Approximate the probability of a chance event by collecting data on an event and observing its long-run relative frequen...

Develop a probability model and use it to find probabilities of simple events. Compare experimental and theoretical prob...

Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probab...

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Use appropriate graphical displays and numerical summaries from data distributions with categorical or quantitative (num...

Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of fun...

Show and explain that a function is a rule that assigns to each input exactly one output.

Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph th...

Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.

Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represe...

Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y₁) = m(x - x₁)...

Write a linear function defined by an expression in different but equivalent forms to reveal and explain different prope...

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial val...

Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models, an...

Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to des...

Solve practical, linear problems involving situations using bivariate quantitative data.

Show that straight lines are widely used to model relationships between two quantitative variables. For scatter plots th...

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slop...

Explain the meaning of the predicted slope (rate of change) and the predicted intercept (constant term) of a linear mode...

Use appropriate graphical displays from data distributions involving lines of best fit to draw informal inferences and a...

Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.

Interpret and solve relevant mathematical problems leading to two linear equations in two variables.

Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersectio...

Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by ins...

Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.

Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or ne...

Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain re...

Explain a proof of the Pythagorean Theorem and its converse using visual models.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical proble...

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical ...

Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics...

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic appli...

Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats e...

Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, an...

Solve problems involving radicals and integer exponents including relevant application situations; apply place value und...

Apply the properties of integer exponents to generate equivalent numerical expressions.

Use square root and cube root symbols to represent solutions to equations. Recognize that x² = p (where p is a positive ...

Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many ti...

Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and s...

Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear in...

Interpret expressions and parts of an expression, in context, by utilizing formulas or expressions with multiple terms a...

Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no ...

Create and solve linear equations and inequalities in one variable within a relevant application.

Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequalit...

Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solutio...

Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant...

Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; c...

Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional...

Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all i...