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2nd Grade
Adding & Subtracting Fluently within 20
• Add by making a ten.
• Add and subtract on a number line
• Subtract by finding the difference on a number line.
• Add and subtract using fact families.
Add & Subtract within 100 to solve one- and two-step word problems.
* Solve word problems by counting.
* Solve word problem with missing parts by drawing bar.
* Solve two-step problems by writing an equation.
* Solve two-step problems by making a model.
Working with equal groups to gain foundations for multiplication.
* Determine whether a group contains an even or odd number.
* Use the digit in the ones place to determine if a number is even or odd.
* Understanding arrays.
* Count objects by using an array.
Understand the Place Value
* Understand the value of a number.
* Combine tens, ones, and hundreds to create numbers.
* Draw a visual representation of a 3-digit number.
* Understand the value of digits using pictures.
Count within 1000; skip-count by 5s, 10s, and 100s.
* Identify number patterns by skip-counting with base ten blocks.
* Identify patterns when counting by 5.
* Identify patterns when counting by 10.
* Identify patterns when counting by 100.
Compare two three-digit numbers.
* Compare numbers using a number chart and counting sequence.
* Identify an equal number of ones, tens, and hundred.
* Represent a 2-digit number using a place value model.
* Show numbers in different ways by taking models apart.
Fluently add and subtract within 100
* Add within 100 on an open number line.
* Add within 100 using base ten blocks.
* Subtract numbers within 100 using an open number line.
* Subtract numbers within 100 using base ten blocks.
Add up to four two-digit numbers
* Add three 2-digit numbers by decomposing.
* Add three and four 2-digit numbers by making 10s.
* Add up to four 2-digit numbers using place value.
* Add up to four 2-digit numbers using the properties of addition
Add and subtract within 1000.
* Add within 1000 using a number line.
* Add within 1000 using base 10 blocks.
* Subtract three-digit numbers with a number line.
* Subtract within 1000 using base 10 blocks.
Mentally Add & Subtract 10 or 100
* Mentally add 10 or 100 visualizing base ten blocks.
* Mentally add or subtract 10 using a hundreds chart.
* Mentally subtract 10 or 100 using base ten blocks.
* Subtract using expanded notation.
Explain why addition and subtraction works.
* Choose appropriate strategies to explain.
* Explain addition using place value.
* Explain subtraction by decomposing numbers.
* Explain subtraction using place value.
Choose the appropriate measurement tool
* Measure using a ruler
* Measure with foot and yard-length units
* Measure with inch length-units
* Measure in centimeter and meter-length units
Relate addition and subtraction to length.
* Solve length word problems using a bar model.
* Solve length word problems using a ruler.
* Solve length word problems using color tiles.
* Find unknowns by creating number bonds.
Work with time and money.
* Tell time using the hour hand
* Tell time to the nearest 5 minutes using analog and digital
* Solve money word problems using base ten blocks
* Count money by drawing pictures
Represent and interpret data
Create a data table
Display data from a word problem on a line plot
Collect data by recording tally marks in a table
Solve compare problems using information from a picture graph
Reason with shapes and their attributes
Draw a triangle
Draw a quadrilateral
Draw a hexagon
Draw a pentagon
Identifying shapes and their attributes
Identify triangles,
Identity quadrilaterals,
Identity pentagons
Identify hexagons
Partition a rectangle into rows and columns
Partition a rectangle into columns
Partition a rectangle into rows
Partition rectangles using same-sized squares
Find the number of same-size squares in a rectangles
Partition circles and rectangles into shares
Count unit fractions
Partition a circle into equal shares
Compare equal shares from different wholes
Partition a circle into two, three, or four equal shares
3rd Grade
Represent and solve problems involving multiplication & Division
* Represent equal groups using multiplication
* Solve multiplication problems by skip counting
* Understand division problems matching equations
* Solve division problems by subtracting equal groups
Use multiplication and division to solve word problems
* Understand multiplication problems using equal groups
* Solve word problems using the idea of equal groups
* Find the missing quotient in a division problem
* Solve division problems using properties of 1 and 0
Understand relationship between multiplication and division
* Understand the commutative property of multiplication in word
* Solve multiplication problems using distributive property
* Interpret division as an unknown factor problem using a bar
* Interpret division as an unknown factor problem using arrays
Multiplication and Division up to 100
* Understand division with 0 and 1
* Divide using fact families
* Multiply by combining known facts
* Solve multiplication problems using associative property
Identify and explain patterns in arithmetic
* Estimate solutions to two-step word problems
* Solve two-step problems using letters to represent unknowns
* Identify addition and subtraction patterns using a hundreds
* Find number patterns by using multiplication and division
Use place value understanding to round whole numbers
* Understand the value of a digit in a multi-digit number
* Find benchmark numbers using a number line
* Round to the nearest ten using base ten blocks
* Round to the nearest ten or hundred in real world situation
Fluently add and subtract within 1000
* Solve addition problems using partial sums
* Solve addition problems with numbers up to 1,000
* Solve subtraction problems using a number line
* Solve subtraction word problems by identifying key phrases
Multiply one-digit whole numbers by multiples of 10
* Multiply by multiples of 10 using number lines
* Multiply by multiples of 10 with base ten blocks
* Multiply by multiples of 10 by breaking apart the multiple
* Multiply by multiples of 10 using arrays
Understanding of fractions as numbers
* Understand fractions create mini-stories
* Count fractions to make 1 whole
* Represent fractions in different ways
* Solve fraction word problems using key words and pictures
Fraction on the number line
* Place fractions on a number line
* Plot a unit fraction on a number line
* Plot fractions greater than one on a number line
* identify a fraction as a point on a number line using area
Understand and generate equivalent fractions
* Identify equivalent fractions using fraction models
* Use a number line to generate equivalent fractions
* Generate equivalent fractions using fraction models
* Use area models to generate equivalent fractions
Express whole numbers as fractions & compare two fractions
* Express whole numbers as fractions
* Express fractions equivalent to 1 using a number line
* Compare unit fractions
* Recognize when comparisons are valid by reasoning
Tell and write time and solve word problems involving time
* Reading the exact minute on a clock
* Identifying the start time, change of time, and end time
* Solving elapsed time word problems to the nearest hour
* Solving elapsed time word problems to the nearest minute
Measure and estimate liquid volumes and solve word problems
* Find the volume of liquids
* Estimate the volume of a liquid
