Virginia Standards of Learning for Mathematics

The student will model and solve single-step contextual problems using addition and subtraction with whole numbers withi...

Use objects, drawings, words, or numbers to compose and decompose numbers less than or equal to 5 in multiple ways.

Recognize and describe with fluency part-part-whole relationships for numbers up to 5 in a variety of configurations. 

Model and identify the number that makes 5 when added to a given number less than or equal to 5. 

Use objects, drawings, words, or numbers to compose and decompose numbers less than or equal to 10 in multiple ways.

Model and identify the number that makes 10 when added to a given number less than or equal to 10.

Model and solve single-step contextual problems (join, separate, and part-part-whole) using 10 or fewer concrete objects...

The student will reason mathematically by making direct comparisons between two objects or events using the attributes o...

lengths of two objects using the terms longer or shorter;

heights of two objects using the terms taller or shorter;

weights of two objects using the terms heavier or lighter;

volumes of two containers using the terms more or less; and

amount of time spent on two events using the terms longer or shorter.

The student will identify, describe, name, compare, and construct plane figures (circles, triangles, squares, and rectan...

Identify and name concrete and pictorial representations of circles, triangles, squares, and rectangles regardless of th...

Describe triangles, squares, and rectangles to include the number of sides and number of vertices. 

Describe a circle using terms such as round and curved. 

Distinguish between examples and nonexamples of identified plane figures (circles, triangles, squares, and rectangles). 

Compare and contrast two plane figures using characteristics to describe similarities and differences.

Construct plane figures (circles, triangles, squares, and rectangles) using a variety of materials (e.g., straws, sticks...

The student will describe the units of time represented in a calendar.

Identify a calendar as a tool used to measure time.

Name the days of the week and state that there are seven days in one week.

Determine the day before and after a given day (e.g., yesterday, today, tomorrow).

Name the twelve months of the year and state that there are twelve months in one year.

Distinguish between days of the week and months of the year.

The student will utilize flexible counting strategies to determine and describe quantities up to 100.

Use one-to-one correspondence to determine how many are in a given set containing 30 or fewer concrete objects (e.g., cu...

Recognize and explain that the number of objects remains the same regardless of the arrangement or the order in which th...

Represent forward counting by ones using a variety of tools, including five-frames, tenframes, and number paths (a prelu...

Count forward orally by ones from 0 to 100. 

Count forward orally by ones, within 100, starting at any given number.

Count backward orally by ones when given any number between 1 and 20.

State the number after, without counting, when given any number between 0 and 30.

State the number before, without counting, when given any number between 1 and 20.

Use objects, drawings, words, or numbers to compose and decompose numbers 11-19 into a ten and some ones.

Group a collection of up to 100 objects (e.g., counters, pennies, cubes) into sets of ten and count by tens to determine...

The student will identify, represent, and compare quantities up to 30.

Read, write, and identify the numerals 0 through 30.

Construct a set of objects that corresponds to a given numeral within 30, including an empty set.

Determine and write the numeral that corresponds to the total number of objects in a given set of 30 or fewer concrete o...

Given a set of up to 30 objects, construct another set which has more, fewer, or the same number of objects using concre...

Given a numeral up to 30, construct a set which has more, fewer, or the same number of objects using concrete or pictori...

Compare two sets containing up to 30 concrete objects or pictorial models, using the terms more, fewer, or the same as (...

Compare numbers up to 30, to the benchmarks of 5 and 10 using various models (e.g., five frames, ten frames, number path...

The student will identify, describe, extend, and create simple repeating patterns using various representations.

Identify and describe the core found in repeating patterns.

Extend a repeating pattern by adding at least two complete repetitions of the core to the pattern.

Create and describe a repeating pattern using objects, colors, sounds, movements, or pictures.

The student will apply the data cycle (pose questions; collect or acquire data; organize and represent data; and analyze...

Sort and classify concrete objects into appropriate subsets (categories) based on one attribute (e.g., size, shape, colo...

Describe and label attributes (e.g., size, color, shape) of a set of objects (e.g., coins, counters, buttons) that has b...

Pose questions, given a predetermined context, that require the collection of data (limited to 25 or fewer data points f...

Determine the data needed to answer a posed question, and collect the data using various methods (e.g., counting objects...

Organize and represent a data set (vertically or horizontally) by sorting concrete objects into organized groups to form...

Organize and represent a data set (vertically or horizontally) using pictures to form a simple picture graph. 

ask and answer questions about the data represented in object graphs and picture graphs (e.g., how many in each category...

draw conclusions about the data and make predictions based on the data.

The student will recall with automaticity addition and subtraction facts within 10 and represent, solve, and justify sol...

Recognize and describe with fluency part-part-whole relationships for numbers up to 10 in a variety of configurations. 

Demonstrate fluency with addition and subtraction within 10 by applying reasoning strategies (e.g., count on/count back,...

Recall with automaticity addition and subtraction facts within 10.

Investigate, recognize, and describe part-part-whole relationships for numbers up to 20 in a variety of configurations (...

Solve addition and subtraction problems within 20 using various strategies (e.g., inverse relationships: if 9 + 3 = 12 t...

Represent, solve, and justify solutions to single-step addition and subtraction problems (join, separate, and part-part-...

Determine the unknown whole number that will result in a sum or difference of 10 or 20 (e.g., 14 - __ = 10 or 15 + __ = ...

Identify and use (+) as a symbol for addition and (-) as a symbol for subtraction.

Describe the equal symbol (=) as a balance representing an equivalent relationship between expressions on either side of...

Use concrete materials to model, identify, and justify when two expressions are not equal (e.g., 10 - 3 is not equal to ...

Use concrete materials to model an equation that represents the relationship of two expressions of equal value. 

Write an equation that could be used to represent the solution to an oral, written, or picture problem.

The student will reason mathematically using nonstandard units to measure and compare objects by length, weight, and vol...

lengths of two objects (units laid end to end with no gaps or overlaps) and compare the measurements using the terms lon...

weights of two objects (using a balance scale or a pan scale) and compare the measurements using the terms lighter, heav...

volumes of two containers and compare the measurements using the terms more, less, or the same as.

Measure the length, weight, or volume of the same object or container with two different units and describe how and why ...

The student will describe, sort, draw, and name plane figures (circles, triangles, squares, and rectangles), and compose...

Describe triangles, squares, and rectangles using the terms sides, vertices, and angles. Describe a circle using terms s...

Sort plane figures based on their characteristics (e.g., number of sides, vertices, angles, curved).

Draw and name the plane figure (circle, square, rectangle, triangle) when given information about the number of sides, v...

Identify, name, and describe representations of circles, squares, rectangles, and triangles, regardless of orientation, ...

Recognize and name the angles found in rectangles and squares as right angles.

Compose larger plane figures by combining two or three simple plane figures (triangles, squares, and/or rectangles). 

The student will demonstrate an understanding of the concept of passage of time (to the nearest hour and half-hour) and ...

Identify different tools to measure time including clocks (analog and digital) and calendar.

Describe the units of time represented on a clock as minutes and hours. 

Tell time to the hour and half-hour, using analog and digital clocks.

Describe the location of the hour hand relative to time to the hour and half-hour on an analog clock.

Describe the location of the minute hand relative to time to the hour and half-hour on an analog clock. 

Match the time shown on a digital clock to an analog clock to the hour and half-hour. 

Identify specific days/dates on a calendar (e.g., What date is Saturday? How many Fridays are in October?). 

