Curriculum for Grade 2

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

Adding to groups of ten

Students will solve equations that require them to add a single-digit number 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

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

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

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

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

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

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

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

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

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 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

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 within 100

Practice addition and subtraction within 100. The sums do not cross the tens

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

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 2)

Find sums and differences within 100 across tens. Enter the answer the equation. No models are given

Solve +/- equations within 100

Practice addition and subtraction within 100 across tens. Enter the answer the equation. No models are given

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

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 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

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

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

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

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

Draw a line segment of a given length

Practice drawing a segment of a given length along a ruler

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

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.

Count to measure lengths of objects in meters

Measure objects using a meter stick. Learn the relationship between centimeters and meters. Then, measure large objects in terms of whole meters

Learn about the relationship between meters and centimeters, and compare the two units of length

Deepen knowledge about centimeters and meters by comparing measurements in each unit and determining which is greater

Use the greater than, less than, or equal to signs to compare measurements in centimeters and meters. Then, decide which unit fits a situation best

Compare measurements given in centimeters and meters using symbols. Then, observe real-world objects and determine whether measurement in meters or centimeters fits best

Match estimated lengths and units to objects

Identify whether given objects are measured in meters or centimeters. Match the correct units to the measurement of one object. Then, match the correct value and units to 2 or 3 given objects

Measure approximate lengths of objects aligned to a ruler

Estimate the approximate lengths of objects aligned to a ruler. First, state the approximate length of objects to the nearest centimeter. Then, estimate the length of larger objects to the nearest meter

Measure the approximate lengths of objects using a meter stick

Estimate the length of real world objects using meter sticks. First, identify the measurement closest to the endpoint. Less support is provided as students deepen their knowledge

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.

Measure objects that exceed the length of the ruler

Measuring objects longer than one ruler length. Align a 10 cm ruler with one endpoint, then shift the ruler to its other endpoint and add the measurements. Then, measure with a longer ruler and reading off lengths greater than 10 cm

Subtract to compare lengths of measured objects

Compare the lengths of two objects. Measure each with a ruler, then choose whether to add or subtract the measurements to find how much longer the greater measurement is

Add or subtract lengths of measured objects

Measure two segments and find their sum or difference. Then, measure the length and width of a rectangle and find the difference between them

Subtract lengths of measured objects to solve word problems

Apply finding the difference in length measurements to growing lifeforms. Measure the lengths and subtract to find how much growth happened

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

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

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

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

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 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

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

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.

Count by tens up to one hundred

Students learn to count by tens to one hundred. They will write the names of the tens as they count

Use base ten blocks to determine the number

Students will use base ten blocks to determine place values under 200

Build the number using base ten blocks

Students use base ten blocks and their understanding of place value to build the given three-digit number

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.

Counting by hundreds

Students will learn to count by hundreds to one thousand. Students will write both the names of the tens and the numbers

Build three-digit numbers with base ten blocks

Students use base-ten blocks and their understanding of place value to build each three-digit number given

Skip counting by ones and tens

Students master patterns of skip counting by ones and skip counting by tens

Skip counting by fives and hundreds

Students master patterns of skip counting by fives and hundreds

Identify and continue the pattern

Identify and continue the skip counting pattern

Students learn to represent the same number in different ways, including standard, unit, word, and expanded forms. They will apply their knowledge of place value to understand how numbers are converted between forms.

Represent numbers using a place value chart

Represent 3-digit numbers on a place value chart noting hundreds, tens, and ones

Explore numbers in standard form

Learn that numbers in standard form are written with only digits. Given several representations, choose the number in standard form

Explore numbers in unit form

Learn to represent 3-digit numbers in unit form, including scenarios where there are no tens or ones. Select numbers written in unit form from several representations

Explore numbers in word form

Learn to represent numbers in word form. Select the correct name for a 3-digit number in word form. Then, select the correct standard form representation of a number given in word form

Explore numbers in expanded form

Represent numbers on a place value chart to begin to understand the concept of expanded form. Then, they will select and represent given 3-digit numbers in expanded form

Identify the value of numerals in 3-digit numbers

Use understandings of place value to identify the value of each numeral in a 3-digit number