* Solve word problems about volume by adding and subtracting
* Solve multiplication and division word problems about volume
Solve problems involving mass of an object
* Find the mass of an object using a balance scale
* Measure mass in kilograms
* Solve mass and volume word problems using addition and subtraction
* Solve multiplication and division word problems about mass
Represent and interpret data
* Draw bars on a graph
* Label and title a graph
* Identify questions that can be answered using graphs
* Title and label graphs by looking at data collected
Solve one- and two-step problems using graphs
* One-step questions about a bar graph
* One-step questions about a picture graph
* Two-step questions about a picture graph
* Two-step story problems about a bar graph
Generate measurement data by measuring lengths using rulers
* Collect and display measurement data
* Collect and show data on a line plot
* Creating and reading a ruler to measure objects
* Measuring objects using whole, half, and quarter inches
Understand concepts of area measurement
* Cover the area of a shape using square unit
* Use equal square units to find the area
* Use grid paper to find the area
* Determine which unit of measurement to use to find the area
Measure areas by counting unit squares
* Determine which unit of measurement to use to find the area
* Find the area of a polygon using a key
* Find the area of a shape using a key to find the unit of measurement
* Find the area of a square or rectangle by counting unit square
Relate area to the operations of multiplication and addition
* Find area by counting square units
* Apply mathematical reasoning to a known area to find unknown
* Find area of a polygon using multiplication
* Find area using multiplication in real world problems
Find the area of a rectangle using side lengths
* Find the area of a rectangle by counting columns and rows
* Find the area of a rectangle by multiplying side lengths
* Find missing side lengths by drawing arrays
* Find the area of a rectangle using side lengths
Decompose area models & apply distributive property
* Decompose a rectangle
* Apply the distributive property using area models
* Use area models to represent the distributive property
* Find area by using multiplication
Find & recognize the perimeter
* Find perimeter with missing side lengths
* Find the perimeter of a polygon with more than 4 sides
* Use a chart to understand how rectangles
* Find the perimeter of a polygon in real world problems
Identify shapes in different categories
* Identify rectangles
* Identify rhombuses
* Identify squares
* Identifying trapezoids and parallelogram
Reason with shapes and their attributes
* Reason with shapes and their attributes
* Recognize shape attributes
* Identify a polygon by its attributes
* Sort quadrilaterals by their attributes
Partition shapes into parts, area of each part as a unit fraction
* Partition a shape into equal shares
* Count the unit fractions of one whole using fraction
* Describe a fraction as an equal share of a whole
* Write unit fractions as a number
4th Grade
Interpret a multiplication equation as a comparison
* The commutative property
* Compare numbers using bar models
* See multiplication as a comparison using number sentences
Multiply to solve word problems involving multiplicative comparison,
* Solve word problems by drawing pictures
*Solve multiplicative comparison word problems by using a multiply
* Solve multiplicative comparison word problems by using bar model
* Solve multiplicative comparison word problems using multiplies
Divide to solve word problems involving multiplicative comparison
* Interpret the remainder of a division problem
* Solve multiplicative comparison word problems by using a div
* Solve division work problems using a variable
* Represent unknown numbers using symbols or letters
Solve multi-step word problems posed with whole numbers
Solve multi-step problems using multiple operations
Solve multi-step word problems by writing two equations
Solve multi-step word problems by drawing a picture
Solve multi-step word problems using estimation
Solve multi-step word problems posed with whole numbers
Solve multi-step problems using multiple operations
Solve multi-step word problems by writing two equations
Solve multi-step word problems by drawing a picture
Solve multi-step word problems using estimation
Find all factor pairs for a whole number in the range 1-100
* Find all factor pairs of a number using a chart
* Find all the factor pairs of a number using area models
* Find multiples by using a number line
Determine whether a given whole number in the range 1-100
* Determine multiples of a number using a table
* Determine multiples of a number using area models
* Determine if a number is prime or composite
* Use divisibility rules to determine if a number is a multiple
Generate a number or shape pattern that follows a given rule
Generate a pattern sequence using a chart
Extend a fraction pattern using a number line
Find missing elements in growing patterns
Using a table to find the rule for a geometric shape pattern
Place Value for Multi-Digit Numbers
* Model numbers using base ten blocks
* Understand relationships between digits and their place value
* Use a place value chart and arrow cards to understand larger number
Find and compare using place values
* Find place value using pictures
* Compare numbers using place values
* Creating numbers based on given conditions
* Write numbers in word form using place values
Read and write multi-digit whole numbers
* Read and write numbers with zeros
* Read and write numbers in numeric form
* Read and write numbers in expanded form
* Write numbers in word form using punctuation
Use place value to round multi-digit whole numbers to any place
Round numbers to a specified place on a number line
Round numbers to the leading digit using a number line
Round number in real-life situations
Fluently add and subtract multi-digit whole numbers
Add using the standard addition algorithm
Subtract using an open number line
Subtract using the standard subtraction algorithm
Answer one-step questions about a bar graph by drawing
Multiply four digits by a one-digit whole number, and multiply two two-digit numbers
Solve 1 by 1 digit multiplication problems using area model
Use an area model for multiplication of two-digit numbers
Solve 2 by 2 digit multiplication problems using partial
Find remainders with up to four-digit dividends
Report remainders as whole numbers by drawing pictures
Divide two-digit dividends using multiples
Report remainders as fractions
Recognize and generate equivalent fractions
Create equivalent fractions using an area model
Create equivalent fractions using a number line
Recognize equivalent fractions using area models
Recognize equivalent fractions using number lines
Compare two fractions with different numerators and denominators
Compare fractions using a set model
Compare fractions using an area model
Compare fractions with different denominators
Compare fractions with different numerators and denominators
Compare fractions to a benchmark fraction such as 1/4, 1/2 & 3/4
Compare fractions to the same whole
Compare fractions to the benchmark of 1/2
Compare fractions to the benchmark of 1/4
Compare fractions to the benchmark of 3/4
Compare fractions to a benchmark fractions
Compare fractions to a benchmark of one using number lines
Compare fractions to a benchmark of one using area models
Compare fractions to a benchmark of one half using number line