Use ordinal numbers first through tenth to describe the relative position of specific days/dates (e.g., What is the firs...

Determine the day/date before and after a given day/date (e.g., Today is the 8 th , so yesterday was the ?), and a date ...

The student will utilize flexible counting strategies to determine and describe quantities up to 120.

Count forward orally by ones from 0 to 120 starting at any number between 0 and 120.

Count backward orally by ones when given any number between 1 and 30.

Represent forward counting patterns when counting by groups of 5 and groups of 10 up to 120 using a variety of tools (e....

Represent forward counting patterns when counting by groups of 2 up to at least 30 using a variety of tools (e.g., beade...

Group a collection of up to 120 objects into tens and ones, and count to determine the total (e.g., 5 groups of ten and ...

Identify a penny, nickel, and dime by their attributes and describe the number of pennies equivalent to a nickel and a d...

Count by ones, fives, or tens to determine the value of a collection of like coins (pennies, nickels, or dimes), whose t...

The student will represent, compare, and order quantities up to 120. 

Read and write numerals 0-120 in sequence and out of sequence.

Estimate the number of objects (up to 120) in a given collection and justify the reasonableness of an answer. 

Create a concrete or pictorial representation of a number using tens and ones and write the corresponding numeral up to ...

Describe the number of groups of tens and ones when given a two-digit number and justify reasoning.

Compare two numbers between 0 and 120 represented pictorially or with concrete objects using the terms greater than, les...

Order three sets, each set containing up to 120 objects, from least to greatest, and greatest to least.

The student will use mathematical reasoning and justification to solve contextual problems that involve partitioning mod...

Represent equal shares of a whole with two or four sharers, when given a contextual problem.

Represent and name halves and fourths of a whole, using a region/area model (e.g., pie pieces, pattern blocks, paper fol...

Describe and justify how shares are equal pieces or equal parts of the whole (limited to halves, fourths) when given a c...

The student will identify, describe, extend, create, and transfer repeating patterns and increasing patterns using vario...

Identify and describe repeating and increasing patterns. 

Analyze a repeating or increasing pattern and generalize the change to extend the pattern using objects, colors, movemen...

Create a repeating or increasing pattern using objects, pictures, movements, colors, or geometric figures.

Transfer a repeating or increasing pattern from one form to another.

The student will apply the data cycle (pose questions; collect or acquire data; organize and represent data; and analyze...

Sort and classify concrete objects into appropriate subsets (categories) based on one or two attributes, such as size, s...

Describe and label attributes of a set of objects that has been sorted.

Pose questions, given a predetermined context, that require the collection of data (limited to 25 or fewer data points f...

Determine the data needed to answer a posed question and collect the data using various methods (e.g., counting objects,...

Organize and represent a data set by sorting the collected data using various methods (e.g., tallying, T-charts).

Represent a data set (vertically or horizontally) using object graphs, picture graphs, and tables.

ask and answer questions about the data represented in object graphs, picture graphs, and tables (e.g., total number of ...

draw conclusions about the data and make predictions based on the data.

The student will recall with automaticity addition and subtraction facts within 20 and estimate, represent, solve, and j...

Apply strategies (e.g., rounding to the nearest 10, compatible numbers, other number relationships) to estimate a soluti...

Apply strategies (e.g., the use of concrete and pictorial models, place value, properties of addition, the relationship ...

Represent, solve, and justify solutions to single-step and multistep contextual problems (e.g., join, separate, part-par...

Demonstrate fluency with addition and subtraction within 20 by applying reasoning strategies (e.g., doubles, near double...

Recall with automaticity addition and subtraction facts within 20.

Use patterns, models, and strategies to make generalizations about the algebraic properties for fluency (e.g., 4 + 3 is ...

Determine the missing number in an equation (number sentence) through modeling and justification with addition and subtr...

Use inverse relationships to write all related facts connected to a given addition or subtraction fact model within 20 (...

Describe the not equal symbol (≠) as representing a relationship where expressions on either side of the not equal symbo...

Represent and justify the relationship between values and expressions as equal or not equal using appropriate models and...

The student will reason mathematically using standard units (U.S. Customary) with appropriate tools to estimate, measure...

identifying a ruler as an instrument to measure length;

identifying different types of scales as instruments to measure weight; and

identifying different types of measuring cups as instruments to measure liquid volume.

the length of an object to the nearest inch, using a ruler; 

the weight of an object to the nearest pound, using a scale; and

the liquid volume of a container to the nearest cup, using a measuring cup.

The student will demonstrate an understanding of the concept of time to the nearest five minutes, using analog and digit...

Identify the number of minutes in an hour (60 minutes) and the number of hours in a day (24 hours). 

Determine the unit of time (minutes, hours, days, or weeks) that is most appropriate when measuring a given activity or ...

Show, tell, and write time to the nearest five minutes, using analog and digital clocks. 

Match a written time (e.g., 1:35, 6:20, 9:05) to the time shown on an analog clock to the nearest five minutes.

The student will identify, describe, and create plane figures (including circles, triangles, squares, and rectangles) th...

Explore a figure using a variety of tools (e.g., paper folding, geoboards, drawings) to show and justify a line of symme...

Create figures with at least one line of symmetry using various concrete and pictorial representations.

Describe the two resulting figures formed by a line of symmetry as being congruent (having the same shape and size).

The student will describe, name, compare, and contrast plane and solid figures (circles/spheres, squares/cubes, and rect...

Trace faces of solid figures (cubes and rectangular prisms) to create the set of plane figures related to the solid figu...

Compare and contrast models and nets (cutouts) of cubes and rectangular prisms (e.g., number and shapes of faces, edges,...

Given a concrete or pictorial model, name and describe the solid figure (sphere, cube, and rectangular prism) by its cha...

Compare and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms) accordi...

The student will utilize flexible counting strategies to determine and describe quantities up to 200.

Represent forward counting patterns when counting by groups of 2 up to at least 50, starting at various multiples of 2 a...

Represent forward counting patterns created when counting by groups of 5s, 10s, and 25s starting at various multiples up...

Describe and use patterns in skip counting by multiples of 2 (to at least 50), and multiples of 5, 10, and 25 (to at lea...

Represent forward counting patterns when counting by groups of 100 up to at least 1,000 starting at 0 using a variety of...

Represent backward counting patterns when counting by groups of 10 from 200 or less using a variety of tools including o...

Describe and use patterns in skip counting backwards by 10s (from at least 200) to justify the next number in the counti...

Choose a reasonable estimate up to 1,000 when given a contextual problem (e.g., What would be the best estimate for the ...

Represent even numbers (up to 50) with concrete objects, using two equal groups or two equal addends.

Represent odd numbers (up to 50) with concrete objects, using two equal groups with one leftover or two equal addends pl...

Determine whether a number (up to 50) is even or odd using concrete objects and justify reasoning (e.g., dividing collec...

The student will demonstrate an understanding of the ten-to-one relationships of the base 10 number system to represent,...

Write the three-digit whole number represented by a given model (e.g., concrete objects, pictures of base 10 blocks).

Read, write, and represent three-digit numbers in standard form, expanded form, and word form, using concrete or pictori...

Apply patterns within the base 10 system to determine and communicate, orally and in written form, the place (ones, tens...

Investigate and explain the ten-to-one relationships among ones, tens, and hundreds, using models.

Compose and decompose whole numbers up to 200 by making connections between a variety of models (e.g., base 10 blocks, p...

