Curriculum for Grade 2

Students master operations in the hundreds, perform exchanges confidently, and take first steps toward multiplication as they rely on number sense, place value understanding, and number flexibility.

MODULE 1. Sums and Differences to 100

Topic A: Foundations for Fluency with Sums and Differences Within 100

Students extend their understanding of addition and subtraction within 100. Use of base-10 blocks reinforces the concept of "tens" and "ones" to build place value understanding. Students move quickly from concrete models to more abstract equations. Students build their fluency with addition and subtraction facts, including those across a 10, by modeling the underlying concept of exchanging and memorizing number bonds of 10.

Review addition facts with a sum of 10

Students will choose the numbers that make a sum of ten
Review addition facts with a sum of 10

Adding to groups of ten

Students will solve equations that require them to add a single-digit number to groups of ten
Adding to groups of ten

Use models to practice addition equations with a one- and two-digit addend

Students will label sets of base-10 blocks with numerals. They will split two-digit addends into tens and ones, then model addition by adding cubes to the ones place. Then, students will solve similar equations without models
Use models to practice addition equations with a one- and two-digit addend

Solve addition equations with a one- and two-digit addend

Students will solve addition equations with one- and two-digit addends without support of models
Solve addition equations with a one- and two-digit addend

Use models to solve subtraction equations with a one- and two-digit number

Students will use base-10 cubes to model subtraction from a two-digit number. They will break the two-digit number into tens and ones and model subtraction by taking away from the ones place. Students will solve similar equations without models
Use models to solve subtraction equations with a one- and two-digit number

Solve subtraction equations with a one- and two-digit number

Students will solve subtraction equations taking away a one-digit number from a two-digit number without support of models
Solve subtraction equations with a one- and two-digit number

Add groups of ten to a two-digit number (Part 1)

Students will use base-10 blocks to model adding groups of ten to a two-digit number. Students break the two-digit number into tens and ones, and add the groups of ten together before adding the ones to find the sum. Students then solve without models
Add groups of ten to a two-digit number (Part 1)

Adding one- and two-digit numbers

Using knowledge of place value, students will solve equations adding one- or two-digit numbers to another two-digit number
Adding one- and two-digit numbers

Use models to solve subtraction equations with two-digit number

Students will use base-10 cubes to model subtraction from a two-digit number. They will break the two-digit number into tens and ones and model subtraction by taking away from the tens place. Students will solve similar equations without models
Use models to solve subtraction equations with two-digit number

Add groups of ten to a two-digit number (Part 2)

Students will add groups of ten to a two-digit number without support of models
Add groups of ten to a two-digit number (Part 2)

Develop fluency with addition and subtraction of one- and two-digit numbers

Students will solve addition and subtraction equations involving one- and two-digit numbers, without support of models
Develop fluency with addition and subtraction of one- and two-digit numbers

Topic B: Initiating Fluency with Addition and Subtraction Within 100

Students add and subtract with exchanging as represented by crossing a ten on the number line or making/breaking rods with base-10 blocks. Students use strategies such as "resting" on a round number to add or subtract across a ten or using 10 in place of 8 or 9 and adjusting their answer. Students build their fluency with +/- facts within 20. They work with equations with three addends.

Identify a missing single-digit addend to reach the next round number with and without a model of base-10 blocks

Find the single digit number that must be added for a total of 20. At first, cube models are provided to assist in finding the missing addend. Then, just the equations are given
Identify a missing single-digit addend to reach the next round number with and without a model of base-10 blocks

Identify a missing addend to reach a sum of 20 with and without a model of base-10 blocks

Enter the missing addend for a sum of 20. A pair of related equations make up each problem. Cube models are provided if assistance is needed
Identify a missing addend to reach a sum of 20 with and without a model of base-10 blocks

Solve +/- equations that do not cross a ten based on a number line model

Use a number line to solve addition problems with a 2-digit number plus a 1-digit number. Put the grasshopper at the 2-digit number and then move him the number of spaces indicated by 1-digit number. Enter the result into the equation
Solve +/- equations that do not cross a ten based on a number line model

Solve +/- equations within 100

Practice addition and subtraction within 100. The sums do not cross the tens
Solve +/- equations within 100

Model and solve +/- equations across 10 using base-10 blocks

Add or subtract across 10. Represent the numbers with cubes. For a sum, fill one tens rod and move the leftover ones. Enter the sum. For a difference, pop the subtracted cubes and enter the difference
Model and solve +/- equations across 10 using base-10 blocks

Solve +/- equations across 10 (Part 1)

Practice addition and subtraction across 10 without any models. Only the equations are given
Solve +/- equations across 10 (Part 1)

Solve +/- equations across 10 (Part 2)

Find sums and differences within 100 across tens. Enter the answer the equation. No models are given
Solve +/- equations across 10 (Part 2)

Solve +/- equations within 100

Practice addition and subtraction within 100 across tens. Enter the answer the equation. No models are given
Solve +/- equations within 100

MODULE 2. Addition and Subtraction of Length Units

Topic A: Understand Concepts About the Ruler

Students learn the basic principles of linear measure. They measure objects and line segments arranged horizontally, vertically, and randomly. They practice with increasingly abstract units of measure, from real objects to bricks to isolated centimeters to a centimeter ruler. Students learn to align an object to 0 on the ruler to measure length.

Count to measure lengths of objects in non-standard units

Measure the length of objects using building blocks as a non-standard unit. Choose an object and enter the length in number of blocks shown
Count to measure lengths of objects in non-standard units

Measure lengths of objects from endpoint to endpoint with no gaps or overlaps

Learn how to measure the length of objects using building blocks as a non-standard unit. The measuring units have to be laid correctly between the endpoints
Measure lengths of objects from endpoint to endpoint with no gaps or overlaps

Measure lengths of objects by laying non-standard units correctly

Measure the length of objects using building blocks as a non-standard unit. The measuring units have to be laid correctly between the endpoints. Then, enter the measurement
Measure lengths of objects by laying non-standard units correctly

Compare lengths measured in different non-standard units

Compare the lengths of two objects, using the shorter object as a non-standard unit of the longer item. Then, learn why using two similar non-standard unit can result in different length of the same object
Compare lengths measured in different non-standard units

Count to measure lengths of objects in centimeters

Learn to use the standard unit of centimeters to measure objects. Enter the length of objects using centimeter squares shown
Count to measure lengths of objects in centimeters

Measure lengths of objects aligned to a centimeter ruler

Measure the length of objects aligned to centimeter units. First, use centimeter squares to determine the length. Then, learn how to use a centimeter ruler
Measure lengths of objects aligned to a centimeter ruler

Align objects to a centimeter ruler to measure length

Learn how to measure the length of an object using a centimeter ruler. Line up the ruler with one endpoint of the object, then read where the other endpoint falls on the ruler. Enter the value of the length
Align objects to a centimeter ruler to measure length

Draw a line segment of a given length

Practice drawing a segment of a given length along a ruler
Draw a line segment of a given length

Measure side lengths of 2-D objects using a centimeter ruler

Use a centimeter ruler to measure two sides of shapes. The ruler is automatically placed along the side. Read off and enter the measurement
Measure side lengths of 2-D objects using a centimeter ruler

Topic B: Measure and Estimate Length Using Different Measurement Tools

Students explore the ruler to relate millimeters to centimeters. They then convert among millimeters, centimeters, decimeters, and meters using real objects as a frame of reference.