Compare fractions to a benchmark of one half using area model
Create common denominators or numerators
Understand the denominator
Create common denominators using number lines
Create common denominators using area models
Create common denominators finding the least common multiple
Represent fraction results of comparisons
Identify fractions as values between 0 and 1
Represent a fraction greater than one using area models
Use a number line to represent a fraction greater than one
Addition and subtraction of fractions as joining and separating parts
Add fractions with like denominators using a number line
Add fractions by joining parts
Decompose a fraction into a sum of fractions using an area model
Subtract fractions by separating parts
Decompose a fraction into a sum of fractions with the same denominator
Subtract fractions with like denominators using a number line
Subtract fractions with like denominators using an area model
Decompose fractions into unit fractions
Add mixed numbers with like denominators
Add mixed numbers using a number line
Add mixed numbers by creating equivalent fractions
Add fractions with like denominators from two different whole
Add mixed numbers using properties of operations
Subtract mixed numbers with like denominators
Subtract mixed numbers using a number line
Subtract mixed numbers by creating equivalent fractions
Subtract fractions with like denominators labeling sets
Subtract mixed numbers by finding equivalent fractions
Solve word problems involving addition and subtraction of fractions
Add fractions with like denominators using visual models
Add fractions with like denominators by decomposing
Subtract fractions with like denominators using a number line
Subtract fractions with like denominators by decomposing
Understand a fraction a/b as a multiple of 1/b
Multiply fractions by whole numbers using repeated addition
Represent a fraction as the sum of unit fractions using number line
Write a fraction to describe part of a set
Write fractions of a set
Understand a multiple of a/b as a multiple of 1/b
Use repeated addition for multiplication of fractions
Use a fraction model for multiplication of fractions and whole
Estimate products in multiplication of whole numbers and fraction
Solve word problems involving multiplication of a fraction by a whole number
Solve problems involving a fraction and a whole number
Solve problems involving multiplying a fraction and a whole number
Solve word problems involving multiplying a fraction by a whole Number
Solve word problems involving multiplying a fraction
Express a fraction with denominator 10 as an equivalent fraction with denominator 100
Use a number line to show how fractions with denominators 10
Generate equivalent fractions using a grid model
Add fractions with denominators 10 and 100
Add fractions with tenths and hundredths denominators
Use decimal notation for fractions with denominators 10 or 100
Convert fractions into decimals to the tenths place
Convert fractions into decimals to the hundredths place
Convert decimals to fractions to the hundredths place
Compare two decimals to hundredths by reasoning about their size
Compare two decimal lengths using a ruler
Compare two decimals to the hundredths place
Compare two decimals to the hundredths place using fraction
Compare two decimal dollar amounts using coin values
Measurement units within one system of units
Recognize common units of measurement
Determine the correct unit to use when measuring
Measure weight in U.S. customary units
Convert a larger unit into a smaller unit
Compare and convert units of length, weight and volume
Compare and convert metric units of weight
Compare and convert metric units of volume
Compare and convert metric units of length
Compare and convert customary units of weight
Solve word problems involving distances, time,volumes, mass and money
Solve problems involving distance
Solve problems involving mass
Solve problems involving money
Solve problems involving volume
Solve problems involving time
Apply the area and perimeter formulas for rectangles
Apply area and perimeter formulas
Find the perimeter of a rectangle
Find the area of a rectangle
Find a missing rectangle side length using formulas
Solve problems addition and subtraction of fractions by using line plots
Create a line plot with fractions of a unit like denominatorsom
Create a line plot with fractions of a unit unlike denominators
Solve word problems involving the addition of fractions
Solve word problems involving the subtraction of fractions
Understand concepts of angle measurement
Identify angles using angle characteristics
Measure full and half rotations
Measure quarter and three-quarter rotations
Solve real world problems involving angle measurement
Measure angles in whole-number degrees using a protractor
Introduction to protractors
Measure angles to the nearest 10 by reading a protractor
Measure angles to the nearest degree with protractor
Sketch angles that are not multiples of 10 degrees
Solve addition and subtraction problems to find unknown angles
Compose and decompose angles
Find unknown angles using diagrams
Find unknown angles using angle properties
Write an equation to solve for a missing angle meas
Draw Lines, Angles, and Shapes
Classify and draw various types of angles
Draw geometric figures using their characteristics
Draw parallel and perpendicular lines
Draw points, lines, and line segments
Identifying Lines, Angles, and Shapes
Identify angles by comparing them to square angles
Identify geometric figures by observing characteristics
Identify points, lines, line segments, and rays
Identify points, lines, rays and angles in a two-dimensional
Classify two-dimensional figures
Classify parallelograms by examining their angles and sides
Classify polygons by observing the presence or absence of perpendicular lines
Classify quadrilaterals by examining their sides
Classify two-dimensional figures by examining their properties
Recognize right triangles as a category, and identify right triangle
Identify angles by comparing them to square angles
Identify geometric figures by observing characteristics
Identify points, lines, line segments, and rays
Identify points, lines, rays and angles in a two-dimensional
Recognize a line of symmetry for a two-dimensional figure
Identify line symmetry in a geometric figure
Identify line symmetry in irregular polygons
Identify line symmetry in regular polygons
Recognize a line of symmetry by folding a two-dimensional figure
5th Grade
Use parentheses, brackets, or braces in numerical expression
* Add parentheses to an expression to make it easier to solve
* Change the value of an expression by moving parentheses
* Determine if parentheses change the value of an expression
* Make equations with fractions or decimals true by adding
Write simple expressions that record calculations with numbers
* Write expressions to represent numerical situations
* Write a numerical expression to represent a verbal description
* Record a numerical expression as a written description
* Determine if a verbal description matches a numerical expressions
Use numerical expression to solve real world problems
* Describe relationships between expressions
* Compose a real world problem by interpreting a given numerical expression
* Represent a real world situation as a numerical expression
* Use expressions with parentheses to solve problems
Generate two numerical patterns & analyze patterns and relationships.