Plot and justify the position of a given number up to 100 on a number line with pre-marked benchmarks of 1s, 2s, 5s, 10s...

Compare two whole numbers, each 999 or less, represented concretely, pictorially, or symbolically, using words (greater ...

Order up to three whole numbers, each 999 or less, represented concretely, pictorially, or symbolically from least to gr...

The student will use mathematical reasoning and justification to solve contextual problems that involve partitioning mod...

Model and describe fractions as representing equal-size parts of a whole.

Describe the relationship between the number of fractional parts needed to make a whole and the size of the parts (i.e.,...

Compose the whole for a given fractional part and its value (in context) for halves, fourths, eighths, thirds, and sixth...

Using same-size fraction pieces, from a region/area model, count by unit fractions up to two wholes (e.g., zero one-four...

region/area models (e.g., pie pieces, pattern blocks, geoboards);

length models (e.g., paper fraction strips, fraction bars, rods, number lines); and

set models (e.g., chips, counters, cubes).

Compare unit fractions for halves, fourths, eighths, thirds, and sixths using words (greater than, less than or equal to...

The student will solve problems that involve counting and representing money amounts up to $2.00.

Identify a quarter and its value and determine multiple ways to represent the value of a quarter using pennies, nickels,...

Count by ones, fives, tens, and twenty-fives to determine the value of a collection of mixed coins and one-dollar bills ...

Construct a set of coins and/or bills to total a given amount of money whose value is $2.00 or less.

Represent the value of a collection of coins and one-dollar bills (limited to $2.00 or less) using the cent (¢) and doll...

The student will describe, extend, create, and transfer repeating and increasing patterns (limited to addition of whole ...

Identify and describe repeating and increasing patterns.

Analyze a repeating or increasing pattern and generalize the change to extend the pattern using objects, pictures, and n...

Create a repeating or increasing pattern using various representations (e.g., objects, pictures, numbers).

Transfer a given repeating or increasing pattern from one form to another (e.g., objects, pictures, numbers) and explain...

The student will apply the data cycle (pose questions; collect or acquire data; organize and represent data; and analyze...

Pose questions, given a predetermined context, that require the collection of data (limited to 25 or fewer data points f...

Determine the data needed to answer a posed question and collect the data using various methods (e.g., voting; creating ...

Organize and represent a data set using a pictograph where each symbol represents up to 2 data points. Determine and use...

Organize and represent a data set using a bar graph with a title and labeled axes (limited to 25 or fewer data points fo...

ask and answer questions about the data represented in pictographs and bar graphs (e.g., total number of data points rep...

draw conclusions about the data and make predictions based on the data.

The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including thos...

Determine and justify whether an estimate or an exact answer is appropriate when solving single-step and multistep conte...

Apply strategies (e.g., rounding to the nearest 10 or 100, using compatible numbers, using other number relationships) t...

Apply strategies (e.g., place value, properties of addition, other number relationships) and algorithms, including the s...

Identify and use the appropriate symbol to distinguish between expressions that are equal and expressions that are not e...

Represent, solve, and justify solutions to single-step and multistep contextual problems involving addition and subtract...

The student will recall with automaticity multiplication and division facts through 10 × 10; and represent, solve, and j...

Represent multiplication and division of whole numbers through 10 × 10, including in a contextual situation, using a var...

Use inverse relationships to write the related facts connected to a given model for multiplication and division of whole...

Apply strategies (e.g., place value, the properties of multiplication and/or addition) when multiplying and dividing who...

Demonstrate fluency with multiplication facts through 10 × 10 by applying reasoning strategies (e.g., doubling, add-a-gr...

Represent, solve, and justify solutions to single-step contextual problems that involve multiplication and division of w...

Recall with automaticity the multiplication facts through 10 × 10 and the corresponding division facts.

Create an equation to represent the mathematical relationship between equivalent expressions using multiplication and/or...

The student will reason mathematically using standard units (U.S. Customary and metric) with appropriate tools to estima...

Justify whether an estimate or an exact measurement is needed for a contextual situation and choose an appropriate unit.

length of an object to the nearest U.S. Customary unit (1 2 inch, inch, foot, yard) and metric unit (centimeter, meter);

weight/mass of an object to the nearest U.S. Customary unit (pound) and metric unit (kilogram); and 

liquid volume to the nearest U.S. Customary unit (cup, pint, quart, gallon) and metric unit (liter). 

Compare estimates of length, weight/mass, or liquid volume with the actual measurements. 

The student will use multiple representations to estimate and solve problems, including those in context, involving area...

describe and give examples of area as a measurement in contextual situations; and

estimate and determine the area of a given surface by counting the number of square units, describe the measurement (usi...

describe and give examples of perimeter as a measurement in contextual situations;

estimate and measure the distance around a polygon (with no more than six sides) to determine the perimeter and justify ...

given the lengths of all sides of a polygon (with no more than six sides), determine its perimeter and justify the measu...

The student will demonstrate an understanding of the concept of time to the nearest minute and solve single-step context...

Tell and write time to the nearest minute, using analog and digital clocks.

Match a written time (e.g., 4:38, 7:09, 12:51) to the time shown on analog and digital clocks to the nearest minute.

the starting time and the ending time, determine the amount of time that has elapsed;

the starting time and amount of elapsed time in one-hour increments, determine the ending time; or

the ending time and the amount of elapsed time in one-hour increments, determine the starting time.

The student will identify, describe, classify, compare, combine, and subdivide polygons. 

Describe a polygon as a closed plane figure composed of at least three line segments that do not cross.

Classify figures as polygons or not polygons and justify reasoning.

Identify and describe triangles, quadrilaterals, pentagons, hexagons, and octagons in various orientations, with and wit...

Identify and name examples of polygons (triangles, quadrilaterals, pentagons, hexagons, octagons) in the environment.

Classify and compare polygons (triangles, quadrilaterals, pentagons, hexagons, octagons).

Combine no more than three polygons, where each has three or four sides, and name the resulting polygon (triangles, quad...

Subdivide a three-sided or four-sided polygon into no more than three parts and name the resulting polygons.

The student will use place value understanding to read, write, and determine the place and value of each digit in a whol...

Read and write six-digit whole numbers in standard form, expanded form, and word form.

Apply patterns within the base 10 system to determine and communicate, orally and in written form, the place and value o...

Compose, decompose, and represent numbers up to 9,999 in multiple ways, according to place value (e.g., 256 can be 1 hun...

The student will demonstrate an understanding of the base 10 system to compare and order whole numbers up to 9,999.

Compare two whole numbers, each 9,999 or less, using symbols (>, <, =, ≠) and/or words (greater than, less than, equal t...

Order up to three whole numbers, each 9,999 or less, represented with and without models, from least to greatest and gre...

The student will use mathematical reasoning and justification to represent and compare fractions (proper and improper) a...

region/area models (e.g., pie pieces, pattern blocks, geoboards); 

length models (e.g., paper fraction strips, fraction bars, rods, number lines); and

set models (e.g., chips, counters, cubes).

Identify a fraction represented by a model as the sum of unit fractions.

Use a model of a fraction greater than one to count the fractional parts to name and write it as an improper fraction an...

Compose and decompose fractions (proper and improper) with denominators of 2, 3, 4, 5, 6, 8, and 10 in multiple ways (e....

Compare a fraction, less than or equal to one, to the benchmarks of 0, 1 2 , and 1 using area/region models, length mode...

