Curriculum for Grade 2

Students extend their understanding of addition and subtraction within 20. Use of base-10 blocks reinforces the concept of a "ten" 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.

Balance the scales

Add or subtract weights from a scale to match a number on a present. Place the matching sum of weights on the right side to balance the scale. There are several weights with different numbers below the scale. If needed remove weights on the right side

Identify a missing addend in equations with a sum of 10 and their turnaround facts

Complete equations for the sum of 10. First, a cube model is provided for the fact family in the equation. Then, two addition equations for the same fact family are given. Enter the missing addend in each equation

Match two addends to reach a sum of 10

Practice pairs of numbers that have a sum of 10. Out of 3 or 4 coins, select the two that add up to 10 to buy an item

Record a model of base-10 blocks as two related equations that show subtraction from 10

Write addition and subtraction equations within a fact family of 10. A cube model is shown with a total of 10 cubes in two colors. Complete the addition equation represented by the model. Then complete one or two subtraction equations with the same facts

Solve +/- equations within 10

Practice addition and subtraction within 10. Only the equations are given without any models

Solve +/- equations that include the number 10 (Part 1)

Solve addition or subtraction problems within 19 where one element is 10. Cube models are shown to offer assistance

Solve +/- equations that include the number 10 (Part 2)

Solve addition or subtraction problems within 19 where one element is 10. Just the equations are shown with no models

Add ones to numbers in the second ten using base-10 blocks

Add a 1-digit number to a number between 11 and 19. The 2-digit number is separated into tens and ones. Drag the additional ones to the ones column to help find the sum. Enter the total into the equation

Subtract from numbers 11-20 using base-10 blocks

Subtract a 1-digit number from a number between 11 and 19. The 2-digit number is separated into tens and ones. Pop the subtracted ones in the ones column to help find the difference. Enter the answer into the equation

Solve +/- equations that include a 2-digit number with sums and differences 11-19

Practice addition and subtraction within 11 to 19. Only the equations are given without any 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

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

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 apply their counting and place value skills to three-digit numbers to 200. They reinforce their understanding of a hundred using the base-10 flat, place value cards, and a set of filled ten-frames.

Add across 100 using base-10 blocks

Learn the meaning of 3-digit numbers and how they are represented with base-10 blocks. Identify each number modeled by the blocks. Then, write the 3-digit number shown by the model. Practice reading a model of base-10 blocks by entering the total

Determine a 3-digit total of objects in ten-frames (aligned)

Find a 3-digit total. Given are a truck that can hold 10 boxes of 10 fruits, additional boxes, and individual fruits. Create 100 by grouping ten 10-frames. Then, enter the total of number of objects shown by adding up the hundreds, tens, and ones

Determine a 3-digit total of objects in ten-frames (scattered)

Find a 3-digit total. Given are a truck that can hold 10 boxes of 10 fruits and individual boxes and fruits. Create 100 by moving 10-frame boxes into the truck. Then enter the total number of objects by adding the hundreds, tens and ones

Count across a ten using 3-digit numbers on a number line

Learn to count forwards and backwards across 100 with the help of a number line. Fill in the three missing numbers on the number line within 90 to 110

Students apply their counting, reading, and place value skills to three-digit numbers. Students use the hundred chart as well as vertical and horizontal number lines to count forward and backward, identify missing numbers, and identify number names. Students address the challenging skill of counting across tens within a hundred and across a hundred. They strengthen their conceptual understanding of counting patterns and their ability to count mentally in the hundreds.

Determine a missing 3-digit round number on a number line and identify its written name (Part 1)

Learn to count by hundreds. First, select the names of the hundreds displayed on a number line. Then, enter all of the hundreds between 0 and 1000 on a number line going forwards and backwards

Determine a missing 3-digit round number on a number line and identify its written name (Part 2)

Practice counting by hundreds. Enter the missing hundred on a number line and select its name out of a choice of three options

Determine a missing 3-digit round number on a number line and identify its written name (Part 1)

Practice counting by hundreds. Enter the missing hundred on a number line and select its name out of a choice of three options

Position 3-digit round numbers, in both digits and words, on a vertical number line

Place the hundreds numbers in their correct location on the number line. First, the digits are given. Then, the names in words are given

Count multiple hundreds crossing from nineties to hundreds based on a model of base-10 blocks

Learn how to represent multiples of 100 with base-10 blocks. State the number represented by layers of hundred-squares. Then, identify the number represented by the tens-rods and state the total

Determine a 3-digit total of base-10 blocks with and without a model of place value cards

State the 3-digit number represented by base-10 blocks. Identify each place value and enter the total

Count across a ten using 3-digit numbers on a number line

Practice counting 3-digit numbers forwards across tens on a number line. Enter the three missing numbers on the number line

Count backward across a ten using 3-digit numbers on a number line

Practice counting 3-digit numbers backwards across tens on a number line. Enter the three missing numbers on the number line

Count forward and backward across a hundred using 3-digit numbers on a number line

Count 3-digit numbers forwards and backwards across hundreds on a number line. Enter the three missing numbers on the number line

Determine a missing 3-digit number on a number line and identify its written name

Find and name the missing 3-digit number on a number line. Enter the digits, then select the name out of three options

Recognize equivalencies between ones, tens, hundreds, and a thousand using base-10 blocks

Learn the relationship between ones, tens, hundreds, and a thousand. Rename 10 ones as 1 ten, 10 tens as 1 hundred. Then, stack hundreds, counting by hundreds to 1000

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.

