# 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 two-digit +/- problems without exchanging. Students 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)

A. Solve 2-digit addition equations without exchanging with and without modeling with base-10 blocksB. Solve 2-digit addition equations without exchanging by adding tens and ones separately using place value cardsC. Solve 2-digit subtraction equations without exchanging with and without modeling with base-10 blocksD. Solve 2-digit subtraction equations without exchanging by subtracting tens and ones separately with and without place value cardsE. Solve 2-digit +/- equations without exchanging by adding or subtracting tens and ones separately using a hundred chartF. Identify and solve an equivalent expression to a 2-digit +/- equation without exchangingG. Solve 2-digit +/- equations without exchanging using a hundred chart with limited numberingH. Identify and solve an equivalent expression to a 2-digit +/- equations without exchanging

Students use familiar manipulatives to solve two-digit addition problems with understanding. They rely on place value knowledge and understanding of round numbers to solve problems with exchanging. These exercises reinforce the strategy of adding all tens and all ones and then combining the two. As students use place value cards, they learn to maintain values even without placeholder zeros.

A. Determine the closest round numbers (greater than and less than) to a given 2-digit number and identify the one that is closer with and without a number lineB. Complete +/- equations to reach the nearest round number to a given 2-digit numberC. Determine a missing addend to reach 100 with and without using base-10 blocksD. Identify 2-digit addends to reach a sum of 100E. Identify 2-digit addends to reach a given round number sumF. Identify 2-digit addends to reach round number sums and solveG. Identify 2-digit addends to make a round number and add on a third addendH. Add a single-digit number to a two-digit number with exchanging based on a model of objects in ten-framesI. Model and solve 2-digit addition equations with and without exchanging using base-10 blocksJ. Model and solve 2-digit addition equations with and without exchanging using base-10 blocksK. Solve 2-digit addition equations with and without exchanging by adding tens and ones separately using base-10 blocksL. Solve 2-digit addition equations with and without exchanging by adding tens and ones separately using place value cardsM. Solve 2-digit addition equations with exchanging based on a model of base-10 blocksN. Solve 2-digit addition equations with and without exchanging by decomposing each number into tens (with placeholder zeros) and onesO. Solve 2-digit addition equations without exchanging by decomposing each number into tens (without placeholder zeros) and onesP. Solve 2-digit addition equations with exchanging by decomposing each number into tens (without placeholder zeros) and onesQ. Solve 2-digit addition equations by determining whether or not an exchange is necessary

Students use familiar manipulatives to solve two-digit subtraction problems with understanding. They rely on place value knowledge and understanding of round numbers to solve problems with exchanging. Students learn to determine whether or not an exchange is needed and if so, how to do so with understanding. As students use place value cards, they learn to maintain values even without placeholder zeros.

A. Count forward and backward by hundreds or tens from a non-round 3-digit number on a number lineB. Subtract a single-digit number from a 2-digit number with exchanging based on a model of objects in ten-framesC. Identify a number line model that represents a subtraction equation across a ten and solveD. Model and solve 2-digit subtraction equations with and without exchanging using base-10 blocksE. Solve 2-digit subtraction equations with and without exchanging by subtracting tens and ones separately using place value cardsF. Identify and solve an equivalent expression to a 2-digit subtraction equation with exchangingG. Solve 2-digit subtraction equations with exchanging by decomposing each number into tens (with placeholder zeros) and onesH. Solve 2-digit +/- equations with and without exchanging by decomposing each number into tens (with placeholder zeros) and onesI. Solve 2-digit subtraction equations with and without exchanging by decomposing each number into tens (with placeholder zeros) and onesJ. Solve 2-digit subtraction equations with and without exchanging by decomposing each number into tens (without placeholder zeros) and onesK. Solve 2-digit subtraction equations with and without exchanging by decomposing each number into tens (without placeholder zeros) and ones