Compare two fractions (proper or improper) and/or mixed numbers with like numerators of 2, 3, 4, 5, 6, 8, and 10 (e.g., ...

Compare two fractions (proper or improper) and/or mixed numbers with like denominators of 2, 3, 4, 5, 6, 8, and 10 (e.g....

Represent equivalent fractions with denominators of 2, 3, 4, 5, 6, 8, or 10, using region/area models and length models.

The student will solve problems, including those in context, that involve counting, comparing, representing, and making ...

Determine the value of a collection of bills and coins whose total is $5.00 or less.

Construct a set of bills and coins to total a given amount of money whose value is $5.00 or less. 

 Compare the values of two sets of coins or two sets of bills and coins, up to $5.00, with words (greater than, less tha...

Solve contextual problems to make change from $5.00 or less by using counting on or counting back strategies with concre...

The student will identify, describe, extend, and create increasing and decreasing patterns (limited to addition and subt...

Identify and describe increasing and decreasing patterns using various representations (e.g., objects, pictures, numbers...

Analyze an increasing or decreasing pattern and generalize the change to extend the pattern or identify missing terms us...

Solve contextual problems that involve identifying, describing, and extending patterns.

Create increasing and decreasing patterns using objects, pictures, numbers, and number lines.

Investigate and explain the connection between two different representations of the same increasing or decreasing patter...

The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and an...

Formulate questions that require the collection or acquisition of data.

Determine the data needed to answer a formulated question and collect or acquire existing data (limited to 30 or fewer d...

Organize and represent a data set using pictographs that include an appropriate title, labeled axes, and key. Each picto...

Organize and represent a data set using bar graphs with a title and labeled axes, with and without the use of technology...

describe the categories of data and the data as a whole (e.g., data were collected on preferred ways to cook or prepare ...

identify parts of the data that have special characteristics, including categories with the greatest, the least, or the ...

make inferences about data represented in pictographs and bar graphs;

use characteristics of the data to draw conclusions about the data and make predictions based on the data (e.g., it is u...

solve one- and two-step addition and subtraction problems using data from pictographs and bar graphs.

The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including thos...

Determine and justify whether an estimate or an exact answer is appropriate when solving contextual problems involving a...

Apply strategies (e.g., rounding to the nearest 100 or 1,000, using compatible numbers, other number relationships) to e...

Apply strategies (e.g., place value, properties of addition, other number relationships) and algorithms, including the s...

Estimate, represent, solve, and justify solutions to single-step and multistep contextual problems involving addition an...

The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including thos...

Determine and justify whether an estimate or an exact answer is appropriate when solving contextual problems involving m...

Recall with automaticity the multiplication facts through 12 × 12 and the corresponding division facts.*

Create an equation using addition, subtraction, multiplication, and division to represent the relationship between equiv...

Identify and use the appropriate symbol to distinguish between expressions that are equal and expressions that are not e...

Determine all factor pairs for a whole number 1 to 100, using concrete, pictorial, and numerical representations.

Determine common factors and the greatest common factor of no more than three numbers.

a two-digit factor and a one-digit factor;* 

a three-digit factor and a one-digit factor;* or

a two-digit factor and a two-digit factor.* 

Estimate, represent, solve, and justify solutions to single-step and multistep contextual problems that involve multipli...

Apply strategies (e.g., rounding, compatible numbers, place value) and algorithms, including the standard algorithm, to ...

Estimate, represent, solve, and justify solutions to single-step contextual problems involving division with whole numbe...

Interpret the quotient and remainder when solving a contextual problem.

The student will estimate, represent, solve, and justify solutions to single-step problems, including those in context, ...

Estimate and determine the sum or difference of two fractions (proper or improper) and/or mixed numbers, having like den...

Estimate, represent, solve, and justify solutions to single-step contextual problems using addition and subtraction with...

Solve single-step contextual problems involving multiplication of a whole number, limited to 12 or less, and a unit frac...

Apply the inverse property of multiplication in models (e.g., use a visual fraction model to represent 4 4 or 1 as the p...

The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including thos...

Apply strategies (e.g., rounding to the nearest whole number, using compatible numbers) and algorithms, including the st...

decimals do not exceed the thousandths; and

addends, subtrahends, and minuends are limited to four digits.

Estimate, represent, solve, and justify solutions to single-step and multistep contextual problems using addition and su...

The student will reason mathematically to solve problems, including those in context, that involve length, weight/mass, ...

length in both U.S. Customary (inch, foot, yard, mile) and metric units (millimeter, centimeter, meter);

weight/mass in both U.S. Customary (ounce, pound) and metric units (gram, kilogram); and

liquid volume in both U.S. Customary (cup, pint, quart, gallon) and metric units (milliliter, liter). 

length of an object to the nearest U.S. Customary unit (1 2 inch, 1 4 inch, 1 8 inch, foot, yard) and nearest metric uni...

weight/mass of an object to the nearest U.S. Customary unit (ounce, pound) and nearest metric unit (gram, kilogram); and

liquid volume to the nearest U.S. Customary unit (cup, pint, quart, gallon) and nearest metric unit (milliliter, liter)....

Compare estimates of length, weight/mass, or liquid volume with the actual measurements.

length (inches and feet, feet and yards, inches and yards);

weight/mass (ounces and pounds); and

liquid volume (cups, pints, quarts, and gallons).

The student will solve single-step and multistep contextual problems involving elapsed time (limited to hours and minute...

the starting time and the ending time, determine the amount of time that has elapsed in hours and minutes;

the starting time and amount of elapsed time in hours and minutes, determine the ending time; or

the ending time and the amount of elapsed time in hours and minutes, determine the starting time.

The student will use multiple representations to develop and use formulas to solve problems, including those in context,...

Use concrete materials and pictorial models to develop a formula for the area and perimeter of a rectangle (including a ...

Determine the area and perimeter of a rectangle when given the measure of two adjacent sides (in whole number units), wi...

Determine the area and perimeter of a square when given the measure of one side (in whole number units), with and withou...

Use concrete materials and pictorial models to explore the relationship between area and perimeter of rectangles.

Identify and represent rectangles with the same perimeter and different areas or with the same area and different perime...

Solve contextual problems involving area and perimeter of rectangles and squares.

The student will identify, describe, and draw points, rays, line segments, angles, and lines, including intersecting, pa...

Identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices.

Describe endpoints and vertices in relation to lines, line segments, rays, and angles. 

Draw representations of points, line segments, rays, angles, and lines, using a ruler or straightedge. 

Identify parallel, perpendicular, and intersecting lines and line segments in plane and solid figures, including those i...

Use symbolic notation to name points, lines, line segments, rays, angles, and to describe parallel and perpendicular lin...

The student will classify and describe quadrilaterals (parallelograms, rectangles, squares, rhombi, and/or trapezoids) u...

Develop definitions for parallelograms, rectangles, squares, rhombi, and trapezoids through the exploration of propertie...

Identify and describe points, line segments, angles, and vertices in quadrilaterals.

Identify and describe parallel, intersecting, perpendicular, and congruent sides in quadrilaterals.

parallel sides; 

perpendicular sides;

congruence of sides; and

number of right angles.

Denote properties of quadrilaterals and identify parallel sides, congruent sides, and right angles by using geometric ma...

Use symbolic notation to name line segments and angles in quadrilaterals.

The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (n...