* Identify how patterns are related by making a chart
* Graph and compare patterns on a coordinate plane
* Identify numerical patterns by forming and graphing
* Identify patterns by sketching
Understand the place value system
* Understand the value of a digit using a place-value chart
* Use number lines to show decreases in place value
* Understand that the value of a digit in one place is 10 time
* Understand that a digit in one place is 1/10
Compare & recognize value of the digits
* Identify the value of a digit by looking at its place
* Compare the value of the digits in a decimal number
* Compare the value of the digits in a multi-digit whole number
* Recognize place value relationships by multiplying and divide
Explain patterns in the number of zeros of the product when multiplying
* Explain patterns in zeros when multiplying by a power of ten
* Multiply decimal numbers by a power of ten
* Multiply whole numbers and decimals by powers of ten
* Use whole number exponents to denote powers of ten
Explain patterns in the number of zeros of the product when dividing
* Understand how division by a power of ten causes decimal shifts
* Divide a whole number by a power of ten
* Divide whole numbers and decimals by powers of ten
* Write a value as a multiplication or division expression
Read and write decimals to thousandths using base-ten numerals
* Represent decimal values to the thousandths using base ten
* Read and write decimals to the thousandths using a place value
* Name decimals through the thousandths place
* Write decimals in expanded form
Compare two decimals to thousandths
* Compare decimals using base ten blocks
* Compare decimals using fractions
* Compare and order numbers written as fractions or decimals
* Compare and order numbers to the millions place
Use place value to round decimals to any place
* Round decimals to the nearest hundredth using a number line
* Round decimals to the nearest whole number using a number line.
* Round decimals to the nearest tenth
* Round decimals to the nearest hundredth
Fluently multiply multi-digit whole numbers using the standard algorithm
* Multiply multi-digit numbers using an area model
* Multiply multi-digit numbers using partial products
* Use partial products for multiplication
* Use the standard algorithm for multiplication
Four-digit dividends and two-digit divisors and explain by using rectangular array or area models
* Divide 4-digit dividends by 2-digit divisors by setting up
* Divide 4-digit dividends by 2-digit divisors by using a rectangular array
* Divide 4-digit dividends by 2-digit divisors by using expanded notation
* Divide decimals using knowledge of multiplication
Add and subtract decimals to hundredths, using concrete models or drawings
* Add decimals using a number line
* Subtract decimals using base-ten blocks
* Subtract decimals using a number line
* Estimate the addition and subtraction of decimals
Multiply and divide decimals to hundredths, using concrete models or drawings
* Multiply decimals by whole numbers by using an area model
* Multiply decimals to the hundredths by using fractions
* Divide decimals by using a number line
* Divide decimals using knowledge of multiplication
Add fractions with unlike denominators including mixed numbers
* Add fractions with different denominators using fraction bar
* Add fractions with unlike denominators by creating area model
* Add mixed numbers with unlike denominators using fraction base
* Add unlike fractions using equivalent fractions and the number
Subtract fractions with unlike denominators including mixed numbers
* Subtract fractions with different denominators using fraction
* Subtract fractions with unlike denominators by creating area
* Subtract unlike fractions using equivalent fractions
* Subtract mixed numbers with unlike denominators
Solve word problems involving addition and subtraction of fractions
* Write equations to solve word problems by determining key information
* Use a number line to solve word problems involving addition
* Solve word problems involving the addition and subtraction
* Solve word problems with subtraction of unlike denominators
Estimate answers to problems involving fractions
* Estimate answers to problems involving fractions using area model
* Estimate answers to problems involving fractions using number line
* Estimate the addition of fractions with unlike denominators
* Estimate mentally to assess the reasonableness of answers
Interpret a fraction as division of the numerator by the denominator
* Understand numerators and denominators
* Write fractions labeling important information
* Place improper fractions on a number line
* Express improper fractions as mixed numbers
Solve word problems involving multiplication & division of whole numbers
* Solve a division problem by writing a multiplication equation
* Solve division problems by partitioning the whole
* Solve word problems involving division of whole numbers
* Solve division story problems by representing the answers
Multiply a fraction or whole number by a fraction
* Multiply fractions by fractions using a sequence of operation
* Multiply a whole number by a fraction using area models
* Multiply by fractions using repeated addition
* Multiply fractions by fractions finding a part of a part
Find the area of a rectangle with fractional side lengths
* Find the area of a rectangle by multiplying a fraction
* Find the product of a fraction and a mixed number by using area models
* Find the product of a whole number and a fraction by using area models
* Multiply a whole number by a fraction using area models
Interpret multiplication as scaling by comparing & explaining
* Understand how numbers scale using multiplication
* Interpret multiplication as scaling using visual models
* Predict products by comparing factors
* Solve multiplication word problems by comparing the size of the product and factors
Solve real world problems involving multiplication of fractions and mixed numbers
* Multiply fractions by mixed numbers using visual representation
* Multiply a fraction by a whole number using visual representation
* Write equations to multiply fractions and mixed numbers
* Solve word problems with positive and negative fractions
Divide unit fractions by whole numbers and whole numbers by unit fractions
* Divide unit fractions by whole numbers by drawing a model
* Divide unit fractions by whole numbers by using the multiplication
* Divide a whole number by a unit fraction
* Divide by unit fractions using the number line
Solve real world problems involving division of unit fractions
* Solve word problems involving division of whole numbers
* Solve problems involving division of unit fractions by whole
* Solve word problems involving division of fractions by whole numbers
* Solve word problems involving division of whole numbers 1/2
Convert like measurement units within a given measurement system
* Select appropriate measurement conversions
* Solve multi-step word problems involving metric conversions
* Solve real world distance problems with unit conversions
* Solve real world mass problems with unit conversions
Make a line plot to display a data set of measurements
* Represent and interpret data
* Redistribute items equally using the information in a line
* Use the information from more than one line plot
* Solve multi-step word problem using information provided in line plot
Measurement: understand concepts of volume
* Understanding volume
* Describe cubic volume measures
* Find volume by counting cubes
* Find volume by counting cubes
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft
* Compute volume using knowledge of addition and multiplication
* Count unit cubes in a rectangular prism
* Identify and label three-dimensional figures
* Multiply and divide to find volume using improvised units
Find the volume of a right rectangular prism & apply formulas V = l × w × h and V = b × h
* Recognize that volume is additive by finding the volume
* Use volume to understand the associative property
* Find the volume of complex rectangular prisms
* Use multiplication (V = l x w x h) to find the volume
Graph points on the coordinate plane to solve real-world and mathematical problems
* Plot points on a coordinate plane
* Use a model to identify parts of a coordinate plane
* Move a point and describe its location on a coordinate plane
* Determine the shortest distance between two points on a coordinate plane
Classify two-dimensional figures into categories based on their properties
* Analyze and compare triangles by their sides
* Identify attributes of polygons
* Classify and compare quadrilaterals
* Classify quadrilaterals by looking at multiple attributes
6th Grade
Understand the concept of a ratio
* Identify part-to-part ratios using a diagram
* Identify part-to-total ratios using a diagram
* Identify all types of ratios using a diagram
* Understand the difference between fractions and ratios
Ratio relationship between two quantities
* Understand the importance of order in ratios
* Convert between part-to-part and part-to-total ratios by drawing a picture
* Understanding ratios and fractions by analyzing a picture
* Simplify ratios by finding patterns in a picture
Understand the concept of a unit rate
* Understand rates as a type of ratio
* Create unit rate using diagram
* Create unit rate using tape diagram
* Define unit rate using double number line
Make tables of equivalent ratios relating quantities
* Find missing values in ratio problems using a table
* Solve missing values in ratio problems using a double number line
* Solve missing values in ratio problems using multiplicative
* Graph ratios using a table
Use ratio and rate reasoning to solve real-world problems
* Solve rate problems using double number lines
* Solve rate problems using multiplicative reasoning
* Compare ratios using tables and percents
* Solve percent problems using a ratio table
Apply understanding of division to divide fractions by fractions.