Topic C: Measure and Compare Lengths Using Different Length Units

Students apply their understanding of measurement to add and subtract lengths using a ruler. They solve the problems of measuring objects that aren't aligned to 0 on the ruler as well as objects that exceed the length of the ruler by using addition and subtraction.

Topic D: Relate Addition and Subtraction to Length

Students use real objects and abstract objects to determine lengths using addition and subtraction. They subtract to determine length when objects are not aligned to zero on a ruler. Students learn to use tape diagrams to represent and solve addition and subtraction word problems, including those with a missing addend or subtrahend.

Represent change in length as addition or subtraction

Measure a length in centimeters, then increase or decrease the length by a given amount. Enter the original length and the final sum or difference
Represent change in length as addition or subtraction

Add three measurements to find the total length of a path

Select locations and find the sum of three distances. The distances in meters are given when the selection appears, so no measuring is required
Add three measurements to find the total length of a path

Count to determine length of an object that isn't aligned to 0 on a ruler

Learn how to measure a length in centimeters when the 0 of the ruler is not aligned to an endpoint. First, the skip counting between centimeters is provided. Then, just the ruler is shown below the object
Count to determine length of an object that isn't aligned to 0 on a ruler

Subtract to determine length of an object that isn't aligned to 0 on a ruler

Practice subtracting two measurements. First, a longer and a shorter bar are measured and the difference between their lengths is found. Then, a ruler whose 0 is not aligned to the endpoint of an object is used to the find the length by subtraction
Subtract to determine length of an object that isn't aligned to 0 on a ruler

Use the difference between two numbers to measure a given object

Given an object not aligned to zero on a ruler, use the difference between two points to measure the object's length. Represent the concept of "difference" through the subtraction symbol. Given points include numbers between 0 and 25
Use the difference between two numbers to measure a given object

Use a tape diagram to solve a +/- word problem involving length

Learn how to use a tape diagram to model a word problem involving lengths. Hints are given to help set up the diagram to create the correct expression to solve
Use a tape diagram to solve a +/- word problem involving length

Show the question/solution element of a word problem on a tape diagram and solve

Distinguish between a story and a math problem. Use a tape diagram to model a word problem involving lengths. Hints are given to help set up the diagram to create the correct expression to solve
Show the question/solution element of a word problem on a tape diagram and solve

MODULE 3. Place Value, Counting, and Comparison of Numbers to 1000

Topic A: Forming Base Ten Units of Ten and Hundred

Students reinforce their counting and place value skills to three-digit numbers to 200. They will use base ten blocks to practice finding place values less than 200.

Topic B: Understanding Place Value Units of One, Ten, and a Hundred

Students will apply their counting, reading, and place value skills to three-digit numbers. They will use the base-ten block model to identify and build three-digit numbers. They strengthen their conceptual understanding of counting patterns and practice skip counting by ones, fives, tens, and hundreds.

Topic C: Three-Digit Numbers in Unit, Standard, Expanded, and Word Forms

Students rely on solid place value understanding to focus on the relationship between a three-digit number and its constituent parts. They strengthen their recognition of written number names and begin working with numbers that have placeholder zeros.

Topic D: Modeling Numbers Within 1,000 with Place Value Disks

Students are introduced to the thousand cube base-10 block as they build their concept of a thousand. They also explore the relationships between ones, tens, hundreds, and thousands as well as the count sequence using familiar representations.

Recognize and represent 2-digit numbers as tens and ones (Part 1)

Decompose a 2-digit number into its place values. First, identify the number of tens and ones and put the place value label under each digit. Then, represent the number with coins labeled 10 and 1
Recognize and represent 2-digit numbers as tens and ones (Part 1)

Recognize and represent 2-digit numbers as tens and ones (Part 2)

Write the 2-digit number represented by a place value chart. Disks labeled 10 and 1 are displayed in a chart. State the total
Recognize and represent 2-digit numbers as tens and ones (Part 2)

Recognize and represent 3-digit numbers as hundreds, tens, and ones

Decompose a 3-digit number. First, label each digit and column with its place value label. Then represent the number with coins labeled 100, 10 and 1. Finally, reverse the process and state the 3-digit number
Recognize and represent 3-digit numbers as hundreds, tens, and ones

Recognize and represent 3-digit numbers with placeholder zeros as hundreds, tens, and ones

Decompose a 3-digit number. One of the place values is a placeholder 0. Represent the number with coins 100, 10 and 1. Then reverse the process and state the 3-digit. Compare the place values of a 2-digit and 3-digit numbers containing the same digits
Recognize and represent 3-digit numbers with placeholder zeros as hundreds, tens, and ones

Determine how many more ones, tens, or hundreds to reach the next ten, hundred, or thousand using a number line (Level 1)

Learn the relationship between ones, tens, hundreds, and thousands. Use a number line counting by ones, identify 10 ones as 1 ten. Similarly, use a number line and count by tens to rename 10 tens as 1 hundred and to rename 10 hundreds as 1 thousand
Determine how many more ones, tens, or hundreds to reach the next ten, hundred, or thousand using a number line (Level 1)

Convert among ones, tens, hundreds, and thousands using number and unit notation

Convert between ones, tens, hundreds, and thousands. Given 10, 100, or 1000, state how many of the other units are equivalent
Convert among ones, tens, hundreds, and thousands using number and unit notation

Convert among ones, tens, hundreds, and thousands using unit notation

Convert between ones, tens, hundreds, and thousands. Given 1 of any of the units, state how many of another unit are equivalent
Convert among ones, tens, hundreds, and thousands using unit notation

Review the concept of 1s, 10s, and 100s to build understanding of 1000

Students will use base-10 blocks to build their understanding of ones, tens, hundreds, and one thousand. Students will count cubes and convert them as needed by making equivalencies in the next unit of place value
Review the concept of 1s, 10s, and 100s to build understanding of 1000

Convert among ones, tens, hundreds, and one thousand using base-10 blocks

Students will label a given set of base-10 blocks with the correct name/value. They will review the equivalent values for converting between ones, tens, hundreds, and one thousand
Convert among ones, tens, hundreds, and one thousand using base-10 blocks

Review conversion values among ones, tens, hundreds, and one thousand

Given the values 10, 100, and 1000, students will convert the numbers into the next smallest place value
Review conversion values among ones, tens, hundreds, and one thousand

Topic E: Comparing Two Three-Digit Numbers

Students develop their deep understanding of place value to compare and order three-digit numbers. They master common pitfalls, such as placeholder zeros and transposed numbers. Students move from using base-10 models and place value cards to visual recognition of number order and place value.