Rewrite numbers in expanded form

Represent a number given in standard form as expanded form, including the appropriate symbol

Review unit form

Convert a number given in standard form to unit form

Review standard, unit, and word forms

Match a number given in one form to its equal representation in another. Review the standard, unit, and word forms of numbers

Represent numbers in different forms

Students will master the ability to represent numbers in each of the different forms

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 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 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 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

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

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 unit notation

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

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

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

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

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 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 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 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 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 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 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 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 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

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 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 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

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 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 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 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 3)

Students determine 1, 10, and 100 more and less than the same 3-digit number

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

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 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

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 10s or 100s (3-digit numbers)

Students complete a counting sequence of three-digit numbers counting up or back by tens or hundreds

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

Count up by 10s

Students determine 10 more (repeated) of a 3-digit number

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

Counting patterns (Level 2)

Students determine missing numbers within patterns of counting up or down by 1s, 10s, or 100s

Students practice strategies for solving 2-digit +/- problems with and without exchanging. They use familiar representations (base-10 blocks and place value cards) and new strategies (decomposing numbers and making tens) to solve equations.

Use base-10 blocks to add a 2-digit number to a tens number

Students use base-10 block models to solve addition equations with 2-digit addends, one of which is a tens number

Add a 2-digit number to a tens number, without a model

Students solve simple addition equations with 2-digit addends, one of which is a tens number

Use base-10 blocks to add 2-digit numbers

Students use base-10 block models to solve addition equations with 2-digit addends. They first add the ones, then the tens, then both together to find the sum

Use understanding of place value to solve addition equations

Students use place value cards to solve addition equations with 2-digit addends. Students then use knowledge of place value to solve equations without card models

Solve addition equations with 2-digit numbers

Students solve simple addition equations with two 2-digit addends

Solve more addition equations with 2-digit numbers

Students solve more simple addition equations with two 2-digit addends

Use base-10 blocks to solve addition equations requiring exchanges

Students use base-10 block models to solve 2-digit addition problems. When there are 10 or more ones, students make an exchange into the tens, then solve

Use place value cards to solve addition equations requiring exchanges

Students use place value cards to solve 2-digit addition equations requiring exchanges. Students then use knowledge of place value to solve equations without card models

Solve 2-digit addition problems without a model

Students use their knowledge of place value to solve 2-digit addition equations requiring exchanges

Use base-10 models to solve subtraction equations

Students use base-10 blocks to solve 2-digit subtraction equations where the subtrahend is a tens number

Solve 2-digit subtraction equations

Students solve 2-digit subtraction equations where the subtrahend is a tens number. They subtract the tens, then write the ones to solve

Decompose 2-digit numbers

Students decompose 2-digit numbers into tens and ones

Decompose numbers as a strategy to solve 2-digit subtraction equations

Students solve 2-digit subtraction equations by decomposing the subtrahend into tens and ones. Then, they subtract by parts: first the tens, then the ones

Solve more 2-digit subtraction equations by decomposing numbers

Students solve more 2-digit subtraction equations by decomposing the subtrahend into tens and ones. Then, they subtract by parts: first the tens, then the ones

Use making tens as a strategy to solve 2-digit subtraction equations

Students solve subtraction equations using the strategy of making 10. They break the subtrahend into parts; one part, when subtracted, makes a tens number, then they subtract the remainder

Use number bonds to solve 2-digit subtraction equations

Students use the prior strategies to solve 2-digit subtraction equations

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

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

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

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 2)

Students practice column addition with two digit addends

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

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 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

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 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 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 2)

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

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 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 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

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.

Solve subtraction problems using disk models

Students will represent and solve subtraction problems using disk models. Problems do not require regrouping

Use disk models to support solving column subtraction

Students will rewrite a subtraction problem as column subtraction. Then, students will use the familiar disk model to help solve the column subtraction, without regrouping

Solve column subtraction with scaffolding

Students will rewrite subtraction problems as column subtraction. Students will then practice column subtraction step-by-step. Problems do not require regrouping

Use disk models to practice exchanging into the tens

Students will use disk models to understand when exchanging into the tens needs to occur to solve subtraction problems

Solve subtraction problems with regrouping (Level 1)