Decompose 3-digit numbers into hundreds, tens, and ones

Decompose a 3-digit number into its place values. First, select the correct hundreds, tens, and ones that form the given number. Then write the decomposition in expanded form as an addition expression

Compose 3-digit numbers based on a set of place value cards showing hundreds, tens, and ones

Create a 3-digit number from place value cards. Given are a hundreds number, a tens number, and a ones number, combine them to enter a 3-digit number. Two sets of cards are given on each screen

Compose a 3-digit number based on its written name

Translate the written name of a number into the digits. A 3-digit number is stated in words. Enter the digits that represent that number

Compose a 3-digit number with or without placeholder zeros based on its written name

Write the digits for the written name of a number. A 3-digit number is stated in words. Enter the digits that represent that number. The tens or ones digit may be 0

Compose 3-digit numbers based on a given number of hundreds, tens, and ones

Decompose a 3-digit number into its place values. First, determine how many hundreds, tens, and ones are contained in a given number. Then, reverse the process and state the 3-digit number that contains the given hundreds, tens, and ones

Determine 3-digit totals based on a set of base-10 blocks

Identify the total number of cubes shown in base-10 cubes. Enter the number of hundreds, tens, and ones that are shown. Then, give the 3-digit total

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

Recognize equivalencies between ones, tens, hundreds, and a thousand with and without base-10 blocks (Part 1)

Determine equivalencies between units of ones, tens, hundreds, and thousands. Given a unit in base-10 blocks, state how many cubes there are and choose a unit equivalency. Then complete a multiple-choice equivalency without the block model

Recognize equivalencies between ones, tens, hundreds, and a thousand with and without base-10 blocks (Part 2)

Practice equivalencies between units of ones, tens, hundreds, and thousands. Enter the correct answer to an equivalency question

Determine how many more ones, tens, or hundreds to reach the next ten, hundred, or thousand using a number line (Level 2)

State the number of ones, tens, or hundreds to reach the next ten, hundred, or thousand. Using a number line, identify how many units are needed to reach a specified endpoint from the starting point

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 numbers in ascending and descending order (Part 1)

Arrange 3-digit numbers in increasing or decreasing order. Identify three 3-digit numbers represented by place value charts. Then put those numbers in the specified order. Finally, three numbers to be ordered are given without models

Arrange numbers in ascending and descending order (Part 2)

Arrange 3-digit numbers in increasing or decreasing order. Three 3-digit numbers represented either in digits, written words, or place value amounts. Write each number in standard form, and then put those numbers in the specified order

Arrange two- and three-digit numbers in ascending order

Practice arranging numbers in increasing order. Three 3-digit numbers are give. Drag them into the correct order

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 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 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

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 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

Record a 2-digit number as tens and ones

Practice place value concepts by breaking a two-digit number into 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

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

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 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 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

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 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

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 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

Subtract 2-digit numbers with and without exchanging using a model of base-10 blocks

Practice subtracting two-digit numbers using base-ten blocks as a model. Remove cubes and rods to represent the number being subtracted. The number of remaining cubes is the answer

Subtract 2-digit numbers with exchanging using a model of base-10 blocks

Practice subtracting two-digit numbers using base-ten blocks as a model. Remove cubes and rods to represent the number being subtracted. The number of remaining cubes is the answer

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

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.

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

Represent two-digit addition problems with a disk model in a place value chart. Then use the model to find the sum. These problems do not require regrouping

Add 2-digit numbers without exchanging using place value cards to add tens and ones separately

Practice adding two two-digit numbers without regrouping by first adding the tens and then adding the ones and then adding the two sums

Solve 2-digit column addition without exchanging (Level 1)

Learn to add two two-digit numbers using the standard algorithm without regrouping. Practice setting up the problem by dragging the digits to the correct positions. Then add the numbers in each place value column, and write the result

Solve 2-digit column addition without exchanging (Level 2)

Practice adding two two-digit numbers using the standard algorithm without regrouping. Practice setting up the problem by typing the digits in the correct positions. Then add the numbers in each place value column, and write the result

Exchange into the tens using a disk model

Practice identifying numbers shown by disks in a place value chart. Recognize that when there are 10 ones, they can be exchanged for 1 ten

Add 2-digit numbers with and without exchanging using a disk model

Add two-digit numbers by representing the numbers using the disk model in a place value chart, and exchanging 10 ones for 1 ten when necessary. To find the sum, tell the total represented by the disks in the chart

Add 2-digit numbers with exchanging using place value cards

Add two two-digit numbers by breaking the numbers apart into tens and ones. Add the ones first. If there are more than 9 ones, move the new 10 to the tens column, and then add the tens