Use >, =, and < to compare a two-digit number with a three-digit numberUse >, =, and < to compare a two-digit number with a three-digit number

Compare 2 and 3 digit numbers using inequality symbols. First, sort 2-digit and 3-digit numbers into separate boxes. Then, represent a 2 and 3 digit number with base-10 blocks and compare their place values to determine their relationship. Finally, choose
Use >, =, and < to compare a two-digit number with a three-digit numberUse >, =, and < to compare a two-digit number with a three-digit number

Use >, =, and < to compare at the hundreds place based on a model of base-10 blocks

Compare two 3-digit numbers at the hundreds place. Base-10 block models are given for each number to assist with the comparison. Select the appropriate inequality symbol to place between the numbers
Use >, =, and < to compare at the hundreds place based on a model of base-10 blocks

Use >, =, and < to compare at the hundreds place with and without place value cards

Compare two 3-digit numbers at the hundreds place. The numbers are decomposed into place value cards to aid in the comparison. Then, compare the numbers without place value cards. Select the appropriate inequality symbol to place between the numbers
Use >, =, and < to compare at the hundreds place with and without place value cards

Use >, =, and < to compare at the tens place based on a model of base-10 blocks

Compare two 3-digit numbers at the tens place. Base-10 block models are given for each number to assist with the comparison. Select the appropriate inequality symbol to place between the numbers
Use >, =, and < to compare at the tens place based on a model of base-10 blocks

Use >, =, and < to compare at the tens and ones place based on place value cards

Compare two 3-digit numbers at the tens and ones place. The numbers are decomposed into place value cards to aid in the comparison. Select the appropriate inequality symbol until the relationship between the original numbers can be established
Use >, =, and < to compare at the tens and ones place based on place value cards

Use >, =, and < to compare at the hundreds and tens place

Practice comparing two 3-digit numbers. Mentally compare the hundreds and tens places, no decomposition is provided. Select the appropriate inequality symbol to place between the numbers
Use >, =, and < to compare at the hundreds and tens place

Use >, =, and < to compare numbers with placeholder zeros

Compare two 3-digit numbers that contain placeholder zeros. The numbers are decomposed into place value cards to aid in the comparison, but then just just the numbers are shown. Select the appropriate inequality symbol to place between the numbers
Use >, =, and < to compare numbers with placeholder zeros

Use >, =, and < to compare numbers with placeholder zeros based on a model of base-10 blocks

Compare two 3-digit numbers that contain placeholder zeros. Base-10 block models are given for each number to assist with the comparison. Select the appropriate inequality symbol to place between the numbers
Use >, =, and < to compare numbers with placeholder zeros based on a model of base-10 blocks

Use >, =, and < to compare numbers with similar digits

Practice comparing two 3-digit numbers that contain the same digits at different place values. No decomposition is provided. Select the appropriate inequality symbol to place between the numbers
Use >, =, and < to compare numbers with similar digits

Arrange three-digit numbers in ascending order (Level 1)

Put a set of five numbers in increasing order. Train cars with 2- or 3-digit numbers are scattered. Place them in the track in ascending order
Arrange three-digit numbers in ascending order (Level 1)

Arrange three-digit numbers in ascending order (Level 2)

Put a set of five numbers in increasing order. Train cars with 3-digit numbers are scattered. Place them in the track in ascending order
Arrange three-digit numbers in ascending order (Level 2)

Arrange three-digit numbers in ascending order (Level 3)

Arrange a set of five numbers in increasing order. Train cars with 3-digit numbers are scattered. Place them in the track in ascending order
Arrange three-digit numbers in ascending order (Level 3)

Topic F: Finding 1, 10, and 100 More or Less Than a Number

Students build number sense by working with 1, 10, and 100 more or less than 2- and 3-digit numbers. They begin with the support of a disk model using a place value chart. Students explore counting patterns up and down.

Determine 10 or 100 more with and without a place value chart

Students determine a 2- or 3-digit number based on a disk model. They add a ten or hundred disk to the chart and determine the new total. They then solve similar problems without the disk model
Determine 10 or 100 more with and without a place value chart

Determine 10 or 100 less with and without a place value chart

Students determine a 2- or 3-digit number based on a disk model. They subtract a ten or hundred disk from the chart and determine the new total. They then solve similar problems without the disk model
Determine 10 or 100 less with and without a place value chart

Determine 1/10/100 more or less (Part 1)

Students determine 1, 10, or 100 more or less than a given 2- or 3-digit number
Determine 1/10/100 more or less (Part 1)

Determine 1/10/100 more or less (Part 2)

Students determine 1, 10, and 100 more than the same 3-digit number. Then they determine 1 and 10 more and less than the same 3-digit number
Determine 1/10/100 more or less (Part 2)

Determine 1/10/100 more or less (Part 3)

Students determine 1, 10, and 100 more and less than the same 3-digit number
Determine 1/10/100 more or less (Part 3)

Compare using 1, 10, or 100 more or less

Students determine how much (1, 10, or 100) more or less a given 3-digit number is compared with another 3-digit number. Students then determine the starting number given a comparison (1, 10, or 100 more or less) and an ending number
Compare using 1, 10, or 100 more or less

Determine 1 or 10 more across place values

Students determine 1 or 10 more than a given 3-digit number across place values. They have the option to solve the problem immediately or use a disk model
Determine 1 or 10 more across place values

Determine 1 or 10 less across place values

Students determine 1 or 10 less than a given 3-digit number across place values. They have the option to solve the problem immediately or use a disk model
Determine 1 or 10 less across place values

Count up and back by 1s (3-digit numbers)

Students complete a counting sequence of three-digit numbers counting up or back by ones
Count up and back by 1s (3-digit numbers)

Count up and back by 10s or 100s (3-digit numbers)

Students complete a counting sequence of three-digit numbers counting up or back by tens or hundreds
Count up and back by 10s or 100s (3-digit numbers)

Counting patterns (Level 1)

Students determine whether a given set of numbers shows counting up or down (by 10s or 100s) and then continue the pattern. They then determine the amount by which a given set of numbers counts up or down (10 or 100) and continue the pattern
Counting patterns (Level 1)

Count up by 10s

Students determine 10 more (repeated) of a 3-digit number
Count up by 10s

Count up by 1s and 100s

Students determine 1 more (repeated) of a 3-digit number. They then determine 100 more (repeated) of a different 3-digit number
Count up by 1s and 100s

Counting patterns (Level 2)

Students determine missing numbers within patterns of counting up or down by 1s, 10s, or 100s
Counting patterns (Level 2)

MODULE 4. Addition and Subtraction Within 200 with Word Problems to 100

Topic A: Sums and Differences Within 100

Students practice strategies for solving 2-digit +/- problems with and without exchanging. They apply their knowledge of place value, addition and subtraction, and number flexibility to solve equations and non-traditional problems using familiar representations (base-10 blocks, place value cards, hundred chart, and equations). Using concrete manipulatives, they begin to solve problems that require exchanging.

