# 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 20

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

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

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

#### Match two addends to reach a sum of 10

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

#### Solve +/- equations within 10

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

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

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

#### Subtract from numbers 11-20 using base-10 blocks

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

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

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

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

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

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

#### Solve +/- equations within 100

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

#### Solve +/- equations across 10 (Part 1)

#### Solve +/- equations across 10 (Part 2)

#### Solve +/- equations within 100

## MODULE 2. Addition and Subtraction of Length Units

### Topic A: Understand Concepts About the Ruler

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

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

#### Measure 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

#### Match estimated lengths and units to objects

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

### 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

#### 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

#### Add or subtract length to solve a word problem

#### 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

#### Use a tape diagram to solve a missing addend word problem involving length

#### Use a tape diagram to solve a missing subtrahend word problem involving length

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

### Topic A: Forming Base Ten Units of Ten, a Hundred, and a Thousand

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#### Compose a 3-digit number based on its written name

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

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

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

### 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

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

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

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

### 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 numbers in ascending and descending order (Part 1)

#### Arrange numbers in ascending and descending order (Part 2)

#### Arrange two- and three-digit numbers in ascending order

#### 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 apply their knowledge of place value to compare numbers and complete counting patterns. They use multiple representations (base-10 blocks, numbered disks, and the number line) to support understanding, paying particular attention to working across place values.

#### Determine 1, 10, and 100 more or less than a given number based on a model of base-10 cubes

#### Determine 1, 10, and 100 more or less than a given number with and without a model of numbered disks (Part 1)

#### Determine 1, 10, and 100 more or less than a given number with and without a model of numbered disks (Part 2)

#### Determine 1, 10, and 100 more or less than the same number

#### Compare two numbers that differ by 1, 10, or 100 with and without a model of numbered disks

#### Compare two numbers by stating whether one is 1, 10, or 100 more or less than the other

#### Determine 1 or 10 more than a given number across place values with and without a model of numbered disks

#### Determine 1 or 10 less than a given number across place values with and without a model of numbered disks

#### Count up and down by 1 in the hundreds with and without a model of numbered disks

#### Count up and down by 1 in the hundreds across tens with a model of numbered disks

#### Count up and down by 10 in the hundreds with and without a model of numbered disks

#### Count up and down by 10 in the hundreds across hundreds with a model of numbered disks

#### Count up and down by 100 in the hundreds with and without a model of numbered disks

#### Count up and down by 1 in the hundreds across tens

#### Count up by 10 in the hundreds across hundreds

#### Count up and down by 100 in the hundreds

#### Identify and complete counting patterns up and down by 1, 10, and 100 (Part 1)

#### Identify and complete counting patterns up and down by 1, 10, and 100 (Part 2)

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

### Topic A: Sums and Differences Within 100

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

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

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

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

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

#### Record a 2-digit number as tens and ones

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#### Exchange into the tens using a disk model

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

#### Add 2-digit numbers with exchanging using place value cards

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

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

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

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

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

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

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

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

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

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

#### Solve 2-digit column subtraction without exchanging

#### Exchange a ten for ones using a disk model

#### Subtract 2-digit numbers with exchanging using a disk model

#### Subtract 2-digit numbers with exchanging using place value cards

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

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

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

#### Solve 2-digit column subtraction with and without exchanging

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

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

### 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 into the hundreds using a disk model

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

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

#### Solve 2-digit column addition with multiple exchanges

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

### 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 with exchanging into the hundreds (Part 1)

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

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

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

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

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

## 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.

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

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

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

#### Determine the total number of objects in equal groups

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

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

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

### Topic B: Arrays and Equal Groups

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

#### Place objects in equal rows or columns

#### Describe an array by rows or columns using repeated addition

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

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

### 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

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

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

### Topic A: 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: 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 B: 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, thrids, and fourths

### Topic C: 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.