# Curriculum for Grade 2

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

## MODULE 1. Sums and Differences to 100

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

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

#### Review addition facts with a sum of 10

#### Adding to groups of ten

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

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

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

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

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

#### Adding one- and two-digit numbers

#### Use models to solve subtraction equations with two-digit number

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

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

#### Pretest. Initiating Fluency with Addition and Subtraction Within 100

### Topic B: Initiating Fluency with Addition and Subtraction Within 100

Students build fluency with addition and subtraction problems within 100. They use number bonds and base-10 block models to practice the strategy of breaking an addend/subtrahend into parts to make a 10, then solving.

#### Identify the connection between a number bond and a fact family

#### Complete number bonds

#### Use a number bond to make 10

#### Use number bonds to solve related addition and subtraction equations

#### Use number bonds to solve addition equations that cross a ten

#### Solve addition equations that cross a ten, where one addend is 9

#### Solve more addition equations that cross a ten, where one addend is 8

#### Solve more addition equations that cross a ten, where one addend is 7

#### Find the missing subtrahend in subtraction equations

#### Use number bonds to make 10 and solve subtraction equations

#### Solve subtraction equations that cross a ten (Level 1)

#### Solve subtraction equations that cross a ten (Level 2)

#### Build fluency solving subtraction equations that cross a ten

#### Subtract single-digit numbers from a tens number, using base-10 blocks for support

#### Use number bonds and base-10 blocks to subtract a 1-digit number from a 2-digit number

#### Use number bonds to subtract a 1-digit number from a 2-digit number, crossing a ten

#### Build fluency solving subtraction equations that cross a tens number

#### Build fluency solving subtraction equations with a 1- and 2-digit number

## MODULE 2. Addition and Subtraction of Length Units

### Topic A: Understand Concepts About the Ruler

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

#### Count to measure lengths of objects in non-standard units

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

#### Measure lengths of objects by laying non-standard units correctly

#### Compare lengths measured in different non-standard units

#### Count to measure lengths of objects in centimeters

#### Measure lengths of objects aligned to a centimeter ruler

#### Align objects to a centimeter ruler to measure length

#### Draw a line segment of a given length

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

### Topic B: Measure and Estimate Length Using Different Measurement Tools

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

#### Count to measure lengths of objects in meters

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

#### 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

#### Match estimated lengths and units to objects

#### Measure approximate lengths of objects aligned to a ruler

#### Measure the approximate lengths of objects using a meter stick

### Topic C: Measure and Compare Lengths Using Different Length Units

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

#### Measure objects that exceed the length of the ruler

#### Subtract to compare lengths of measured objects

#### Add or subtract lengths of measured objects

#### Subtract lengths of measured objects to solve word problems

### Topic D: Relate Addition and Subtraction to Length

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

#### Represent change in length as addition or subtraction

#### Add three measurements to find the total length of a path

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

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

#### Use the difference between two numbers to measure a given object

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

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

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

### Topic A: Forming Base Ten Units of Ten and Hundred

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

#### Count by tens up to one hundred

#### Use base ten blocks to determine the number

#### Build the number using base ten blocks

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

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

#### Counting by hundreds

#### Build three-digit numbers with base ten blocks

#### Skip counting by ones and tens

#### Skip counting by fives and hundreds

#### Identify and continue the pattern

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

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

#### Explore numbers in standard form

#### Explore numbers in unit form

#### Explore numbers in word form

#### Explore numbers in expanded form

#### Identify the value of numerals in 3-digit numbers

#### Rewrite numbers in expanded form

#### Review unit form

#### Review standard, unit, and word forms

#### Represent numbers in different forms

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

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

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

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

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

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

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

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

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

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

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

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

### Topic E: Comparing Two Three-Digit Numbers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#### Compare using 1, 10, or 100 more or less

#### Determine 1 or 10 more across place values

#### Determine 1 or 10 less across place values

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

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

#### Counting patterns (Level 1)

#### Count up by 10s

#### Count up by 1s and 100s

#### Counting patterns (Level 2)

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

### Topic A: Sums and Differences Within 100

Students practice strategies for solving 2-digit +/- problems with and without exchanging. They 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