Relate 1 more or less and 10 more or less to addition and subtraction (Part 1)

Find 1 more,1 less, 10 more, or 10 less than a given two-digit number. Then complete the related addition or subtraction problem
Relate 1 more or less and 10 more or less to addition and subtraction (Part 1)

Relate 1 more or less and 10 more or less to addition and subtraction (Part 2)

Find 1 more,1 less, 10 more, or 10 less than a given two-digit number. Then complete the related addition or subtraction problem
Relate 1 more or less and 10 more or less to addition and subtraction (Part 2)

Identify the rule for a +/- 1 or 10 counting pattern and continue the pattern (Part 1)

Look at a number pattern, and decide if it shows 1 more, 1 less, 10 more, or 10 less, then choose the addition or subtraction operation that can be used to make the pattern. Next, complete a pattern when you know the first number and you know the rule
Identify the rule for a +/- 1 or 10 counting pattern and continue the pattern (Part 1)

Identify the rule for a +/- 1 or 10 counting pattern and continue the pattern (Part 2)

Look at the first three terms in a number pattern, and decide whether the rule is +1, -1, +10, or -10. Then continue the pattern using the rule
Identify the rule for a +/- 1 or 10 counting pattern and continue the pattern (Part 2)

Record a 2-digit number as tens and ones

Practice place value concepts by breaking a two-digit number into tens and ones
Record a 2-digit number as tens and ones

Add a round number to a 2-digit number with and without using number bonds to add tens first

Add a two-digit number and a two-digit multiple of 10. Begin by using a number bond to break the first number into tens and ones, and adding the tens together. Then, solve these problems without the use of a number bond
Add a round number to a 2-digit number with and without using number bonds to add tens first

Subtract a round number from a 2-digit number with and without using number bonds to subtract tens first

Subtract a two-digit multiple of 10 from a two-digit number. Begin by using a number bond to break the first number into tens and ones, and subtract the tens, keeping any ones the same. Then, solve these problems without the use of a number bond
Subtract a round number from a 2-digit number with and without using number bonds to subtract tens first

Add and subtract 2-digit and round numbers including turnaround facts

Practice adding and subtracting two-digit multiples of 10 to and from two-digit numbers. See that the addends in an addition problem can be in any order, and the sum is the same
Add and subtract 2-digit and round numbers including turnaround facts

Add 2-digit numbers using place value cards to add tens and ones separately

Add two-digit numbers by adding tens and ones separately. The first few problems walk you through the steps, and the last few problems provide practice. None of the problems require regrouping
Add 2-digit numbers using place value cards to add tens and ones separately

Add 2-digit numbers with and without using number bonds to add on the tens first

Practice a strategy for adding two two-digit numbers. Break one of the numbers into tens and ones. Then add the tens to the other number, and finally add the ones to the other number
Add 2-digit numbers with and without using number bonds to add on the tens first

Subtract 2-digit numbers with and without using place value cards to subtract tens and ones separately

Subtract two-digit numbers by first breaking the numbers into tens and ones. The first few problems provide steps for using this strategy, and the last few problems allow you to practice the strategy on your own
Subtract 2-digit numbers with and without using place value cards to subtract tens and ones separately

Subtract 2-digit numbers with and without using number bonds to subtract the tens first

Practice a strategy for subtracting two two-digit numbers. Break the second number into tens and ones, then subtract the tens from the first number, and finally subtract the ones from the first number. No regrouping is required for these problems
Subtract 2-digit numbers with and without using number bonds to subtract the tens first

Add 2-digit numbers with and without exchanging using place value cards

Practice adding two two-digit numbers by adding the tens, adding the ones, and then adding these two sums. Some problems require regrouping
Add 2-digit numbers with and without exchanging using place value cards

Add 2-digit numbers with exchanging and without using number bonds

Practice adding two two-digit numbers by breaking the second number apart into tens and ones, and first adding the tens to the first number and then adding the ones. These problems require regrouping
Add 2-digit numbers with exchanging and without using number bonds

Subtract 2-digit numbers with exchanging with and without using number bonds

Practice subtracting two-digit numbers with and without regrouping and with and without using number bonds. Break the second number apart into tens and ones, and first subtract the tens from the first number and then subtract the ones
Subtract 2-digit numbers with exchanging with and without using number bonds

Topic B: Column Addition with Exchanging into the Tens

Students use familiar manipulatives to guide them into using column addition with understanding. They begin by using the strategy of adding all tens and all ones and then combining the two. Then, they move into 2- and 3-digit column addition with and without exchanging ones for a ten.

Identify and build numbers using 10s and 1s on a place value chart

Students determine the number represented by 10s and 1s on a chart. Then, they represent a given number using 10s and 1s on a chart
Identify and build numbers using 10s and 1s on a place value chart

Use a place value chart to add 2-digit numbers

Students model simple addition problems with double digit numbers on a place value chart. First, students represent both addends using 10s and 1s on the chart. Then, they determine the sum
Use a place value chart to add 2-digit numbers

Solve 2-digit column addition without exchanging using a place value chart model

Students are introduced to simple column addition with two-digit addends alongside the place value chart. Then, students solve 2-digit column addition without support
Solve 2-digit column addition without exchanging using a place value chart model

Add 2-digit numbers without exchanging (Part 1)

Students practice column addition with two digit addends. First, students transform horizontal equations into the column format
Add 2-digit numbers without exchanging (Part 1)

Add 2-digit numbers without exchanging (Part 2)

Students practice column addition with two digit addends
Add 2-digit numbers without exchanging (Part 2)

Exchange 1s for 10s on a place value chart when necessary

Students exchange 1s for 10s on a place value chart to determine the number modeled on the chart
Exchange 1s for 10s on a place value chart when necessary

Solve 2-digit column addition with regrouping with the support of a place value chart model

Students add two-digit numbers that require regrouping by modeling the problem using a place value chart. Students exchange 1s for 10s to model regrouping
Solve 2-digit column addition with regrouping with the support of a place value chart model

Solve 2-digit column addition with regrouping using the standard algorithm

Students solve 2-digit column addition problems with two-digit numbers and regrouping with the support of a place value chart model
Solve 2-digit column addition with regrouping using the standard algorithm

Add 2-digit numbers with exchanging (Part 1)

Students practice the standard algorithm for addition of 2-digit addends with regrouping. Students identify when regrouping is necessary
Add 2-digit numbers with exchanging (Part 1)

Add 2-digit numbers with exchanging (Part 2)

Students practice the standard algorithm for addition of 2-digit addends with regrouping. Less support is provided as students deepen their understanding
Add 2-digit numbers with exchanging (Part 2)

Practice the standard algorithm for addition with regrouping with step by step support (Part 1)

Students practice the standard algorithm for addition of 2-digit addends with regrouping. Less support is provided as students deepen their understanding
Practice the standard algorithm for addition with regrouping with step by step support (Part 1)

