# Curriculum for Grade 2

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### MODULE 1. Sums and Differences to 20

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.

A. Identify a missing addend, both visual and numeric, to reach sums to 10B. Match two addends to reach a sum of 10C. Given four addends, make a ten and then add on to find the sumD. Solve +/- equations that include the number 10E. Solve +/- equations that include a 2-digit number with sums and differences 11-19F. Model and solve +/- equations across 10 using base-10 blocksG. Identify a missing addend to reach a sum of 20 with and without a model of base-10 blocksH. Identify a missing single-digit addend to reach the next round number with and without a model of base-10 blocksI. Solve +1 and +10 equations based on a model of base-10 blocks

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.

A. Solve +/- equations that do not cross a ten based on a number line modelB. Solve +/- equations that include a 2-digit number and a round numberC. Solve 2-digit subtraction equations that include a round number and match to a related addition equationD. Add across 10 by first making 10 based on a model of base-10 blocksE. Solve addition equations across 10F. Add across 10 by first making 10 with and without a number line modelG. Solve doubles and doubles plus one addition equationsH. Solve equations that add 9 by changing to a +10 equationI. Solve addition equations across 10J. Solve related equations that add or subtract across a tenK. Solve +/- equations across a tenL. Add across a ten by "resting" on a round number on a number line modelM. Subtract across a ten by "resting" on a round number on a number line modelN. Solve -1 and -10 equations based on a model of base-10 blocksO. Add and subtract across 10 by first making 10 based on a model of base-10 blocksP. Solve +/- equations across 10Q. Model and solve subtraction equations across 10 using the number lineR. Solve related equations that add or subtract 8 or 9 by using 10 and adjustingS. Model and solve an addition equation with three addends and determine a missing addend to 20 using a number lineT. Identify a missing third addend to reach a sum of 20U. Match two addends to reach a given two-digit sum less than 20V. Match three addends to reach a sum of 20

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

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.

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.

A. Identify 10 less, 10 more, 1 less, and 1 more than a given number on a hundred chart with limited numberingB. Count across a ten using 3-digit numbers on a number lineC. Count backward across a ten using 3-digit numbers on a number lineD. Determine a missing 3-digit number on a number line and identify its written nameE. Count across a ten using 3-digit numbers on a number lineF. Count backward across a ten using 3-digit numbers on a number lineG. Determine a missing 3-digit number on a number line and identify its written nameH. Determine a missing 3-digit round number on a number line and identify its written nameI. Determine a missing 3-digit round number on a number line and identify its written name (part 1)J. Position 3-digit round numbers, in both digits and words, on a vertical number line (part 2)K. Count across a ten using 3-digit numbers on a number lineL. Count backward across a ten using 3-digit numbers on a number lineM. Count forward and backward on a number line across obscured numbersN. Count forward and backward across a hundred using 3-digit numbers on a number line (part 1)O. Count forward and backward across a hundred using 3-digit numbers on a number line (part 2)P. Count forward and backward on a number line across obscured numbers

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.

A. Count multiple hundreds crossing from nineties to hundreds based on a model of base-10 blocksB. Determine a 3-digit total of base-10 blocks with and without a model of place value cardsC. Decompose 3-digit numbers into hundreds, tens, and onesD. Compose 3-digit numbers based on a given number of hundreds, tens, and onesE. Compose 3-digit numbers based on a set of place value cards showing hundreds, tens, and onesF. Compose a 3-digit number based on its written nameG. Compose a 3-digit number with or without placeholder zeros based on its written name

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.

A. Recognize equivalencies between ones, tens, hundreds, and a thousand using base-10 blocksB. Determine 3-digit totals based on a set of base-10 blocksC. Recognize and represent 2-digit numbers as tens and onesD. Recognize and represent 3-digit numbers as hundreds, tens, and onesE. Recognize and represent 3-digit numbers with placeholder zeros as hundreds, tens, and onesF. Recognize equivalencies between ones, tens, hundreds, and a thousand with and without base-10 blocksG. Determine how many more ones, tens, or hundreds to reach the next ten, hundred, or thousand using a number line

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.