* Use visual models for division of whole numbers by unit fraction
* Use models for division of fractions by fractions
* Divide fractions by fractions: using the common denominator
* Divide fractions by fractions: using the reciprocal
Apply understanding of multiplication fractions by fractions
* Divide mixed numbers: multiplying by the reciprocal
* Use bar models for multiplication of fractions by whole numbers
* Multiply fractions by fractions using area models
* Multiply fractions by fractions using an algorithm
Solve word problems involving division of fractions by fractions
* Solve word problems involving division of fractions by fraction
* Solve word problems involving division of fractions by whole numbers
* Solve word problems involving division of fractions by fractions using pictures
* Solve word problems involving division of mixed numbers and fractions
Fluently divide multi-digit numbers using the standard algorithm
* Divide 4-digit numbers by 2-digit numbers using long division
* Use double division to divide 4-digit numbers by 3-digit numbers
* Interpret and explain the long division algorithm
* Divide with three-digit divisors using the standard algorithm
Fluently add, subtract, multiply, and divide multi-digit decimals
* Multiply decimals
* Multiply multi-digit decimals using the standard algorithm
* Subtract multi-digit decimals using the standard algorithm
* Solve real-world problems with multi-digit decimals
Find the greatest common factor of two whole numbers
* Find the greatest common factor of two numbers
* Find the least common multiple of two numbers
* Find the GCF and LCM using prime factorization
* Find the GCF of two numbers using the distributive property
Understand positive and negative numbers
* Understand negative numbers using a number line
* Understanding positive and negative numbers using elevations
* Understanding positive and negative numbers with money
* Understanding positive and negative numbers with temperature
Recognize opposite signs of numbers
* Find opposite numbers on the number
* Locate positive rational numbers using a number line
* Understand the opposites of fractions by looking at a number
* Locate positive rational numbers using a number line
Understand & locate a point on coordinate plane
* Understand the coordinate plane as horizontal and vertical number lines
* Graph points on a coordinate plane
* Graph rational numbers on a coordinate plane
* Locate a point on the coordinate plane
Locate points are related by reflections across one or both axes
* Understand the coordinate plane as horizontal and vertical
* Reflect points over the x and y axes by using a coordinate plane
* Translate shapes across the x and y axes by using a coordinate plane
* Translate shapes across the x and y axes
Find and position integers and rational numbers
* Find the value of a number using its distance and direction
* Locate rational numbers using a number line
* Graph rational numbers on a coordinate plane
* Compare fractions using less than 12 or more than 12
Understand relationship & compare positive and negative numbers
* Understand the relationship between two numbers
* Understand the relationship between two negative numbers using a number line
* Compare two positive or negative numbers in real-world situation
* Compare more than two positive or negative numbers in real-world situations
Understand the absolute value of a rational number
* Find absolute value using a number line
* Use a number line to understand the relationship between rational numbers
* Understand how while the value of a negative number decreases
* Interpret absolute value in real-world situations
Solve real-world and mathematical problems by graphing points
* Use absolute value to find distances between points
* Find the distance between two points in different quadrants
* Graph and solve mathematical problems using a coordinate plane
* Graph and solve real-world problems using a coordinate plane
Write and evaluate numerical expressions involving whole-number exponents.
* Write numerical expressions involving whole-number exponents
* Evaluate numerical expressions by using whole-number exponents
* Write numerical expressions using area and volume models
* Write a numerical expression using exponents by interpreting a problem
Write & read algebraic expressions in which letters stand for numbers
* Write word problems as algebraic expressions
* Read and write algebraic expressions using parentheses
* Simplify addition and subtraction expressions combining
* Simplify multiplication and division expressions combining
Identify & evaluate algebraic expressions at specific values
* Evaluate algebraic expressions with exponents
* Evaluate one-step algebraic expressions by substitution
* Evaluate multiple step algebraic expressions by substitution
* Write and evaluate algebraic expressions using formulas
Apply properties of operations to produce equivalent expression
* Write equivalent expressions using the Additive Identity Property
* Write equivalent expressions using the Distributive Property of Multiplication
* Write equivalent expressions using the Additive Inverse Property
* Write equivalent expressions using the Multiplicative Inverse Property
Create and apply equivalent expression using diagrams
* Create an equivalent expression using the standard algorithm
* Create equivalent expressions using diagrams
* Apply the distributive property using diagrams
* Factor expressions using the distributive property and area models
Simplify & regroup algebraic expression
* Simplify algebraic expressions by combining like terms
* Simplify algebraic expressions by applying the distributive property
* Regroup with distributive property by using a visual model
* Simplify algebraic expressions by combining like terms and applying the distributive property
Read and write equivalent expressions with variables
* Read and write equivalent expressions with variables
* Write equivalent expressions by combining like terms
* Write equivalent expressions using visual area model
Understand solving an equation or inequality as a process of answering a question
* Understand equations using a bar model
* Distinguish between equalities and equations
* Understand that equations have one solution using a pan balance
* Understand that inequalities have more than one solution using a number line
Use variables to represent numbers and write expressions
* Understand how variables are used
* Write algebraic expressions using addition and subtraction
* Write an algebraic expression for a real-world scenario addition
* Write an algebraic expression for a real-world scenario multiply
Solve real-world and mathematical problems by writing and solving equations
* Solve algebraic equations involving addition and subtraction
* Solve addition and subtraction problems using 1-step equation
* Solve real-world problems using multiplication and division
* Write an algebraic equation from a real-world scenario
Write an inequality of the form
* Graph an inequality
* Compare inequalities
* Write and graph inequalities shopping
* Write and graph inequalities temperature
Analyze relationships between dependent and independent variables
* Identify variables and their relationship in a real-world situation
* Use a graph and a table to interpret independent and dependent variables
* Identify independent and dependent variables
* Relate independent and dependent variables using a function table
Find the area of right triangles, other triangles, and polygons
* Find the area of a parallelogram by decomposing.