Solve 2-digit column addition with and without exchanging using a disk model

Add two two-digit numbers by using the standard algorithm and the disk model, both with and without regrouping. Find out how trading 10 ones for 1 ten in the place value chart is represented in the standard algorithm

Solve 2-digit column addition with and without exchanging (Level 1)

Add two two-digit numbers with regrouping using the standard algorithm. Support is given to guide you through the steps

Solve 2-digit column addition with and without exchanging (Level 2)

Add two two-digit numbers with regrouping using the standard algorithm. Some support is given to guide you through the steps

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

Add two two-digit numbers both with and without regrouping using the standard algorithm. Set up the problem, add, and state the sum

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

Learn to add a three-digit number and a two-digit number with the standard algorithm with and without regrouping ones. Practice setting up the column addition by lining up digits with the same place value, then add

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

Practice solving two- and three-digit addition problems using the standard algorithm, both with and without regrouping ones

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

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

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

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

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 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

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 (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 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 and without exchanging

Subtract two-digit numbers using the standard algorithm both with and without regrouping, and record the answer

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 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?

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 into the hundreds using a disk model

To prepare for addition with regrouping ones and tens, practice exchanging 10 ones for 1 ten and 10 tens for 1 hundred

Solve 2-digit column addition with exchanging into the hundreds using a disk model

Practice adding two two-digit numbers using the disk model in a place value chart, regrouping 10 ones as a ten, and regrouping 10 tens as a hundred

Solve 2-digit column addition with exchanging into the hundreds with and without a disk model

Practice adding two two-digit numbers with regrouping using the standard algorithm. First, see the connection between the standard algorithm and the disk model and how regrouping in the disk model is shown in the algorithm. For the last two problems, use

Solve 2-digit column addition with multiple exchanges

Practice solving two-digit addition problems using the standard algorithm with regrouping. Hints are given at each step to remind you what to do

Solve 2- and 3-digit column addition with multiple exchanges

Add two- and three-digit numbers with regrouping. Can you solve all four problems before you lose all your lives?

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 with exchanging into the hundreds (Part 1)

Subtract a two-digit number from a three-digit number with regrouping using the standard algorithm. HInts are given to remind you of the steps in the algorithm

Solve 2- and 3-digit column subtraction with exchanging into the hundreds (Part 2)

Subtract a two-digit number from a three-digit number with regrouping 1 hundred for 10 tens, using the standard algorithm. HInts are given to remind you of the steps in the algorithm

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

Subtract a two-digit number from a three-digit number both with and without regrouping using the standard algorithm. Can you solve all four problems before you lose all your lives?

Solve 2- and 3-digit column subtraction with multiple exchanges (Part 1)

Subtract a two-digit number from a three-digit number with multiple regroupings using the standard algorithm. Hints are given to remind you of the steps

Solve 2- and 3-digit column subtraction with multiple exchanges (Part 2)

Subtract a two-digit number from a three-digit number with multiple regroupings using the standard algorithm. Hints are given to remind you of the steps

Solve 2- and 3-digit column subtraction with and without multiple exchanges

Practice subtracting two-digit numbers from three-digit numbers using the standard algorithm with multiple regroupings. Can you solve all four problems before you run out of lives?

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.

Create equal groups by dealing objects one by one into a given number of groups

Begin laying the foundation for multiplication. Practice dividing objects into two equal groups or four equal groups, then tell how many are in each group

Create equal groups by putting objects into groups of a given size

Begin laying the foundation for multiplication. Practice placing objects into equal-sized groups and then telling how many groups there are

Identify the number of groups and the number of objects in each group

Look at pictures of identical groups and identify the number of groups and the number of objects in each group

Determine the total number of objects in equal groups

Look at a picture of identical groups of objects, and use repeated addition to tell how many objects there are in all

Compose a repeated addition sentence to represent equal groups and determine the total

Look at a picture of identical groups of objects. Write an addition sentence using repeated addition to find how many in all

Compose and solve a repeated addition sentence based on equal groups (Part 1)

Look at a picture of identical sets of objects. Find the total number. For the first problems, the addition sentence is given. For the rest of problems, write the addition sentence using repeated addition, then type the total number

Compose and solve a repeated addition sentence based on equal groups (Part 2)

Look at a picture of identical groups of objects. Find the number in all using repeated addition. Create the addition sentence using repeated addition, then tell how many in all

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.

Place objects in equal rows or columns

Place objects in equal rows or columns, then tell how many rows or columns there are. Begin by putting beads in equal rows. Then put them in equal columns. Then put them in both equal rows and equal columns

Describe an array by rows or columns using repeated addition

Describe the number of objects in an array by naming the number of rows and the number in each row, and then naming the number of columns and the number in each column. Then use repeated addition to tell how many in all

Compose and solve a repeated addition sentence based on an array (Part 1)

Write an addition sentence using repeated addition to describe the number of beads in each row and the number of rows, or the number of beads in each column and the number of columns

Compose and solve a repeated addition sentence based on an array (Part 2)

Write and solve an equation to describe the number of objects in an array using repeated addition. Equations are based on both the number of rows and number of columns

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 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

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, thrids, 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

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