A. Use >, =, and < to compare a two-digit number with a three-digit numberUse >, =, and < to compare a two-digit number with a three-digit numberB. Use >, =, and < to compare at the hundreds place based on a model of base-10 blocksC. Use >, =, and < to compare at the hundreds place with and without place value cardsD. Use >, =, and < to compare at the tens place based on a model of base-10 blocksE. Use >, =, and < to compare at the tens and ones place based on place value cardsF. Use >, =, and < to compare at the hundreds and tens placeG. Use >, =, and < to compare numbers with placeholder zerosH. Use >, =, and < to compare numbers with placeholder zeros based on a model of base-10 blocksI. Use >, =, and < to compare numbers with similar digitsJ. Arrange numbers in ascending and descending order (Part 1)K. Arrange numbers in ascending and descending order (Part 2)L. Arrange two- and three-digit numbers in ascending orderM. Arrange three-digit numbers in ascending order (Level 1)N. Arrange three-digit numbers in ascending order (Level 2)O. Arrange three-digit numbers in ascending order (Level 3)P. Arrange three-digit numbers in ascending order (Level 4)Q. Arrange three-digit numbers in ascending order (Level 5)R. Arrange three-digit numbers in ascending order (Level 6)

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.

A. Determine 1, 10, and 100 more or less than a given number based on a model of base-10 cubesB. Determine 1, 10, and 100 more or less than a given number with and without a model of numbered disksC. Determine 1, 10, and 100 more or less than the same numberD. Compare two numbers that differ by 1, 10, or 100 with and without a model of numbered disksE. Compare two numbers by stating whether one is 1, 10, or 100 more or less than the otherF. Determine 1 or 10 more than a given number across place values with and without a model of numbered disksG. Determine 1 or 10 less than a given number across place values with and without a model of numbered disksH. Count up and down by 10 in the hundreds using a number lineI. Determine 10 more and 10 less than a three-digit number across hundreds with and without a number lineJ. Count up and down by 1 in the hundreds with and without a model of numbered disksK. Count up and down by 1 in the hundreds across tens with a model of numbered disksL. Count up and down by 10 in the hundreds with and without a model of numbered disksM. Count up and down by 10 in the hundreds across hundreds with a model of numbered disksN. Count up and down by 100 in the hundreds with and without a model of numbered disksO. Count up and down by 1 in the hundreds across tensP. Count up by 10 in the hundreds across hundredsQ. Count up and down by 10 in the hundreds across hundredsR. Count up by 100 in the hundredsS. Count up and down by 100 in the hundredsT. Identify and complete counting patterns up and down by 1, 10, and 100U. Identify and complete counting patterns up and down by 1, 10, and 100

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

A. Relate 1 more or less and 10 more or less to addition and subtractionB. Identify the rule for a +/- 1 or 10 counting pattern and continue the patternC. Add across 10 by making a ten first using a number line (within 20)D. Add across 10 by making a ten first (within 20)E. Subtract across 10 by making a ten first using a number line (within 20)F. Subtract across 10 by making a ten first (within 20)G. Add across 10 using a ten-frame (within 100)H. Subtract across 10 using a ten-frame (within 100)I. Add across 10 by making a ten first with and without a number line (within 100)J. Subtract across 10 by making a ten first with and without a number line (within 100)K. Add a round number to a 2-digit number with and without using number bonds to add tens firstL. Subtract a round number from a 2-digit number with and without using number bonds to subtract tens firstM. Add and subtract 2-digit and round numbers including turnaround factsN. Add 2-digit numbers using a model of base-10 blocksO. Add 2-digit numbers using place value cards to add tens and ones separatelyP. Identify 1 more and 10 more on a hundred chart with limited numberingQ. Add and subtract 2-digit numbers using a hundred chart to add or subtract tens and ones separatelyR. Add 2-digit numbers using a model of base-10 blocksS. Add 2-digit numbers with and without using number bonds to add on the tens firstT. Subtract 2-digit numbers with and without using a model of base-10 blocksU. Subtract 2-digit numbers with and without using place value cards to subtract tens and ones separatelyV. Subtract 2-digit numbers using a hundred chart to subtract tens and ones separatelyW. Subtract 2-digit numbers using a model of base-10 blocks to subtract tens and ones separatelyX. Subtract 2-digit numbers with and without using number bonds to subtract the tens firstY. Add 2-digit numbers with and without exchanging using a model of base-10 blocksZ. Add 2-digit numbers with and without exchanging using place value cardsAA. Add 2-digit numbers with exchanging using a model of base-10 blocksAB. Add 2-digit numbers with exchanging and without using number bondsAC. Subtract 2-digit numbers with and without exchanging using a model of base-10 blocksAD. Subtract 2-digit numbers with exchanging using a model of base-10 blocksAE. Subtract 2-digit numbers with exchanging with and without using number bonds

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.