Practice the standard algorithm for addition with regrouping with step by step support (Part 2)

Students practice the standard algorithm for addition of 2-digit addends with regrouping. Less support is provided as students deepen their understanding
Practice the standard algorithm for addition with regrouping with step by step support (Part 2)

Practice column addition with one 3-digit and one 2-digit addend

Students perform simple column addition with a 3-digit and a 2-digit addend
Practice column addition with one 3-digit and one 2-digit addend

Practice the standard algorithm of 2-digit column addition with regrouping (Part 1)

Students practice the standard algorithm for addition with regrouping involving 2-digit and 3-digit addends. Less support is provided as students deepen their understanding
Practice the standard algorithm of 2-digit column addition with regrouping (Part 1)

Practice the standard algorithm of 2-digit column addition with regrouping (Part 2)

Students practice the standard algorithm for addition with regrouping involving 2-digit and 3-digit addends. Less support is provided as students deepen their understanding
Practice the standard algorithm of 2-digit column addition with regrouping (Part 2)

Topic C: Column Subtraction with Exchanging into the Tens

Students use familiar manipulatives to guide them into using column subtraction with understanding. Students learn to determine whether or not an exchange is needed and, if so, how to do so with understanding. Then, they move into 2- and 3-digit column subtraction with and without exchanging a ten for ones.

Represent and solve 2-digit subtraction problems without exchanging using a disk model

Learn how to subtract two-digit numbers using the disk model in a place value chart without regrouping. Drag disks into the chart to represent the first number, then remove disks that represent the second number. The number of disks left is the answer
Represent and solve 2-digit subtraction problems without exchanging using a disk model

Subtract 2-digit numbers without exchanging using place value cards to subtract tens and ones separately

Subtract two-digit numbers without regrouping by breaking them apart into tens and ones, and subtracting the tens and ones separately. Then combine the remaining tens and ones to form the answer
Subtract 2-digit numbers without exchanging using place value cards to subtract tens and ones separately

Solve 2-digit column subtraction without exchanging

Subtract two-digit numbers using the standard algorithm without regrouping. First set up the problem, then subtract and record the answer
Solve 2-digit column subtraction without exchanging

Exchange a ten for ones using a disk model

To prepare for subtraction with regrouping ones, practice exchanging a ten for 10 ones using the disk model. Give the creature a certain number of ones disks. If there aren't enough ones disks to give away, then exchange a ten disk for 10 ones disks
Exchange a ten for ones using a disk model

Subtract 2-digit numbers with exchanging using a disk model

Subtract two-digit numbers with regrouping using the disk model. Exchange 1 tens disk for 10 ones disks so that there will be enough ones disks to subtract
Subtract 2-digit numbers with exchanging using a disk model

Subtract 2-digit numbers with exchanging using place value cards

Practice subtracting two-digit numbers with regrouping by breaking the numbers apart into tens and ones first. If there aren't enough ones to subtract, drag a ten from the tens column to the ones column. Then subtract and record the answer
Subtract 2-digit numbers with exchanging using place value cards

Solve 2-digit column subtraction with exchanging using a disk model

Practice two-digit subtraction with regrouping using the standard algorithm alongside the disk model in a place value chart. See the connection between the regrouping in the disk model and the steps in the standard algorithm
Solve 2-digit column subtraction with exchanging using a disk model

Solve 2-digit column subtraction with exchanging (Level 1)

Practice two-digit subtraction with regrouping using the standard algorithm. Each problem guides you through the steps of the standard algorithm
Solve 2-digit column subtraction with exchanging (Level 1)

Solve 2-digit column subtraction with exchanging (Level 2)

Practice two-digit subtraction with regrouping using the standard algorithm. Each problem provides hints to guide you through the steps of the standard algorithm
Solve 2-digit column subtraction with exchanging (Level 2)

Solve 2-digit column subtraction with and without exchanging

Subtract two-digit numbers using the standard algorithm both with and without regrouping, and record the answer
Solve 2-digit column subtraction with and without exchanging

Solve 2- and 3-digit column subtraction with and without exchanging ones (Level 1)

Subtract a two-digit number from a three-digit number both with and without regrouping. Each problem guides you through the steps of the algorithm
Solve 2- and 3-digit column subtraction with and without exchanging ones (Level 1)

Solve 2- and 3-digit column subtraction with and without exchanging ones (Level 2)

Subtract a two-digit number from a three-digit number both with and without regrouping. Can you solve all four problems before you run out of lives?
Solve 2- and 3-digit column subtraction with and without exchanging ones (Level 2)

Topic D: Column Addition with Exchanging into the Hundreds

Students build on their understanding of column addition and exchanging to move into the hundreds place. Disk models and step-by step prompting help ensure conceptual understanding and procedural fluency. A gradual release model helps students become independent with these multi-step problems.

Exchange 1s for 10s and 10s for hundreds on a place value chart. Write the corresponding number

Students review the process of exchanging 1s and 10s on a place value chart and writing the number expressed on the chart
Exchange 1s for 10s and 10s for hundreds on a place value chart. Write the corresponding number

Solve addition problems involving exchanging 1s and 10s using a place value chart for support

Students use a place value chart to represent two-digit addition problems with exchanging of 1s and 10s. Then, students write the final result
Solve addition problems involving exchanging 1s and 10s using a place value chart for support

Practice column addition with exchanging alongside a place value chart

Students use a place value chart to represent two-digit addition problems with exchanging of 1s and 10s and walk through the equivalent steps in column addition using the standard algorithm
Practice column addition with exchanging alongside a place value chart

Use the standard algorithm of 2-digit column addition with regrouping into the hundreds (Part 1)

Students are guided through the standard algorithm of 2-digit column addition with regrouping into the hundreds, including adding a hundreds place as necessary
Use the standard algorithm of 2-digit column addition with regrouping into the hundreds (Part 1)

Use the standard algorithm of 2-digit column addition with regrouping into the hundreds (Part 2)

Students are guided through the standard algorithm of 2-digit column addition with regrouping into the hundreds. Less support is provided as students deepen their understanding
Use the standard algorithm of 2-digit column addition with regrouping into the hundreds (Part 2)

Use the standard algorithm to solve for various combinations of addends of 2 or 3 digits and with or without regrouping into the hundreds

Students practice using the standard algorithm of column addition for both 2 and 3 digit addends with and without regrouping into the hundreds
Use the standard algorithm to solve for various combinations of addends of 2 or 3 digits and with or without regrouping into the hundreds

Topic E: Column Subtraction with Exchanging into the Hundreds

Students build on their understanding of column subtraction and exchanging to move into the hundreds place. Step-by step prompting helps ensure conceptual understanding and procedural fluency. A gradual release model helps students become independent with these multi-step problems.