* Find the area of a right triangle
* Find the area of a trapezoid by composing a parallelogram
* Find the area of polygons by decomposing into triangles, rectangles, parallelograms, and trapezoids
Find the volume of a right rectangular prism
* Find the volume of a rectangular prism: using unit cubes
* Find the volume of a fractional rectangular prism: using unit cubes
* Find the volume of a 3-dimensional figure composed of 2 rectangular prisms
* Find the volume of a rectangular prism by filling it with unit cubes
Draw polygons in the coordinate plane given coordinates for the vertices
* Draw polygons using given coordinates as vertices
* Find perimeter and area by finding the length of sides using coordinates
* Determine unknown ordered pairs using the characteristics of polygons
* Find distances on a map by comparing ordered pairs
Represent three-dimensional figures and use the nets to find the surface area
* Identify the parts of three-dimensional solids
* Represent three-dimensional figures with nets
* Analyze rectangular prisms to find congruent faces
* Analyze triangular prisms to find surface area
* Use congruent faces to find the surface area of rectangular prisms
Understand that a set of data collected
* Find the mean of a data set
* Use and find the range of a data set
* Describe the distribution of data using the mean absolute deviation
* Analyze the shape of a graph to describe the distribution of data
Recognize that a measure of center for a numerical data set
* Summarize the spread of data using range and mean absolute deviation
* Identify clusters, peaks and gaps in a dot plot
* Distinguish between measure of center and measure of variance
* Solve a real-world problem involving measures of center and variance
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
* Construct a dot plot
* Describe a data set
* Choose the best graph for a data set using measures of center
* Describe attributes of a data set by analyzing line plots, histograms, and box plots
Summarize numerical data sets in relation to their context
* Summarize a data set using the mean, median, and mode
* Describe the spread of data by finding range, and mean absolute
* Describe patterns in data sets
* Choose the best measure of center and variability
7th Grade
Compute unit rates associated with ratios of fractions
* Determine unit rates using a table
* Understand unit rates using fractional rates
* Find unit rates in situations involving fractions
* Find the best deal by comparing unit rates
Decide whether two quantities are in a proportional relationship
* Analyze a table to find proportional relationships
* Convert between currencies and find exchange rate
* Determine if two rates are equivalent by graphing
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams
* Identify the constant of proportionality in graphs
* Identify the constant of proportionality from a diagram
* Identify the constant of proportionality by writing an equation in the form y=mx
* Identify rates from verbal descriptions
Represent proportional relationships by equations
* Write an equation that represents a proportional relationship
* Determine the best deal by comparing equations
* Write an equation that expresses the relationship between distance and time
* Write equations to represent the proportional relationship between amount of change
Explain what a point (x, y) on the graph of a proportional relationship
* Graph a proportional relationship using a table
* Describe the relationship between measures by examining
* Evaluate specific points on a graph of a proportional relationship
* Identify proportional relationships by examining the origin
Use proportional relationships to solve percent problems
* Understand percent problems
* Apply taxes, tips, and discounts using a proportion and scale
* Calculate percent increase and decrease in context
* Calculate percent of a number using a proportion model
Use proportional relationships solve multistep ratio & percent problems
* Solve for an unknown percentage
* Solve multi-step ratio and percent problems using proportion
* Solve multistep percent problems using proportions and equation
* Solve percent of a number problems using a proportion model
Represent addition and subtraction on a horizontal or vertical number line
* Determine the values of opposite numbers using a number line
* Understand the concept of additive inverse
* Determine which values combine to make 0
* Find the additive inverse using an equation
Describe situations in which opposite quantities combine to make 0
* Combine opposite quantities to make zero using a number line
* Create zero pairs using integer
* Combine opposite numbers on a number line
* Combine opposite rational numbers on a number line
Add integers with the same & different signs
* Add integers using a number line
* Add integers using color counters
* Add integers with the same sign
* Add integers with different signs
Interpret sums of rational numbers by describing real-world contexts.
* Add integers with the same sign using number lines
* Add rational numbers using algorithms and number lines
* Adding integers with opposite signs using an algorithm
* Solve word problems with rational numbers
Subtract Integers using number line & place value
* Subtract integers by adding the additive
* Subtract integers using integer
* Subtract integers using number lines
* Subtract decimals: using place value chart
Understand subtraction of rational numbers as adding the additive inverse
* Understand subtraction as adding the additive inverse
* Subtract integers by adding the additive inverse
* Find the distance between two points using absolute value
* Subtract rational numbers in real-world contexts
Apply properties of operations as strategies to add rational numbers
* Add mixed fractions using improper fractions
* Adding positive and negative integers on a number line
* Adding two positive or two negative integers on a number line
* Demonstrate the Commutative Property of Addition with a number
Apply properties of operations as strategies to subtract rational numbers
* Subtract mixed numbers regrouping
* Subtract integers using the take away definition of subtract
* Subtract integers using the difference definition of subtract
* Determine the distance between integers
Apply and extend previous understandings of multiplication and of fractions
* Multiply fractions less than one using rectangular models
* Multiply two positive or two negative integers on a number line
* Solve multiplication problems by using the distributive property
* Solve multiplication problems using the commutative and associative properties
Apply and extend previous understandings of division and of fractions
* Multiply to divide proper and improper fractions
* Rewrite division problems using the commutative property
* Rewrite problems with rational numbers using different properties of * Multiplication and division
Use the commutative property to solve division problems
Multiply positive and negative integers using distributive property
* Prove that a negative times a negative equals a positive
* Multiply positive and negative integers by noticing patterns
* Multiply positive and negative integers using the distributive property
* Multiply a negative by a negative using the distributive property
Understand that integers can be divided, provided that the divisor is not zero
* Use division concepts to understand where to put the negative sign in a fraction
* Understand dividing by zero
* Dividing with zero
* Divide positive and negative integers by observing patterns
Mulitply and determine the product of the two integers and describe in real world context
* Multiply a positive integer by a negative integer by thinking about equal groups
* Multiply a negative integer by a positive integer by thinking about equal groups
* Multiply a negative integer by a negative integer by thinking about equal groups
* Multiply integers using the money model
Interpret quotients of rational numbers by describing real-world contexts.