Identify concrete models and pictorial representations of solid figures (cube, rectangular prism, square pyramid, sphere...

Identify and describe solid figures (cube, rectangular prism, square pyramid, and sphere) according to their characteris...

Compare and contrast plane and solid figures (limited to circles, squares, triangles, rectangles, spheres, cubes, square...

The student will use place value understanding to read, write, and identify the place and value of each digit in a nine-...

Read nine-digit whole numbers, presented in standard form, and represent the same number in written form.

Write nine-digit whole numbers in standard form when the numbers are presented orally or in written form. 

Apply patterns within the base 10 system to determine and communicate, orally and in written form, the place and value o...

The student will demonstrate an understanding of the base 10 system to compare and order whole numbers up to seven digit...

Compare two whole numbers up to seven digits each, using words (greater than, less than, equal to, not equal to) and/or ...

Order up to four whole numbers up to seven digits each, from least to greatest or greatest to least.

The student will use mathematical reasoning and justification to represent, compare, and order fractions (proper, improp...

Compare and order no more than four fractions (proper or improper), and/or mixed numbers, with like denominators by comp...

Compare and order no more than four fractions (proper or improper), and/or mixed numbers, with like numerators and unlik...

Use benchmarks (e.g., 0, 1 2 , or 1) to compare and order no more than four fractions (proper or improper), and/or mixed...

Compare two fractions (proper or improper) and/or mixed numbers using fractions with denominators of 12 or less, using t...

Represent equivalent fractions with denominators of 12 or less, with and without models.* 

Compose and decompose fractions (proper and improper) and/or mixed numbers with denominators of 12 or less, in multiple ...

Represent the division of two whole numbers as a fraction given a contextual situation and a model (e.g., 3 5 means the ...

The student will use mathematical reasoning and justification to represent, compare, and order decimals through thousand...

Investigate and describe the ten-to-one place value relationship for decimals through thousandths, using concrete models...

Represent and identify decimals expressed through thousandths, using concrete, pictorial, and numerical representations....

Read and write decimals expressed through thousandths, using concrete, pictorial, and numerical representations.

Identify and communicate, both orally and in written form, the place and value of each digit in a decimal through thousa...

Compare using symbols (<, >, =) and/or words (greater than, less than, equal to) and order (least to greatest and greate...

The student will reason about the relationship between fractions and decimals (limited to halves, fourths, fifths, tenth...

Represent fractions (proper or improper) and/or mixed numbers as decimals through hundredths, using multiple representat...

Identify and model equivalent relationships between fractions (proper or improper) and/or mixed numbers and decimals, us...

Write the decimal and fraction equivalent for a given model (e.g., 1 4 = 0.25 or 0.25 = 1 4 ; 1.25 = 5 4 or 11 4 ; 1.02 ...

The student will identify, describe, extend, and create increasing and decreasing patterns (limited to addition, subtrac...

Identify, describe, extend, and create increasing and decreasing patterns using various representations (e.g., objects, ...

Analyze an increasing or decreasing single-operation numerical pattern found in lists, input/output tables, or function ...

Given a rule, create increasing and decreasing patterns using numbers and input/output tables (including function machin...

Solve contextual problems that involve identifying, describing, and extending increasing and decreasing patterns using s...

The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and an...

Formulate questions that require the collection or acquisition of data.

Determine the data needed to answer a formulated question and collect or acquire existing data (limited to 10 or fewer d...

Organize and represent a data set using line graphs with a title and labeled axes with whole number increments, with and...

describe the characteristics of the data represented in a line graph and the data as a whole (e.g., the time period when...

identify parts of the data that have special characteristics and explain the meaning of the greatest, the least, or the ...

make inferences about data represented in line graphs;

draw conclusions about the data and make predictions based on the data to answer questions; and

solve single-step and multistep addition and subtraction problems using data from line graphs. 

The student will model and determine the probability of an outcome of a simple event.

Describe probability as the degree of likelihood of an outcome occurring using terms such as impossible, unlikely, equal...

Model and determine all possible outcomes of a given simple event where there are no more than 24 possible outcomes, usi...

Write the probability of a given simple event as a fraction between 0 and 1, where there are no more than 24 possible ou...

Determine the likelihood of an event occurring and relate it to its whole number or fractional representation (e.g., imp...

Create a model or contextual problem to represent a given probability.

The student will estimate, represent, solve, and justify solutions to single-step and multistep contextual problems usin...

Estimate the sum, difference, product, and quotient of whole numbers in contextual problems. 

sums, differences, and products do not exceed five digits;

factors do not exceed two digits by three digits; 

divisors do not exceed two digits; or 

dividends do not exceed four digits.

Interpret the quotient and remainder when solving a contextual problem.

The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including thos...

Determine the least common multiple of two numbers to find the least common denominator for two fractions. 

Estimate and determine the sum or difference of two fractions (proper or improper) and/or mixed numbers, having like and...

Estimate and solve single-step and multistep contextual problems involving addition and subtraction with fractions (prop...

Solve single-step contextual problems involving multiplication of a whole number, limited to 12 or less, and a proper fr...

The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including thos...

Apply estimation strategies (e.g., rounding to the nearest whole number, tenth or hundredth; compatible numbers, place v...

a two-digit factor and a one-digit factor (e.g., 2.3 × 4; 0.08 × 0.9; .16 × 5);* 

a three-digit factor and a one-digit factor (e.g., 0.156 × 4, 3.28 × 7, 8.09 × 0.2);* and

Estimate and determine the product of two numbers using strategies and algorithms, including the standard algorithm, whe...

Estimate and determine the quotient of two numbers using strategies and algorithms, including the standard algorithm, in...

quotients do not exceed four digits with or without a decimal point; 

quotients may include whole numbers, tenths, hundredths, or thousandths; 

divisors are limited to a single digit whole number or a decimal expressed as tenths; and 

no more than one additional zero will need to be annexed. 

Solve single-step and multistep contextual problems involving addition, subtraction, and multiplication of decimals by a...

Solve single-step contextual problems involving division with decimals by applying strategies (e.g., estimation, modelin...

The student will simplify numerical expressions with whole numbers using the order of operations.

Use order of operations to simplify numerical expressions with whole numbers, limited to addition, subtraction, multipli...

expressions may contain no more than one set of parentheses; 

simplification will be limited to five whole numbers and four operations in any combination of addition, subtraction, mu...

whole numbers will be limited to two digits or less; and

expressions should not include braces, brackets, or fraction bars. 

Given a whole number numerical expression involving more than one operation, describe which operation is completed first...

The student will reason mathematically to solve problems, including those in context, that involve length, mass, and liq...

length (millimeters, centimeters, meters, and kilometers);

mass (grams and kilograms); and

liquid volume (milliliters and liters).

length (millimeters, centimeters, and meters);

mass (grams and kilograms); and 

liquid volume (milliliters and liters).

length (millimeters, centimeters, meters, and kilometers);

mass (grams and kilograms); and

liquid volume (milliliters and liters).

The student will use multiple representations to solve problems, including those in context, involving perimeter, area, ...

Investigate and develop a formula for determining the area of a right triangle.

Estimate and determine the area of a right triangle, with diagrams, when the base and the height are given in whole numb...

Describe volume as a measure of capacity and give examples of volume as a measurement in contextual situations.

Investigate and develop a formula for determining the volume of rectangular prisms using concrete objects. 

Solve problems, including those in context, to estimate and determine the volume of a rectangular prism using concrete o...

Identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation. 

Solve contextual problems that involve perimeter, area, and volume in standard units of measure.

The student will classify and measure angles and triangles, and solve problems, including those in context.

Classify angles as right, acute, obtuse, or straight and justify reasoning.

Classify triangles as right, acute, or obtuse and equilateral, scalene, or isosceles and justify reasoning. 

Identify congruent sides and right angles using geometric markings to denote properties of triangles.

Compare and contrast the properties of triangles.

Identify the appropriate tools (e.g., protractor, straightedge, angle ruler, available technology) to measure and draw a...

Measure right, acute, obtuse, and straight angles, using appropriate tools, and identify measures in degrees.

Use models to prove that the sum of the interior angles of a triangle is 180 degrees and use the relationship to determi...

Solve addition and subtraction contextual problems to determine unknown angle measures on a diagram.

The student will use reasoning and justification to identify and represent equivalency between fractions (with denominat...

Use concrete and pictorial models to represent fractions with denominators that are thirds, eighths, and factors of 100 ...

Use concrete and pictorial models to represent decimals in their equivalent fraction form (thirds, eighths, and factors ...

Identify equivalent relationships between decimals and fractions with denominators that are thirds, eighths, and factors...

Compare (using symbols <, >, =) and order (least to greatest and greatest to least) a set of no more than four decimals ...

The student will demonstrate an understanding of prime and composite numbers, and determine the prime factorization of a...

Given a whole number up to 100, create a concrete or pictorial representation to demonstrate whether the number is prime...

Classify, compare, and contrast whole numbers up to 100 using the characteristics prime and composite.

Determine the prime factorization for a whole number up to 100.

The student will identify, describe, extend, and create increasing and decreasing patterns with whole numbers, fractions...

Identify, describe, extend, and create increasing and decreasing patterns using various representations (e.g., objects, ...

Analyze an increasing or decreasing single-operation numerical pattern found in lists, input/output tables, and function...

Solve contextual problems that involve identifying, describing, and extending increasing and decreasing patterns using s...

The student will investigate and use variables in contextual problems.

Describe the concept of a variable (presented as a box, letter, or other symbol) as a representation of an unknown quant...

Write an equation (with a single variable that represents an unknown quantity and one operation) from a contextual situa...

Use an expression with a variable to represent a given verbal expression involving one operation (e.g., “5 more than a n...

Create and write a word problem to match a given equation with a single variable and one operation.

The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and an...

Formulate questions that require the collection or acquisition of data.

Determine the data needed to answer a formulated question and collect or acquire existing data (limited to 30 or fewer d...

Organize and represent a data set using a line plot (dot plot) with a title, labeled axes, and a key, with and without t...

Organize and represent numerical data using a stem-and-leaf plot with a title and key, where the stems are listed in asc...

describe the characteristics of the data represented in a line plot (dot plot) and stem-andleaf plot as a whole (e.g., t...

make inferences about data represented in line plots (dot plots) and stem-and-leaf plots (e.g., based on a line plot (do...

identify parts of the data that have special characteristics and explain the meaning of the greatest, the least, or the ...

draw conclusions about the data and make predictions based on the data to answer questions; and

solve single-step and multistep addition and subtraction problems using data from line plots (dot plots) and stem-and-le...

The student will solve contextual problems using measures of center and the range. 

Describe mean as fair share.

Describe and determine the mean of a set of data values representing data from a given context as a measure of center. 

Describe and determine the median of a set of data values representing data from a given context as a measure of center.

Describe and determine the mode of a set of data values representing data from a given context as a measure of center.

Describe and determine the range of a set of data values representing data from a given context as a measure of spread. 

The student will determine the probability of an outcome by constructing a model of a sample space and using the Fundame...

Determine the probability of an outcome by constructing a sample space (with a total of 24 or fewer equally likely possi...

Determine the number of possible outcomes by using the Fundamental (Basic) Counting Principle.

The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mix...

Demonstrate/model multiplication and division of fractions (proper or improper) and mixed numbers using multiple represe...

Multiply and divide fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers ar...

Investigate and explain the effect of multiplying or dividing a fraction, whole number, or mixed number by a number betw...

Estimate, determine, and justify the solution to single-step and multistep problems in context that involve addition and...

Estimate, determine, and justify the solution to single-step and multistep problems in context that involve multiplicati...

The student will estimate, demonstrate, solve, and justify solutions to problems using operations with integers, includi...

Demonstrate/model addition, subtraction, multiplication, and division of integers using pictorial representations or con...

Add, subtract, multiply, and divide two integers.* 

Simplify an expression that contains absolute value bars | | and an operation with two integers (e.g., –|5 – 8| or |−12|...

Estimate, determine, and justify the solution to one and two-step contextual problems, involving addition, subtraction, ...

The student will identify the characteristics of circles and solve problems, including those in context, involving circu...

Identify and describe chord, diameter, radius, circumference, and area of a circle. 

Investigate and describe the relationship between diameter and radius

Investigate and describe the relationship between radius and circumference

Investigate and describe the relationship between diameter and circumference

Develop an approximation for pi (3.14) by gathering data and comparing the circumference to the diameter of various circ...

Develop the formula for circumference using the relationship between diameter, radius, and pi.

Solve problems, including those in context, involving circumference and area of a circle when given the length of the di...

The student will reason mathematically to solve problems, including those in context, that involve the area and perimete...

Develop the formula for determining the area of parallelograms and triangles using pictorial representations and concret...

Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.

The student will describe the characteristics of the coordinate plane and graph ordered pairs. 

Identify and label the axes, origin, and quadrants of a coordinate plane. 

Identify and describe the location (quadrant or the axis) of a point given as an ordered pair. Ordered pairs will be lim...

Graph ordered pairs in the four quadrants and on the axes of a coordinate plane. Ordered pairs will be limited to coordi...

Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate plane. Ordered pair...

Relate the coordinates of a point to the distance from each axis and relate the coordinates of a single point to another...

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to determine the length of a s...

The student will determine congruence of segments, angles, and polygons.

Identify regular polygons.

Draw lines of symmetry to divide regular polygons into two congruent parts.

Determine the congruence of segments, angles, and polygons given their properties.

Determine whether polygons are congruent or noncongruent according to the measures of their sides and angles.

The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fracti...

Estimate and determine the percent represented by a given model (e.g., number line, picture, verbal description), includ...

Represent and determine equivalencies among decimals (through the thousandths place) and percents incorporating the use ...

Represent and determine equivalencies among fractions (proper or improper) and mixed numbers that have denominators that...

Represent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that h...

Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than four positive rat...

The student will reason and use multiple strategies to represent, compare, and order integers. 

Represent integers (e.g., number lines, concrete materials, pictorial models), including models derived from contextual ...

Compare and order integers using a number line. 

Compare integers, using mathematical symbols (<, >, =).

Identify and describe the absolute value of an integer as the distance from zero on the number line.

The student will recognize and represent patterns with whole number exponents and perfect squares.

Recognize and represent patterns with bases and exponents that are whole numbers.

Recognize and represent patterns of perfect squares not to exceed 202 , by using concrete and pictorial models.

Justify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning. 

Recognize and represent powers of 10 with whole number exponents by examining patterns in place value.

The student will use ratios to represent relationships between quantities, including those in context.

Represent a relationship between two quantities using ratios.

Represent a relationship in context that makes a comparison by using the notations 𝑎 𝑏 , a:b, and a to b.