Solve 2- and 3-digit column subtraction equations by exchanging 100 for 10 tens to solve

Students will rewrite a horizontal subtraction problem into column subtraction. Students will solve 2- and 3- digit problems within 200 by breaking down each element into its place value. Students will practice trading 100 for 10 tens to solve
Solve 2- and 3-digit column subtraction equations by exchanging 100 for 10 tens to solve

Solve more 2- and 3-digit column subtraction equations by exchanging 100 for 10 tens with or without prompts

Students will solve more 2- and 3-digit column subtraction equations within 200 by exchanging 100 for 10 tens and regrouping. Students will have the choice to solve each equation with or without scaffolding prompts
Solve more 2- and 3-digit column subtraction equations by exchanging 100 for 10 tens with or without prompts

Solve 2- and 3- digit column subtraction equations with and without exchanging into the hundreds

Students will rewrite horizontal subtraction equations into column subtraction. They will solve 2- and 3-digit problems within 200, with and without making exchanges into the 100s. Students practice this skill without prompts
Solve 2- and 3- digit column subtraction equations with and without exchanging into the hundreds

Solve 2- and 3-digit column subtraction equations that require making exchanges into the hundreds and tens, with prompts

Students will practice solving 2-and 3-digit column subtraction equations within 200. Equations include making exchanges into both the 10s and 100s. Students are prompted to make exchanges when the ones and tens cannot be subtracted without an exchange
Solve 2- and 3-digit column subtraction equations that require making exchanges into the hundreds and tens, with prompts

Solve 2- and 3-digit column subtraction equations by exchanging and regrouping with hundreds and tens

Students will solve more 2- and 3-digit column subtraction equations within 200 by making exchanges from both the 100s and 10s. Students are prompted to consider if they can subtract each column as is first, then determine if an exchange is necessary
Solve 2- and 3-digit column subtraction equations by exchanging and regrouping with hundreds and tens

Solve 2- and 3-digit column subtraction equations with and without exchanging into the hundreds and tens

Students will solve 2- and 3-digit column subtraction equations within 200 with and without making exchanges into the 10s and 100s. Students practice this skill without prompting and independently determine if exchanges are necessary
Solve 2- and 3-digit column subtraction equations with and without exchanging into the hundreds and tens

MODULE 5. Addition and Subtraction Within 1,000 with Word Problems to 100

Topic A: Mental Strategies for Addition and Subtraction Within 1,000

Students work with 2- and 3-digit round numbers to develop strategies for mental addition and subtraction. The first strategy teaches them to add on/subtract to the nearest hundred and then add on/subtract what's left. The second strategy teaches students to add on/subtract all of the hundreds and then add on/subtract all of the tens. Both strategies are supported by manipulatives such as a disk model and number line.

Add and subtract 3-digit numbers with no tens or ones

Add and subtract three-digit multiples of 100
Add and subtract 3-digit numbers with no tens or ones

Add 3-digit round numbers with and without using a disk model

Add a three-digit multiple of 10 and a three-digit multiple of 100, first using the disk model, and then without the model. See that adding a multiple of 100 to another three digit number means adding the hundreds digits together
Add 3-digit round numbers with and without using a disk model

Subtract 3-digit round numbers with and without using a disk model

Subtract a three-digit multiple of 100 from a three-digit multiple of 10, first using the disk model, and then without the model. See that subtracting a multiple of 100 from another three digit number means subtracting the hundreds digits
Subtract 3-digit round numbers with and without using a disk model

Add a 2-digit round number to a 3-digit round number by adding hundreds, tens, then ones

Add a three-digit multiple of 10 and a two-digit multiple of 10 by adding the tens digits
Add a 2-digit round number to a 3-digit round number by adding hundreds, tens, then ones

Add up to the next hundred with and without using a number line model

Place a 3-digit multiple of 10 on the number line. Then identify the next multiple of 100 that is greater than the number, and say how much you add to reach this multiple of 100. Next, complete similar problems but without using the number line model
Add up to the next hundred with and without using a number line model

Add a 2-digit number to a 3-digit number using the "Make the Next Hundred" strategy (Part 1)

Learn how to add a three-digit multiple of 10 and a two-digit multiple of 10 by using the make the next hundred strategy
Add a 2-digit number to a 3-digit number using the "Make the Next Hundred" strategy (Part 1)

Add a 2-digit number to a 3-digit number using the "Make the Next Hundred" strategy (Part 2)

Practice adding a three-digit multiple of 10 and a two-digit multiple of 10 by using the make the next hundred strategy
Add a 2-digit number to a 3-digit number using the "Make the Next Hundred" strategy (Part 2)

Add a 2-digit round number to a 3-digit round number using mental math

Practice adding a three-digit multiple of 10 and a two-digit multiple of 10 by using mental math. You may use the make the next hundred strategy, or any other strategy
Add a 2-digit round number to a 3-digit round number using mental math

Subtract a 2-digit round number from a 3-digit round number by subtracting hundreds, tens, then ones

Practice subtracting a two-digit multiple of 10 from a three-digit multiple of 10 without regrouping by subtracting the tens digits
Subtract a 2-digit round number from a 3-digit round number by subtracting hundreds, tens, then ones

Subtract to the next hundred with and without using a number line model

Place a 3-digit multiple of 10 on the number line. Then identify the next multiple of 100 that is less than the number, and say how much you subtract to reach this multiple of 100. Next, complete similar problems but without using the number line model
Subtract to the next hundred with and without using a number line model

Subtract a 2-digit number from a 3-digit number using the "Make the Previous Hundred" strategy (Part 1)

Learn how to subtract a two-digit multiple of 10 from a three-digit multiple of 10 by using the make the previous hundred strategy
Subtract a 2-digit number from a 3-digit number using the "Make the Previous Hundred" strategy (Part 1)

Subtract a 2-digit number from a 3-digit number using the "Make the Previous Hundred" strategy (Part 2)

Practice subtracting a two-digit multiple of 10 from a three-digit multiple of 10 by using the make the previous hundred strategy
Subtract a 2-digit number from a 3-digit number using the "Make the Previous Hundred" strategy (Part 2)

Subtract a 2-digit round number from a 3-digit round number using mental math

Practice subtracting a two-digit multiple of 10 from a three-digit multiple of 10 using mental math. You may use the make the previous hundred strategy, or any other strategy
Subtract a 2-digit round number from a 3-digit round number using mental math

Break a 3-digit number into hundreds and a 2-digit number

Practice breaking a three-digit number into hundreds and the remaining two-digit number. These problems don't require regrouping
Break a 3-digit number into hundreds and a 2-digit number

Add 3-digit numbers by adding on the hundreds first

Learn a strategy for adding two three digit numbers without regrouping by adding on the hundreds first, then adding the rest. Numbers used in the problems are all multiples of 10
Add 3-digit numbers by adding on the hundreds first

Add 3-digit numbers using mental math

Add two 3-digit numbers using mental math. Hints are given about how to complete the addition of the place values
Add 3-digit numbers using mental math