A. Represent and solve 2-digit addition problems without exchanging using a disk modelB. Add 2-digit numbers without exchanging using place value cards to add tens and ones separatelyC. Solve 2-digit column addition without exchanging (Level 1)D. Solve 2-digit column addition without exchanging (Level 2)E. Exchange into the tens using a disk modelF. Add 2-digit numbers with and without exchanging using a disk modelG. Add 2-digit numbers with exchanging using place value cardsH. Solve 2-digit column addition with and without exchanging using a disk modelI. Solve 2-digit column addition with and without exchanging (Level 1)J. Solve 2-digit column addition with and without exchanging (Level 2)K. Solve 2- and 3-digit column addition with and without exchanging ones (Level 1)L. Solve 2- and 3-digit column addition with and without exchanging ones (Level 2)

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.

A. Represent and solve 2-digit subtraction problems without exchanging using a disk modelB. Subtract 2-digit numbers without exchanging using place value cards to subtract tens and ones separatelyC. Solve 2-digit column subtraction without exchangingD. Exchange a ten for ones using a disk modelE. Subtract 2-digit numbers with exchanging using a disk modelF. Subtract 2-digit numbers with exchanging using place value cardsG. Solve 2-digit column subtraction with exchanging using a disk modelH. Solve 2-digit column subtraction with exchanging (Level 1)I. Solve 2-digit column subtraction with exchanging (Level 2)J. Solve 2-digit column subtraction with and without exchangingK. Solve 2- and 3-digit column subtraction with and without exchanging ones (Level 1)L. Solve 2- and 3-digit column subtraction with and without exchanging ones (Level 2)

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.

A. Exchange into the hundreds using a disk modelB. Solve 2-digit column addition with exchanging into the hundreds using a disk modelC. Solve 2-digit column addition with exchanging into the hundreds with and without a disk modelD. Solve 2-digit column addition with multiple exchangesE. Solve 2- and 3-digit column addition with multiple exchanges

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.

A. Solve 2- and 3-digit column subtraction with exchanging into the hundredsB. Solve 2- and 3-digit column subtraction with and without exchanging into the hundredsC. Solve 2- and 3-digit column subtraction with multiple exchangesD. 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

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.

A. Add and subtract 3-digit numbers with no tens or onesB. Add 3-digit round numbers with and without using a disk modelC. Subtract 3-digit round numbers with and without using a disk modelD. Add a 2-digit round number to a 3-digit round number by adding hundreds, tens, then onesE. Add up to the next hundred with and without using a number line modelF. Add a 2-digit number to a 3-digit number using the "Make the Next Hundred" strategyG. Add a 2-digit round number to a 3-digit round number using mental mathH. Subtract a 2-digit round number from a 3-digit round number by subtracting hundreds, tens, then onesI. Subtract to the next hundred with and without using a number line modelJ. Subtract a 2-digit number from a 3-digit number using the "Make the Previous Hundred" strategyK. Subtract a 2-digit round number from a 3-digit round number using mental mathL. Break a 3-digit number into hundreds and a 2-digit numberM. Add 3-digit numbers by adding on the hundreds firstN. Add 3-digit numbers using mental mathO. Add 3-digit numbers with exchanging by adding on the hundreds firstP. Add 3-digit numbers with exchanging using mental mathQ. Subtract 3-digit numbers by subtracting the hundreds firstR. Subtract 3-digit numbers using mental mathS. Subtract 3-digit numbers with exchanging by subtracting the hundreds firstT. Subtract 3-digit numbers with exchanging using mental math

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.

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.

A. Solve 3-digit column subtraction with exchanging with and without using a disk modelB. Solve 3-digit column subtraction with multiple exchangesC. Model 2-step exchanges in subtraction problems using a disk modelD. Solve 3-digit column subtraction with 2-step exchanges with and without using a disk modelE. Solve 3-digit column subtraction with 2-step exchanges

### MODULE 6. Foundations of Multiplication and Division

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.

A. Create equal groups by dealing objects one by one into a given number of groupsB. Create equal groups by putting objects into groups of a given sizeC. Identify the number of groups and the number of objects in each groupD. Determine the total number of objects in equal groupsE. Compose a repeated addition sentence to represent equal groups and determine the totalF. Compose and solve a repeated addition sentence based on equal groups (Part 1)G. Compose and solve a repeated addition sentence based on equal groups (Part 2)

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.

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.