Represent different comparisons within the same quantity or between different quantities (e.g., part to part, part to wh...

Create a relationship in words for a given ratio expressed symbolically.

Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a ratio.

Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a contex...

The student will identify and represent proportional relationships between two quantities, including those in context (u...

Identify the unit rate of a proportional relationship represented by a table of values, a contextual situation, or a gra...

Determine a missing value in a ratio table that represents a proportional relationship between two quantities using a un...

Determine whether a proportional relationship exists between two quantities, when given a table of values, context, or g...

When given a contextual situation representing a proportional relationship, find the unit rate and create a table of val...

Make connections between and among multiple representations of the same proportional relationship using verbal descripti...

The student will write and solve one-step linear equations in one variable, including contextual problems that require t...

Identify and develop examples of the following algebraic vocabulary: equation, variable, expression, term, and coefficie...

Represent and solve one-step linear equations in one variable, using a variety of concrete manipulatives and pictorial r...

Apply properties of real numbers and properties of equality to solve a one-step equation in one variable. Coefficients a...

Confirm solutions to one-step linear equations in one variable using a variety of concrete manipulatives and pictorial r...

Write a one-step linear equation in one variable to represent a verbal situation, including those in context.

Create a verbal situation in context given a one-step linear equation in one variable.

The student will represent a contextual situation using a linear inequality in one variable with symbols and graphs on a...

Given the graph of a linear inequality in one variable on a number line, represent the inequality in two equivalent ways...

Write a linear inequality in one variable to represent a given constraint or condition in context or given a graph on a ...

Given a linear inequality in one variable, create a corresponding contextual situation or create a number line graph.

Use substitution or a number line graph to justify whether a given number in a specified set makes a linear inequality i...

Identify a numerical value(s) that is part of the solution set of a given inequality in one variable.

The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and an...

Formulate questions that require the collection or acquisition of data with a focus on circle graphs. 

Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various ...

Determine the factors that will ensure that the data collected is a sample that is representative of a larger population...

Organize and represent data using circle graphs, with and without the use of technology tools. The number of data values...

Analyze data represented in a circle graph by making observations and drawing conclusions.

Compare data represented in a circle graph with the same data represented in other graphs, including but not limited to ...

The student will represent the mean as a balance point and determine the effect on statistical measures when a data poin...

Represent the mean of a set of data graphically as the balance point represented in a line plot (dot plot). 

Determine the effect on measures of center when a single value of a data set is added, removed, or changed.

Observe patterns in data to identify outliers and determine their effect on mean, median, mode, or range.

The student will estimate, solve, and justify solutions to multistep contextual problems involving operations with ratio...

Estimate, solve, and justify solutions to contextual problems involving addition, subtraction, multiplication, and divis...

The student will solve problems, including those in context, involving proportional relationships.

Given a proportional relationship between two quantities, create and use a ratio table to determine missing values.

Write and solve a proportion that represents a proportional relationship between two quantities to find a missing value,...

Apply proportional reasoning to solve problems in context, including converting units of measurement, when given the con...

Estimate and determine the percentage of a given whole number, including but not limited to the use of benchmark percent...

Develop the formulas for determining the volume of right cylinders and solve problems, including those in contextual sit...

Develop the formulas for determining the surface area of rectangular prisms and right cylinders and solve problems, incl...

Determine if a problem in context, involving a rectangular prism or right cylinder, represents the application of volume...

Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a factor of 1 4 ...

Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a factor o...

The student will solve problems and justify relationships of similarity using proportional reasoning.

Identify corresponding congruent angles of similar quadrilaterals and triangles, through the use of geometric markings.

Identify corresponding sides of similar quadrilaterals and triangles.

Given two similar quadrilaterals or triangles, write similarity statements using symbols.

Write proportions to express the relationships between the lengths of corresponding sides of similar quadrilaterals and ...

Recognize and justify if two quadrilaterals or triangles are similar using the ratios of corresponding side lengths. 

Solve a proportion to determine a missing side length of similar quadrilaterals or triangles.

Given angle measures in a quadrilateral or triangle, determine unknown angle measures in a similar quadrilateral or tria...

Apply proportional reasoning to solve problems in context including scale drawings. Scale factors shall have denominator...

The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and an...

Compare and contrast properties of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoi...

Compare and contrast properties of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoi...

Compare and contrast properties of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoi...

Sort and classify quadrilaterals as parallelograms, rectangles, trapezoids, rhombi, and/or squares based on their proper...

Sort and classify quadrilaterals as parallelograms, rectangles, trapezoids, rhombi, and/or squares based on their proper...

Sort and classify quadrilaterals as parallelograms, rectangles, trapezoids, rhombi, and/or squares based on their proper...

Given a diagram, determine an unknown angle measure in a quadrilateral, using properties of quadrilaterals.

Given a diagram, determine an unknown side length in a quadrilateral using properties of quadrilaterals.

The student will apply dilations of polygons in the coordinate plane.

Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been dilated. Scal...

Sketch the image of a dilation of a polygon limited to a scale factor of 1 4 , 1 2 , 2, 3, or 4. The center of the dilat...

Identify and describe dilations in context including, but not limited to, scale drawings and graphic design.

The student will investigate and describe the concept of exponents for powers of ten and compare and order numbers great...

Investigate and describe powers of 10 with negative exponents by examining patterns.

Represent a power of 10 with a negative exponent in fraction and decimal form.

Convert between numbers greater than 0 written in scientific notation and decimals.*

Compare and order no more than four numbers greater than 0 written in scientific notation. Ordering may be in ascending ...

The student will reason and use multiple strategies to compare and order rational numbers.

Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare (using symbols <, >, =) and order (a set...

The student will recognize and describe the relationship between square roots and perfect squares.

Determine the positive square root of a perfect square from 0 to 400.*

Describe the relationship between square roots and perfect squares.* 

The student will investigate and analyze proportional relationships between two quantities using verbal descriptions, ta...

Determine the slope, m, as the rate of change in a proportional relationship between two quantities given a table of val...

Identify and describe a line with a slope that is positive, negative, or zero (0), given a graph. 

Graph a line representing a proportional relationship, between two quantities given an ordered pair on the line and the ...

Graph a line representing a proportional relationship between two quantities given the equation of the line in the form ...

Make connections between and among representations of a proportional relationship between two quantities using problems ...

The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable,...

Use the order of operations and apply the properties of real numbers to simplify numerical expressions. Exponents are li...

Represent equivalent algebraic expressions in one variable using concrete manipulatives and pictorial representations (e...

Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and propertie...

Use the order of operations and apply the properties of real numbers to evaluate algebraic expressions for given replace...

The student will write and solve two-step linear equations in one variable, including problems in context, that require ...

Represent and solve two-step linear equations in one variable using a variety of concrete materials and pictorial repres...

Apply properties of real numbers and properties of equality to solve two-step linear equations in one variable. Coeffici...

Confirm algebraic solutions to linear equations in one variable.

Write a two-step linear equation in one variable to represent a verbal situation, including those in context.

Create a verbal situation in context given a two-step linear equation in one variable.

Solve problems in context that require the solution of a two-step linear equation.

The student will write and solve one- and two-step linear inequalities in one variable, including problems in context, t...

Apply properties of real numbers and the addition, subtraction, multiplication, and division properties of inequality to...

Investigate and explain how the solution set of a linear inequality is affected by multiplying or dividing both sides of...

Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number...

Write one- or two-step linear inequalities in one variable to represent a verbal situation, including those in context.