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

#### Use base-10 blocks to add 2-digit numbers

#### Use understanding of place value to solve addition equations

#### Solve addition equations with 2-digit numbers

#### Solve more addition equations with 2-digit numbers

#### Use base-10 blocks to solve addition equations requiring exchanges

#### Use place value cards to solve addition equations requiring exchanges

#### Solve 2-digit addition problems without a model

#### Use base-10 models to solve subtraction equations

#### Solve 2-digit subtraction equations

#### Decompose 2-digit numbers

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

#### Solve more 2-digit subtraction equations by decomposing numbers

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

#### Use number bonds to solve 2-digit subtraction equations

### Topic B: Column Addition with Exchanging into the Tens

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

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

#### Use a place value chart to add 2-digit numbers

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

#### Add 2-digit numbers without exchanging (Part 1)

#### Add 2-digit numbers without exchanging (Part 2)

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

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

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

#### Add 2-digit numbers with exchanging (Part 1)

#### Add 2-digit numbers with exchanging (Part 2)

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

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

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

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

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

### Topic C: Column Subtraction with Exchanging into the Tens

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

#### Solve subtraction problems using disk models

#### Use disk models to support solving column subtraction

#### Solve column subtraction with scaffolding

#### Use disk models to practice exchanging into the tens

#### Solve subtraction problems with regrouping (Level 1)

#### Solve subtraction problems with regrouping (Level 2)

#### Solve subtraction problems with regrouping (Level 3)

#### Solve subtraction problems with regrouping (Level 4)

#### Solve column subtraction, making decisions about exchanging into the tens

#### Practice solving column subtraction problems independently (Part 1)

#### Practice solving column subtraction problems independently (Part 2)

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

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

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

### Topic D: Column Addition with Exchanging into the Hundreds

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

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

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

#### Practice column addition with exchanging alongside a place value chart

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

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

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

### Topic E: Column Subtraction with Exchanging into the Hundreds

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

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

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

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

#### Solve 2- and 3-digit column subtraction equations by exchanging into the 10s and 100s (Level 1)

#### Solve 2- and 3-digit column subtraction equations by exchanging into the 10s and 100s (Level 2)

#### Solve 2- and 3-digit column subtraction equations by exchanging into the 10s and 100s (Level 3)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#### Add 3-digit numbers by adding on the hundreds first

#### Add 3-digit numbers using mental math

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

#### Add 3-digit numbers with exchanging using mental math

#### Subtract 3-digit numbers by subtracting the hundreds first

#### Subtract 3-digit numbers using mental math

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

#### Subtract 3-digit numbers with exchanging using mental math

### Topic B: 3-Digit Column Addition

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

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

#### Solve 3-digit column addition with exchanging ones or tens

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

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

### Topic C: 3-Digit Column Subtraction

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

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

#### Solve 3-digit column subtraction with multiple exchanges

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

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

#### Solve 3-digit column subtraction with 2-step exchanges

## MODULE 6. Foundations of Multiplication and Division

### Topic A: Formation of Equal Groups

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

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

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

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

#### Making two equal groups (Part 1)

#### Making equal groups (Part 2)

#### Making sets of a particular number (Part 1)

#### Making sets of a particular number (Part 2)

#### More practice counting real-world objects and equal groups

#### Using sets of equal groups to solve repetitive addition equations

#### Representing sets of equal groups as a repetitive addition equation

### Topic B: Arrays and Equal Groups

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

#### Explore the concept of columns

#### Identify the number of columns and the objects within them

#### Identify the number of rows and the objects within them

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

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

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

#### Describe arrays in terms of their columns and rows

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

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

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

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

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

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

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

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

### Topic D: The Meaning of Even and Odd Numbers

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

#### Add two equal addends to get an even number sum

#### Pair objects to determine whether the total is even

#### Determine whether a set of objects is even or odd

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

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

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

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

#### Identify several digit numbers as even or odd

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

#### Identify 3-digit numbers as odd or even

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

### Topic A: Creating an inch ruler

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

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

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

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

#### Measure the sides of rectangles and compare their lengths

#### Students learn about feet as a unit of measurement

### Topic B: Displaying Measurement Data

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

#### Create and interpret a line plot (Part 1)

#### Determine minimum and maximum on a line plot

#### Create and interpret a line plot (Part 2)

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

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

### Topic A: Attributes of Geometric Shapes

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

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

#### Discover the attributes of a quadrilateral

#### Determine if a given shape is or is not a quadrilateral

#### Draw triangles and quadrilaterals

#### Match a given label to the corresponding shape

#### Discover the attributes of a hexagon

#### Learn that triangles, quadrilaterals, and hexagons are all polygons

#### Discover the attributes of a pentagon

#### Identify pentagons based on their attributes

#### Identify different types of polygons

#### Answer questions that compare polygons

#### Discover the attributes of a cube

### Topic B: Composite Shapes and Fraction Concepts

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

#### Rotate and align two indentical triangles to fill a pattern

#### Rotate and align triangles and a square to fill a pattern

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

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

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

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

#### Identify shapes that are split into halves

#### Split shapes in half and complete the missing half of shapes

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

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

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

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

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

### Topic D: Application of Fractions to Tell Time

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