Add 3-digit numbers with exchanging by adding on the hundreds first

Practice adding two three-digit multiples of 10 without regrouping using mental math. You may use any strategy, including adding on hundreds first
Add 3-digit numbers with exchanging by adding on the hundreds first

Add 3-digit numbers with exchanging using mental math

Practice adding two three-digit multiples of 10 with regrouping using mental math. You may use any strategy, including first adding on hundreds, then adding on tens
Add 3-digit numbers with exchanging using mental math

Subtract 3-digit numbers by subtracting the hundreds first

Practice subtracting two-digit multiples of 10 without regrouping by first subtracting the hundreds then subtracting the tens
Subtract 3-digit numbers by subtracting the hundreds first

Subtract 3-digit numbers using mental math

Practice subtracting two-digit multiples of 10 without regrouping using mental math. You may use any strategy, including first subtracting the hundreds then subtracting the tens
Subtract 3-digit numbers using mental math

Subtract 3-digit numbers with exchanging by subtracting the hundreds first

Subtract three-digit multiples of 10 with regrouping by first subtracting hundreds and then subtracting tens
Subtract 3-digit numbers with exchanging by subtracting the hundreds first

Subtract 3-digit numbers with exchanging using mental math

Subtract three-digit multiples of 10 with regrouping using mental math. You can use any strategy, including first subtracting hundreds and then subtracting tens
Subtract 3-digit numbers with exchanging using mental math

Topic B: 3-Digit Column Addition

Students use column addition to add 3-digit numbers with one or more exchanges. A gradual release model helps students become independent with these multi-step problems.

Topic C: 3-Digit Column Subtraction

Students use column subtraction to subtract 3-digit numbers with one or more exchanges. A gradual release model helps students become independent with these multi-step problems.

MODULE 6. Foundations of Multiplication and Division

Topic A: Formation of Equal Groups

Students work with identical real-world objects to form equal groups given either the number of groups or the number of objects to put in each group. They also determine the number of groups, the number of objects in each group, and the total number of objects. Students relate repeated addition number sentences to visual representations of equal groups.

Counting real-world objects and equal groups (Part 1)

Students will count the number of real-world objects in equal groups, then the number of equal groups
Counting real-world objects and equal groups (Part 1)

Counting real-world objects and equal groups (Part 2)

Students will have more practice counting the number of real-world objects in equal groups, then the number of equal groups
Counting real-world objects and equal groups (Part 2)

Using sets of real-world objects as models for repetitive addition equations

Using real-world objects in equal groups, students complete statements "X groups of X objects" based on models, then match statements to repetitive addition equations and solve
Using sets of real-world objects as models for repetitive addition equations

Making two equal groups (Part 1)

Students will split a given number of objects into two equal groups. Students will begin to notice if the original number is unable to be split equally
Making two equal groups (Part 1)

Making equal groups (Part 2)

Students will split a given number of objects into equal groups, then count the amount of objects in each group
Making equal groups (Part 2)

Making sets of a particular number (Part 1)

Given a number of objects, students will count out a particular number of objects to make each set. They will then label the number of groups and amount of objects in each set
Making sets of a particular number (Part 1)

Making sets of a particular number (Part 2)

Students will determine how many groups can be made by splitting objects into sets of a particular number
Making sets of a particular number (Part 2)

More practice counting real-world objects and equal groups

Students will label a number of real-world objects with the number of equal groups and the amount of objects in each group
More practice counting real-world objects and equal groups

Using sets of equal groups to solve repetitive addition equations

Students will learn that a set of equal groups can be represented through a repetitive addition problem, where each addend is the number of objects in a group. Students will represent a picture with such an equation and find the sum
Using sets of equal groups to solve repetitive addition equations

Representing sets of equal groups as a repetitive addition equation

Given a set of equal groups, students will compose an addition equation and solve for the total amount
Representing sets of equal groups as a repetitive addition equation

Topic B: Arrays and Equal Groups

Students work with abstract objects in arrays to determine number of columns/rows, number of objects in each column/row, and total number of objects. They use repeated addition to represent arrays, looking at an array both as a set of rows and a set of columns.

Topic C: Rectangular Arrays as a Foundation for Multiplication and Division

Students move from a collection of objects arranged in an array to arrays composed of a grid of squares. As in the previous topic, they determine the number of objects in each column/row and the total number of objects, as well as using repeated addition to represent the array.

Describe a rectangular array by rows or columns using repeated addition (Part 1)

Describe a rectangular array of squares by naming the number of rows and the number in each row, or the number of columns and the number in each column. Then use repeated addition to tell how many in all
Describe a rectangular array by rows or columns using repeated addition (Part 1)

Describe a rectangular array by rows or columns using repeated addition (Part 2)

Describe a rectangular array of squares by naming the number of rows and the number in each row, or the number of columns and the number in each column. Then use repeated addition to tell how many in all
Describe a rectangular array by rows or columns using repeated addition (Part 2)

Describe a rectangular array by rows or columns using repeated addition (Part 3)

Describe a rectangular array of squares by naming the number of rows and the number in each row, or the number of columns and the number in each column. Then use repeated addition to tell how many in all
Describe a rectangular array by rows or columns using repeated addition (Part 3)

Create an array and label it using repeated addition (Level 1)

Use squares to build a rectangle with the given number of rows or columns and a given number of squares in each row or column, then write a repeated addition equation to show how many squares there are in all. The frame for the rectangle is given
Create an array and label it using repeated addition (Level 1)

Create an array and label it using repeated addition (Level 2)

Use squares to build a rectangle with the given number of rows or columns and a given number of squares in each row or column. Check your work after each column or row you build. Then write a repeated addition equation to show how many squares there are
Create an array and label it using repeated addition (Level 2)

Create an array and label it using repeated addition (Level 3)

Use squares to build a rectangle with a given number of rows or columns and a given number of squares in each row or column. Then write a repeated addition equation to show how many squares there are in all
Create an array and label it using repeated addition (Level 3)

Topic D: The Meaning of Even and Odd Numbers

Students explore the concept of even and odd in multiple ways. They determine that the sum of two equal addends is even. They use pairing, addition patterns, and number line patterns to determine even and odd. They also use ending digits to determine even or odd in numbers up to three digits.