Create a verbal situation in context given a one or two-step linear inequality in one variable. 

Solve problems in context that require the solution of a one- or two-step inequality.

Identify a numerical value(s) that is part of the solution set of as given one- or two-step linear inequality in one var...

Describe the differences and similarities between solving linear inequalities in one variable and linear equations in on...

The student will use statistical investigation to determine the probability of an event and investigate and describe the...

Determine the theoretical probability of an event.

Given the results of a statistical investigation, determine the experimental probability of an event.

Describe changes in the experimental probability as the number of trials increases.

Investigate and describe the difference between the probability of an event found through experiment or simulation versu...

The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and an...

Formulate questions that require the collection or acquisition of data with a focus on histograms.

Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various ...

Determine how sample size and randomness will ensure that the data collected is a sample that is representative of a lar...

Organize and represent numerical data using histograms with and without the use of technology

Investigate and explain how using different intervals could impact the representation of the data in a histogram.

Compare data represented in histograms with the same data represented in other graphs, including but not limited to line...

Analyze data represented in histograms by making observations and drawing conclusions. Determine how histograms reveal p...

The student will estimate and apply proportional reasoning and computational procedures to solve contextual problems.

Estimate and solve contextual problems that require the computation of one discount or markup and the resulting sale pri...

Estimate and solve contextual problems that require the computation of the sales tax, tip and resulting total.

Estimate and solve contextual problems that require the computation of the percent increase or decrease.

Identify and describe the relationship between pairs of angles that are vertical, adjacent, supplementary, and complemen...

Use the relationships among supplementary, complementary, vertical, and adjacent angles to solve problems, including tho...

The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-...

Determine the surface area of square-based pyramids by using concrete objects, nets, diagrams, and formulas. 

Determine the volume of cones and square-based pyramids, using concrete objects, diagrams, and formulas.

Examine and explain the relationship between the volume of cones and cylinders, and the volume of rectangular prisms and...

Solve problems in context involving volume of cones and square-based pyramids and the surface area of square-based pyram...

The student will apply translations and reflections to polygons in the coordinate plane.

Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated ve...

Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been reflected ove...

Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated an...

Sketch the image of a polygon that has been translated vertically, horizontally, or a combination of both. 

Sketch the image of a polygon that has been reflected over the x- or y-axis.

Sketch the image of a polygon that has been translated and reflected over the x- or y-axis, or reflected over the x- or ...

Identify and describe transformations in context (e.g., tiling, fabric, wallpaper designs, art).

The student will apply the Pythagorean Theorem to solve problems involving right triangles, including those in context.

Verify the Pythagorean Theorem using diagrams, concrete materials, and measurement.

Determine whether a triangle is a right triangle given the measures of its three sides.

Identify the parts of a right triangle (the hypotenuse and the legs) given figures in various orientations.

Determine the measure of a side of a right triangle, given the measures of the other two sides.

Apply the Pythagorean Theorem, and its converse, to solve problems involving right triangles in context.

The student will solve area and perimeter problems involving composite plane figures, including those in context. 

Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, circles, and semicircles. Dete...

Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, and semicircles. Use the attri...

Apply perimeter, circumference, and area formulas to solve contextual problems involving composite plane figures.

The student will compare and order real numbers and determine the relationships between real numbers.

Estimate and identify the two consecutive natural numbers between which the positive square root of a given number lies ...

Use rational approximations (to the nearest hundredth) of irrational numbers to compare, order, and locate values on a n...

Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than five real numbers...

The student will investigate and describe the relationship between the subsets of the real number system.

Describe and illustrate the relationships among the subsets of the real number system by using representations (e.g., gr...

Classify and explain why a given number is a member of a particular subset or subsets of the real number system.

Describe each subset of the set of real numbers and include examples and non-examples.

The student will represent, simplify, and generate equivalent algebraic expressions in one variable. 

Represent algebraic expressions using concrete manipulatives or pictorial representations (e.g., colored chips, algebra ...

Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and propertie...

The student will determine whether a given relation is a function and determine the domain and range of a function. 

Determine whether a relation, represented by a set of ordered pairs, a table, or a graph of discrete points is a functio...

Identify the domain and range of a function represented as a set of ordered pairs, a table, or a graph of discrete point...

The student will represent and solve problems, including those in context, by using linear functions and analyzing their...

Determine how adding a constant (b) to the equation of a proportional relationship y = mx will translate the line on a g...

Describe key characteristics of linear functions including slope (m), y-intercept (b), and independent and dependent var...

Graph a linear function given a table, equation, or a situation in context. 

Create a table of values for a linear function given a graph, equation in the form of y = mx + b, or context.

Write an equation of a linear function in the form y = mx + b, given a graph, table, or a situation in context.

Create a context for a linear function given a graph, table, or equation in the form y = mx + b.

The student will write and solve multistep linear equations in one variable, including problems in context that require ...

Represent and solve multistep linear equations in one variable with the variable on one or both sides of the equation (u...

Apply properties of real numbers and properties of equality to solve multistep linear equations in one variable (up to f...

Write a multistep linear equation in one variable to represent a verbal situation, including those in context.

Create a verbal situation in context given a multistep linear equation in one variable.

Solve problems in context that require the solution of a multistep linear equation.

Interpret algebraic solutions in context to linear equations in one variable.

Confirm algebraic solutions to linear equations in one variable.

The student will write and solve multistep linear inequalities in one variable, including problems in context that requi...

Apply properties of real numbers and properties of inequality to solve multistep linear inequalities (up to four steps) ...

Represent solutions to inequalities algebraically and graphically using a number line.

Write multistep linear inequalities in one variable to represent a verbal situation, including those in context.

Create a verbal situation in context given a multistep linear inequality in one variable.

Solve problems in context that require the solution of a multistep linear inequality in one variable.

Identify a numerical value(s) that is part of the solution set of a given inequality.

Interpret algebraic solutions in context to linear inequalities in one variable.

The student will use statistical investigation to determine the probability of independent and dependent events, includi...

Determine whether two events are independent or dependent and explain how replacement impacts the probability. 

Compare and contrast the probability of independent and dependent events. 

Determine the probability of two independent events. 

Determine the probability of two dependent events. 

The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and an...

Formulate questions that require the collection or acquisition of data with a focus on boxplots.

Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various ...

Determine how statistical bias might affect whether the data collected from the sample is representative of the larger p...

Organize and represent a numeric data set of no more than 20 items, using boxplots, with and without the use of technolo...

Identify and describe the lower extreme (minimum), upper extreme (maximum), median, upper quartile, lower quartile, rang...

Describe how the presence of an extreme data point (outlier) affects the shape and spread of the data distribution of a ...

Analyze data represented in a boxplot by making observations and drawing conclusions.

Compare and analyze two data sets represented in boxplots. 

Given a contextual situation, justify which graphical representation (e.g., pictographs, bar graphs, line graphs, line p...

Identify components of graphical displays that can be misleading. 

The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and an...

Formulate questions that require the collection or acquisition of data with a focus on scatterplots.

Determine the data needed to answer a formulated question and collect the data (or acquire existing data) of no more tha...

Organize and represent numeric bivariate data using scatterplots with and without the use of technology.

Make observations about a set of data points in a scatterplot as having a positive linear relationship, a negative linea...

Analyze and justify the relationship of the quantitative bivariate data represented in scatterplots. 

Sketch the line of best fit for data represented in a scatterplot.