* Understand rational quotients
* Rewrite negative fractions
* Compare fraction and decimal division
Convert a rational number to a decimal using long division
* Understand relationship between fractions and decimals
* Convert fractions and mixed numbers to decimals
* Determine whether a fraction will convert to a repeating decimal
* Convert fractions to decimals using division
Solve real-world and mathematical problems involving rational numbers
* Use addition and subtraction to solve real-world problems involving fractions
* Use addition and division to solve real-world problems with rational numbers
* Simplify expressions with order of operations
Apply properties of operations as strategies and expand linear expressions
Add linear expressions by combining like terms
Expand linear expressions using the distributive property
Expand linear expressions with fractions using the distribution
Factor an expression
Apply properties of operations as strategies and simplify an expression
* Simplify an expression by distributing a negative
* Simplify an expression with a fraction by adding or subtract
* Simplify an expression with a fraction using the distributive
* Simplify expressions using distribution and combining
Understand that rewriting an expression in different forms
* Rewrite an expression by expanding it
* Write a percent decrease problem as a product of the original
* Write an expression to find the cost of a discounted item
* Write an expression to find the cost of an item with tax
Solve real-life and mathematical problems using numerical and algebraic expressions and equation
* Solve problems using a chart
* Solve multi-step problems by creating diagrams
* Describe a real-world situation with an equation
* Solve problems by writing and solving equations
Solve problems involving scale drawings of geometric figures
* Generate a scale drawing
* Generate a scale drawing using fraction and decimal scale factors
* Identify scale factors using rectangle side length
* Calculate distance on a map using a scale
Draw geometric shapes with given conditions.
* Draw geometric shapes given the length of sides
* Draw triangles using given angles
* Draw a polygon using more than one condition
* Determine if given measurements will allow you to create shape
Describe the two-dimensional figures that result from slicing three-dimensional figures
* Describe 2-dimensional cross sections of right rectangular prisms
* Describe 2-dimensional cross sections of right rectangular pyraminds
Know the formulas for the area and circumference of a circle
* Determine the measures of a circle
* Find the area of a circle
* Find the circumference of a circle
Use facts about supplementary, complementary, vertical, and adjacent angles
* Find angle measurements using complementary and supplementary angles
* Use vertical and adjacent angles to find unknown angles
* Write and solve equations using complementary and supplementary angle
* Write equations for problems using facts about angle relation
Solve real-world and mathematical problems involving area, volume and surface area
* Choose the appropriate measurement for solving a problem
* Find missing dimensions using the volume formula
* Find surface area of cubes and prisms by pulling them apart
* Find surface area of cubes and prisms using formulas
Understand random sample & representative samples
* Identify a random sample
* Identify a representative sample
* Generate a representative sample
* Understanding biased samples
Use data from a random sample to draw inferences about a population
* Make inferences about a population by analyzing random sample
* Use proportional reasoning to make estimates about a population
* Make estimates about a population using the mean of multiple
Informally assess two numerical data distributions with similar variability
* Compare two data sets by looking at their means and mean absolute deviations
* Compare two data sets by looking at their medians and ranges
* Use variability and measures of center to persuade
* Analyze deceptive advertising using measures of center
Draw informal comparative inferences about two populations
* Compare populations using mean
* Compare two populations using the median
* Compare two populations using mean absolute deviation
* Compare two populations using range and interquartile range
Understand probability of a chance event is a number between 0 and 1
* Calculate the probability of an event by creating a ratio
* Describe the probability of an event using a number line
* Calculate the probability of an event by making a sum of 1
Approximate the probability of a chance event by collecting data
* Find the experimental probability by creating a ratio
* Compare experimental and theoretical probability to interpret data
* Predict the frequency of an event using results from experiments
* Predict the frequency of an event using the theoretical probability
Develop a probability model and use it to find probabilities of events
* Analyze the probability of an event by assigning equal probability
* Find the probability of events with multiple possibilities
* Understand the law of large numbers by comparing experimental
Find probabilities of compound events using organized lists, tables, tree diagrams
* Analyze independent and dependent events
* Find the probability of a compound event by creating an organized list
* Find the probability of a compound event by creating a table
* Find the probability of a compound event by creating a tree
8th Grade
Know that there are numbers that are not rational, and approximate them by rational numbers.