Add two equal addends to get an even number sum

Learn that even numbers are the sum of two equal addends. State the number of items shown and then double the amount and state the total. then, practice finding the sums of equal addends
Add two equal addends to get an even number sum

Pair objects to determine whether the total is even

Count two sets of similar objects. Learn that pairing objects can determine if the total is even
Pair objects to determine whether the total is even

Determine whether a set of objects is even or odd

Identify whether the set of given objects is even or odd. Learn that when objects in a set cannot be paired, then the number is odd
Determine whether a set of objects is even or odd

Identify how addition pattern of +1 or +2 relates to even and odd

Learn how relationship between even and odd numbers happens by adding 1 or 2 to an even number
Identify how addition pattern of +1 or +2 relates to even and odd

Determine whether a hidden number on a number line is even or odd

Practice counting by 2s within one-, two-, or three-digit numbers. Identify the value of consecutive numbers on a number line and whether they are even or odd. Also, learn that zero is an even number
Determine whether a hidden number on a number line is even or odd

Identify even numbers as ones ending in 0, 2, 4, 6, or 8

Count by 2s to fill in a grid of even numbers to learn that all even numbers end in 0, 2, 4, 6, or 8. Then practice giving even numbers; one-, two-, or three-digit numbers are accepted
Identify even numbers as ones ending in 0, 2, 4, 6, or 8

Identify odd numbers as ones ending in 1, 3, 5, 7, or 9

Learn that all odd numbers end in 1, 3, 5, 7, or 9. Then practice entering odd numbers; one-, two-, or three-digit numbers are accepted
Identify odd numbers as ones ending in 1, 3, 5, 7, or 9

Identify several digit numbers as even or odd

Students explore 3 digit numbers and identify them as even or odd based on the number in the ones place. Then, students practice identifying even and odd 3-digit numbers
Identify several digit numbers as even or odd

Determine if a given number is even or odd based on the final digit

Given a large number, determine if it is even or odd based on the digit in the ones place. Numbers range from 6 to 8 digits
Determine if a given number is even or odd based on the final digit

Identify 3-digit numbers as odd or even

Select either all even or all odd numbers out of a set of six 3-digit numbers
Identify 3-digit numbers as odd or even

MODULE 7. Problem Solving with Length, Money, and Data

Topic A: Creating an inch ruler

Students refine their ruler-using skills as they measure various objects using different units of length. In addition, they compare different lengths and units of measurement including centimeters, inches, and feet.

Topic B: Displaying Measurement Data

Students create simple line plots based on weight and length measurements. They answer questions based on line plots, including how many, what measurement, minimum, maximum, most common, least common, and total.

MODULE 8. Time, Shapes, and Fractions as Equal Parts of Shapes

Topic A: Attributes of Geometric Shapes

Students build on their prior knowledge of a shape's defining attributes to recognize and draw categories of polygons with specified attributes: the number of sides, corners, and angles. For example, students see that a rectangle has four straight sides, four right angles, and opposite sides with equal length. Students then relate the square, a special rectangle, to the cube by building a cube from six congruent squares. They describe the cube in terms of its attributes, counting the number of edges, faces, and corners.

Discover that every geometric shape is made up of sides and angles

Identify the angles within geometric shapes. Identify the number of sides and angles in a triangle
Discover that every geometric shape is made up of sides and angles

Discover the attributes of a quadrilateral

Learn about the amount of sides and angles that define a quadrilateral. Identify quadrilaterals based on the number of sides and angles in a given set of shapes
Discover the attributes of a quadrilateral

Determine if a given shape is or is not a quadrilateral

Learn two new attributes of quadrilaterals: their sides cannot intersect and they must be a closed shape. Determine if a given shape is or is not a quadrilateral based on these attributes
Determine if a given shape is or is not a quadrilateral

Draw triangles and quadrilaterals

Use knowledge of attributes of geometric shapes to draw a triangle and quadrilateral on a dot grid. Demonstrate understanding of the features of quadrilaterals by drawing a second that differs from the first
Draw triangles and quadrilaterals

Match a given label to the corresponding shape

Given a set of three shapes, choose the shape that corresponds with the given label. Shapes include triangles, quadrilaterals, and polygons
Match a given label to the corresponding shape

Discover the attributes of a hexagon

Identify a hexagon. Identify the number of sides and angles that define a hexagon
Discover the attributes of a hexagon

Learn that triangles, quadrilaterals, and hexagons are all polygons

Match a label with each corresponding geometric shape. Learn that a polygon is the common name for all geometric shapes that are closed and have sides that do not intersect. Choose polygons from a given set of shapes
Learn that triangles, quadrilaterals, and hexagons are all polygons

Discover the attributes of a pentagon

Draw a pentagon. Identify the number of sides and angles that define a pentagon. Choose pentagons from a given set of shapes
Discover the attributes of a pentagon

Identify different types of polygons

When given the name of a geometric shape, choose that shape from a given set. Shapes include triangles, quadrilaterals, pentagons, and hexagons
Identify different types of polygons

Answer questions that compare polygons

Answer questions about the attributes of polygons. Questions also ask about differences between two polygons, including their number of sides and angles
Answer questions that compare polygons

Discover the attributes of a cube

Explore an interactive model of a cube. Use squares to build a cube. Identify the number of faces on a cube
Discover the attributes of a cube

Topic B: Composite Shapes and Fraction Concepts

Working with triangles and squares, students rotate shapes to fill a pattern. They learn that the number of pieces in the whole are called halves, thirds, fourths, and sixths based on the total number.

Topic C: Halves, Thirds, and Fourths of Circles and Rectangles

Students build upon their knowledge of halves, thirds, and fourths to answer more complex questions about fractional parts of shapes. They split shapes into given fractions, identify the size of fractional parts, and tell how many parts make a whole.

Topic D: Application of Fractions to Tell Time

Students begin with the basics of telling time - identifying the hour and minute hands on a clock, counting around the minutes on a clock, and telling time to the hour and half hour. They progress to telling time to 15 minutes and to 5 minutes, identifying noon and midnight, and using a.m. and p.m. Throughout, students use analog clocks, digital times, and words.

Read and write time to the hour

Students identify the hour hand on a clock and clocks that show the exact hour. They write the time to the exact hour as shown on a clock
Read and write time to the hour

Identify a half hour as 30 minutes and an hour as 60 minutes

Students count the minutes around the clock by 5s. They equate an hour to 60 minutes and half an hour to 30 minutes
Identify a half hour as 30 minutes and an hour as 60 minutes

Tell time to the half hour and write time to the hour

Students learn that 30 minutes past the hour is called "half past." They also identify the digital time that matches analog time to the half hour. Students write time to the exact hour as shown on a clock
Tell time to the half hour and write time to the hour

Tell time to quarter past and quarter to the hour

Students learn that 15 minutes past the hour is called "quarter past" and 15 minutes before the hour is called "quarter to." They also learn that when the hour hand is between numbers, the hour is the lesser number
Tell time to quarter past and quarter to the hour

Tell time to 15 minutes and show a given time on a clock

Students record the minute portion of the time shown on a clock. They choose the time in word form (such as "quarter past 7") to match the time shown on a clock. They move the hands of a clock to show a given time
Tell time to 15 minutes and show a given time on a clock

Tell time to 5 minutes

Students type the hour and minutes to tell the time shown on a clock
Tell time to 5 minutes

Identify midnight and noon

Students learn that a day is from midnight to midnight. They learn how the clock shows midnight and noon
Identify midnight and noon

Use a.m. and p.m. in telling time

Students learn to use a.m. and p.m. in telling time. They identify whether an event takes place in the a.m. or the p.m. They tell time on a clock and determine whether it's a.m. or p.m. based on a picture
Use a.m. and p.m. in telling time