Students will use disk models to solve subtraction problems where exchanging into the tens is a necessary step

Solve subtraction problems with regrouping (Level 2)

Students use disk models to scaffold column subtraction and solve equations where exchanging into the tens is a necessary step

Solve subtraction problems with regrouping (Level 3)

Students solve subtraction problems where exchanging into the tens is a necessary step. Students will use disk models to make the exchanges, then solve using only column subtraction

Solve subtraction problems with regrouping (Level 4)

Students will solve subtraction problems where exchanging into the tens is a necessary step, using only column subtraction

Solve column subtraction, making decisions about exchanging into the tens

Students will solve column subtraction problems by making decisions about whether or not exchanging into the tens is a necessary step

Practice solving column subtraction problems independently (Part 1)

Students will solve column subtraction problems using the strategies they have learned without any additional prompts or scaffolding

Practice solving column subtraction problems independently (Part 2)

Students will continue to practice utilizing strategies to solve column subtraction problems without additional supports

Solve column subtraction problems with 2- and 3-digit components (Level 1)

Students will solve column subtraction problems with 2- and 3-digit components. Students will begin to see that the step of making exchanges apply to subtraction problems with larger values

Solve column subtraction problems with 2- and 3-digit components (Level 2)

Students will solve column subtraction problems with 2- and 3-digit components. Students will have to recall the correct order for subtracting the 1s, 10s, and 100s without prompting

Solve column subtraction problems with 2- and 3-digit components (Level 3)

Students will solve column subtraction problems with 2- and 3-digit components without any additional supports

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

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

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

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 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 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

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 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 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 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 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 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

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 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

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

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 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 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 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 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

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 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 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 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 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

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

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 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 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 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

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 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 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 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

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.

Solve 3-digit column addition with exchanging ones using a disk model

Add three-digit numbers that require regrouping ones, using the standard algorithm and the disk model. The disk model illustrates how and why the ones are regrouped

Solve 3-digit column addition with exchanging ones or tens

Add three-digit numbers that require regrouping ones or tens using the standard algorithm

Solve 3-digit column addition with multiple exchanges (Level 1)

Add three-digit numbers that require regrouping both ones and tens using the standard algorithm

Solve 3-digit column addition with multiple exchanges (Level 2)

Practice adding three-digit numbers that require regrouping both ones and tens using the standard algorithm. Can you solve all four problems before you run out of lives?

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.

Solve 3-digit column subtraction with exchanging with and without using a disk model

Subtract three-digit numbers that require one regrouping using the standard algorithm. The first problems include a disk model to illustrate the subtraction and the regrouping. The remaining problems do not use a disk model

Solve 3-digit column subtraction with multiple exchanges

Practice subtracting three-digit numbers that require more than one regrouping using the standard algorithm

Model 2-step exchanges in subtraction problems using a disk model

Learn how to exchange 1 hundred disk for 10 tens disks, and then 1 of those tens disks for t0 ones disks for a two-step regrouping. This skill is used when there aren't enough ones to subtract, and the tens digit is zero

Solve 3-digit column subtraction with 2-step exchanges with and without using a disk model

Subtract 3-digit numbers that require a 2-step regrouping. A 2-step regrouping is done when there are not enough ones to subtract, and the tens of the minuend is zero. This requires regrouping 1 hundred as 10 tens, and then regrouping 1 ten as 10 ones

Solve 3-digit column subtraction with 2-step exchanges

Subtract 3-digit numbers that require a 2-step regrouping. A 2-step regrouping is done when there are not enough ones to subtract, and the tens of the minuend is zero. This requires regrouping 1 hundred as 10 tens, and then regrouping 1 ten as 10 ones

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 2)

Students will have more practice counting the number of real-world objects in equal groups, then the number of equal groups

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

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 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 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 2)

Students will determine how many groups can be made by splitting objects into sets of a particular number

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

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

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

Students explore the concepts of rows and columns using objects. They begin to learn to describe arrays in terms of their columns and rows, as well as through repeated addition.