Understand and apply the definition of rational numbers
Convert repeating decimals into fractions
Know and apply the properties of integer exponents
* Apply a negative exponent using patterns and rules
* Apply a zero exponent using patterns and rules
* Apply exponents to negative bases
* Evaluate expressions involving exponents
Divide exponential expressions
* Divide exponential expressions
* Divide exponential expressions by noticing patterns
* Divide exponential expressions when exponent in denominator
Simplify equivalent expressions
* Simplify exponential multiplication expressions
* Simplify expressions with 0 and negative exponents
* Simplify expressions with negative exponents
Multiply exponential expressions & convert to scientific notation
* Multiply two or more exponential expressions
* Multiply numbers expressed in scientific notation
* Convert from standard to scientific notation
Use square root and cube root symbols to represent solutions to equations
* Simplify expressions involving square roots
* Understand the relationship between squaring and taking the square roots
* Use squares to find side length of a square
* Solve problems with inverse of squares and square roots
Write & compare small and large numbers in scientific notation
Write small numbers in scientific notation
Write large numbers in scientific notation
Compare small numbers using scientific notation
Compare large numbers using scientific notation
Perform operations with numbers expressed in scientific notation
* Multiply numbers in scientific notation
* Use scientific notation to estimate products
* Divide numbers in scientific notation
* Use scientific notation to estimate quotients
Graph proportional relationships, interpreting the unit rate as the slope of the graph
* Understand proportional relationships by relating graphs and equations
* Display all possibilities in a proportional relationship by graphing
* Find a unit rate using a graph
* Find a fractional unit rate using a graph
Use similar triangles to explain why the slope m is the same
* Find coordinates of points on a straight line
* Find the slope of a line on the coordinate plane
* Describe a line with a unique slope
* Describe positive and negative slopes
Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line
* Derive y=mx using similar triangles
* Derive y=mx+b using similar triangles
Solve linear equations with one solution, many solutions, or no solutions
* Understand a linear equation with one solution
* Understand a linear equation that has no solutions
* Solve equations with no solutions
* Solve equations with infinite solutions
Solve linear equations collecting like terms
* Solving linear equations with a variable on each side
* Solve equations with variables on both sides
* Solve linear equations by combining like terms
* Solving linear equations by choosing from among different techniques
Solve linear equations with rational number
Solving linear equations with decimal coefficient
Solve linear equations with fractional coefficients
Solve linear equations with rational numbers by using integers
Solve linear equations with rational numbers using decimal
Solve linear equations with rational numbers using fractions
Solve linear equations with rational numbers using mixed number
Understand that solutions to a system of two linear equations in two variables
* Determine whether two lines intersect
* Decide whether a point is a solution to a pair of linear equations
* Find the solution to a pair of linear equations by using tables
* Solve pairs of linear equations using patterns
Understand that solutions to a system of two linear equations in two variables
* Determine whether two lines intersect
* Decide whether a point is a solution to a pair of linear equations
* Find the solution to a pair of linear equations by using tables
* Solve pairs of linear equations using patterns
Solve systems of two linear equations in two variables and estimate solutions by graphing
* Solve systems of equations graphing
* Solve systems of equations using elimination
* Solve linear systems algebraically using visual models
* Solve systems of equations through trial and error
Understand & Identify a function
* Identify a function
* Identify function properties
* Identify a function from a graph
* Understand a function as a type of relation
The graph of a function is the set of ordered pairs
* Determine whether a graph is a function
* Define a function by looking at its parts
* Determine whether a set of ordered pairs represents a function
* Determine whether a set of points plotted on a graph is a function
Compare properties of two functions each represented in a different way
* Compare two functions by analyzing an equation and a graph
* Compare two functions by analyzing an equation and a table
* Compare two functions by analyzing an equation and a verbal description
Interpret the equation y = mx + b as defining a linear function
* Identify a linear function by analyzing characteristics of a linear fraction
* Analyze Tables of y = x and y = mx
* Analyze graphs and tables of y = mx + b
* Analyze graphs of y = x and y = mx
Construct a function to model a linear relationship between two quantities.
* Construct a linear function
* Construct linear functions from tables
* Create equation, table, and graph from a situation
* Construct a function by solving for unknown information
Determine the rate of change and initial value of the function
* Determine initial value in a linear relationship
* Determining the constant rate of change
* Determining the y-intercep
* Interpreting slope and y-intercept in context
Describe qualitatively the functional relationship between two quantities
* Compare two linear relations
* Describe function relationships using graphs
* Describe the rate of change on an interval using a graph
* Create a verbal description of a linear relation given a graph
Verify experimentally the properties of rotations, reflections, and translations
*Explore reflections by investigating their effects on line segment and angles
*Explore rotations by investigating their effects on line segment and angles
*Explore translations by investigating their effects on line segment and angles
*Identify what changes and what stays the same when sliding a parallelogram
Verify experimentally the properties of rotations, reflections, and translations
*Explore reflections by investigating their effects on line segment and angles
*Explore rotations by investigating their effects on line segment and angles
*Explore translations by investigating their effects on line segment and angles
*Identify what changes and what stays the same when sliding a parallelogram
Understand that a two-dimensional figure is congruent
* Identify congruent figures
* Recognize congruence by analyzing the sequence of steps
* Demonstrate congruence using a transformation sequence
* Assess congruence using transformation
Apply and assess congruence to rotation, reflections & transformations
* Apply properties of congruence to rotations
* Apply the properties of congruence to reflections
* Investigate translations
* Assess congruence using multiple transformations
Describe the effect of dilations, translations, rotations, and reflections
* Understand how reflections and rotations change coordinates
* Understand how translations change coordinates
* Analyze dilation of parallelograms
* Describe translations using coordinates
Use informal arguments to establish facts about the angle sum and exterior angle of triangles
* Prove two figures are similar after a dilation
* Determine similarity by comparing angles
* Relate angles and transversals
* Understand the properties of the interior angles of triangle
* Understand the relationship between exterior angles
Explain a proof of the Pythagorean Theorem and its converse.
* Identify properties of right triangles
* Apply the Area of Squares Proof to determine if a triangle
* Use the Area of Squares Proof to relate side lengths of a right triangle
* Use the Pythagorean Theorem to see if a triangle is a right
Apply the Pythagorean Theorem in real-world and mathematical problems
* Apply the Pythagorean Theorem to three dimensional figures
* Find the length of the hypotenuse of a right triangle using pythagorean theorem
* Solve for diagonals in rectangular prisms by applying the pythagorean theorem
* Solve for unknown side lengths using the Pythagorean Theorem
Apply the Pythagorean Theorem to find the distance between two points
* Find distance between two points on the coordinate plane using the Pythagorean theorem
* Find the length of a line segment on the coordinate plane using Pythagorean
* Find the distance between two points on the same axis on a coordinate grid
* Find the perimeter of a two dimensional figure on the coording plane
* Solve real-world, mathematical problems involving coordinate plane
Solve real world problem of cones, cylinders, and spheres
* Develop and apply the formula for volume
* Develop and apply the formula for volume of a sphere
* Develop and apply the formula for volume of a cylinder
* Solve real world problems by finding volume of cones
Construct and interpret scatter plots for bivariate measurement data
* Construct a scatter plot
* Describe patterns in scatter plots
* Interpret a scatter plot by identifying clusters and outlier
* Interpret and distinguish linear and non linear scatter plot
Fit a straight line, and informally assess the model fit by data points to the line.
* Construct a line of best fit
* Draw a line of best fit
* Determine the strength of an association by comparing scatter plots
* Use bivariate measurement data to make a prediction
Use the equation of a linear model to interpreting the slope and intercept
* Write an equation for line of best fit
* Interpret the y-intercept of a line of best
* Interpret association in lines of best fit
* Compare linear and non-linear functions
* Use the equation of a line of best fit to make predictions