Explore the concept of rows

Students explore the concept of equal rows. They place objects into rows, then identify the number of rows and objects within each row

Explore the concept of columns

Students explore the concept of equal columns. They place objects into columns, then identify the number of columns and objects within each column

Identify the number of columns and the objects within them

From a given array, students identify the number of columns and the number of objects within each column

Identify the number of rows and the objects within them

From a given array, students identify the number of rows and the number of objects within each row

Compose a repeated addition sentence based on an array's rows

Compose and solve a repeated addition sentence to determine the total number of objects in a given array. The addition equation is based on the number of objects in each row

Compose a repeated addition sentence based on an array's columns

Compose and solve a repeated addition sentence to determine the total number of objects in a given array. The addition equation is based on the number of objects in each column

Represent arrays as their number of rows and objects and as repeated addition sentences

Students explore two ways to name an array- the number of rows and objects in each row, or the same fact represented by repeated addition

Describe arrays in terms of their columns and rows

Students describe the same array based on the number of objects and columns and as the number of objects and rows

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 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 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

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 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 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

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

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

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

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

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

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 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 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

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

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

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.

Compare different units of length and measure objects using centimeters and inches

Students use a ruler to measure objects. Then, students will compare different units of lengths and practice measuring objects in both inches and centimeters

Align 0 on the ruler with the endpoint of objects being measured

Students practice aligning 0 on the ruler with the endpoint of objects as they measure them

Use a ruler to make approximate measurements by rounding up or down to the nearest inch

Students practice identifying the measurement on the ruler that's closest to the endpoint of an object. Then, students round up or down to the nearest inch when measuring objects with a ruler. Finally, students draw lines that match a given measurement

Measure the sides of rectangles and compare their lengths

Students measure the sides of rectangles using a ruler. Then, they compare the length of the sides using subtraction

Students learn about feet as a unit of measurement

Students learn about feet and how many inches are in a foot. Then, students measure objects using feet

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.

Create and interpret a line plot (Part 1)

Create a line plot based on length measurements. Answer questions based on line plots of length measurements

Determine minimum and maximum on a line plot

Answer questions based on line plots of length measurements, with a focus on minimum and maximum measurements

Create and interpret a line plot (Part 2)

Create a line plot based on weight measurements. Answer questions based on line plots of weight measurements

Determine most common, least common, and total on a line plot

Answer questions based on line plots of length measurements, including most common, least common, and total

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 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

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

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

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

Discover the attributes of a hexagon

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

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

Identify pentagons based on their attributes

Given two shapes, students will identify the pentagon based on the attributes of being a closed shape with 5 sides

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

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

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

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.

Rotate and align two indentical triangles to fill a pattern

Given a pattern split into halves, rotate two identical triangles to align with the pattern

Rotate and align triangles and a square to fill a pattern

Given a pattern split into sections, rotate two identical triangles and a square to align with the pattern

Rotate and align triangles that are halves, thirds, fourths, and sixths of a pattern

Rotate triangles to align with a pattern split into halves, thirds, fourths, and sixths

Create different shape patterns using the same three thirds or four fourths

Rotate triangles to align with multiple patterns split into thirds or fourths. Realign halves of two small squares into fourths of one large square

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.

Identify shapes that are split into halves

Given one or more shapes, identify which are split into two equal parts, or halves

Split shapes in half and complete the missing half of shapes

Recognize that some shapes can be split in half in different ways. Split rectangles and hexagons into halves in different ways. Complete the missing half of a given shape

Identify shapes that are split into thirds and split shapes into thirds

Given one or more shapes, identify which are split into three equal parts, or thirds. Split shapes into thirds

Identify shapes that are split into fourths and split shapes into fourths

Given one or more shapes, identify which are split into four equal parts, or thirds. Split shapes into fourths

Sort shapes that are split into halves, thirds, and fourths

Given a shape, identify whether it is split into halves, thirds, or fourths

Identify parts of a whole in shapes split into halves, thirds, and fourths

Identify which fraction a shape is split into. Tell how many of a given fraction are in a whole. Identify how many more of a given fraction are needed to make an incomplete shape whole

Identifying the number of pieces in a shape split in halves, thirds, and fourths

Students will recognize that splitting a shape into halves means two pieces, thirds means three pieces, and fourths means four pieces. Students will identify how many pieces are missing from one whole

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

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

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 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 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 5 minutes

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

Identify midnight and noon

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