# Curriculum for Grade 2

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MODULE 1. Sums and Differences to 20

1A: 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.

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

1B: 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.

- Solve +/- equations that do not cross a ten based on a number line model
- Solve +/- equations that include a 2-digit number and a round number
- Solve 2-digit subtraction equations that include a round number and match to a related addition equation
- Add across 10 by first making 10 based on a model of base-10 blocks
- Solve addition equations across 10
- Add across 10 by first making 10 with and without a number line model
- Solve doubles and doubles plus one addition equations
- Solve equations that add 9 by changing to a +10 equation
- Solve addition equations across 10
- Solve related equations that add or subtract across a ten
- Solve +/- equations across a ten
- Add across a ten by "resting" on a round number on a number line model
- Subtract across a ten by "resting" on a round number on a number line model
- Solve -1 and -10 equations based on a model of base-10 blocks
- Add and subtract across 10 by first making 10 based on a model of base-10 blocks
- Solve +/- equations across 10
- Model and solve subtraction equations across 10 using the number line
- Solve related equations that add or subtract 8 or 9 by using 10 and adjusting
- Model and solve an addition equation with three addends and determine a missing addend to 20 using a number line
- Identify a missing third addend to reach a sum of 20
- Match two addends to reach a given two-digit sum less than 20
- Match three addends to reach a sum of 20

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

3A: 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.

3B: 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.

- Identify 10 less, 10 more, 1 less, and 1 more than a given number on a hundred chart with limited numbering
- 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
- Determine a missing 3-digit number on a number line and identify its written name
- 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
- Determine a missing 3-digit number on a number line and identify its written name
- Determine a missing 3-digit round number on a number line and identify its written name
- 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 (part 2)
- 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 on a number line across obscured numbers
- Count forward and backward across a hundred using 3-digit numbers on a number line (part 1)
- Count forward and backward across a hundred using 3-digit numbers on a number line (part 2)
- Count forward and backward on a number line across obscured numbers

3C: 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.

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

3E: 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.

- Determine a 3-digit total of base-10 blocks with and without a model of place value cards
- Sort 3-digit numbers based on a given place value
- Compose 3-digit numbers based on a nonsequential given number of hundreds, tens, and ones
- Count cubes up to 1000 based on a model of base-10 blocks
- Identify relationships between ones, tens, hundreds, and a thousand
- Count forward and backward by hundreds, tens, and ones on a number line

3F: Comparing Two Three-Digit Numbers

Students compare numbers by sequencing or using inequality symbols. These comparisons rely on identifying differences in the hundreds, tens, or ones digits. Familiar exercises become increasingly challenging by using numbers with placeholder zeros and numbers with transposed digits.

- Align a scattered set of numbered, non-sequential objects in ascending order
- Compare sets of base-10 blocks to the hundreds place using >,<, or =
- Compare 3-digit numbers to the hundreds place using >,<, or =, using place value cards for reference
- Align a scattered set of numbered, non-sequential objects in ascending order
- Compare sets of base-10 blocks to the tens place using >,<, or =
- Compare 3-digit numbers to the ones place using >,<, or =, using place value cards for reference
- Compare 3-digit numbers to the tens place or the ones place using >,<, or =, using place value cards for reference
- Align a scattered set of numbered, non-sequential objects in ascending order
- Compare 3-digit numbers with placeholder zeros or transposed digits using >,<, or =, using place value cards for reference
- Compare sets of base-10 blocks using >,<, or =
- Compare 3-digit numbers with placeholder zeros or transposed digits using >,<, or =, using place value cards for reference
- Align a scattered set of numbered, non-sequential objects in ascending order
- Align a scattered set of numbered, non-sequential objects in ascending order
- Align a scattered set of numbered, non-sequential objects in ascending order
- Compose the largest and smallest possible 3-digit numbers from a given set of place value cards

3G: Finding 1, 10, and 100 More or Less Than a Number

Students reinforce place value understanding by exploring counting patterns. They determine 1 more, 1 less, 10 more, 10 less, 100 more, and 100 less using base-10 blocks, the number line, and equations.

- Add 1, 10, or 100 to a 3-digit number based on a model of base-10 blocks
- Solve equations that add or subtract 1, 10, or 100 to or from a 3-digit number
- Determine 1 more, 1 less, 10 more, 10 less, 100 more, and 100 less than a given number
- Count forward and backward by hundreds from a non-round 3-digit number
- Identify 100 more than a given non-round 3-digit number
- Identify 10 more than a given non-round 3-digit number
- Count forward and backward by tens from a non-round 3-digit number with and without a number line
- Count forward and backward by tens from a non-round number across a hundred with and without a number line
- Count forward and backward by hundreds from a non-round number across obscured numbers on a number line
- Count forward and backward by tens from a non-round number across obscured numbers on a number line

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

4A: Sums and Differences Within 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)

- Solve 2-digit addition equations without exchanging with and without modeling with base-10 blocks
- Solve 2-digit addition equations without exchanging by adding tens and ones separately using place value cards
- Solve 2-digit subtraction equations without exchanging with and without modeling with base-10 blocks
- Solve 2-digit subtraction equations without exchanging by subtracting tens and ones separately with and without place value cards
- Solve 2-digit +/- equations without exchanging by adding or subtracting tens and ones separately using a hundred chart
- Identify and solve an equivalent expression to a 2-digit +/- equation without exchanging
- Solve 2-digit +/- equations without exchanging using a hundred chart with limited numbering
- Identify and solve an equivalent expression to a 2-digit +/- equations without exchanging

4B: Strategies for Composing a Ten

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.

- 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 line
- Complete +/- equations to reach the nearest round number to a given 2-digit number
- Determine a missing addend to reach 100 with and without using base-10 blocks
- Identify 2-digit addends to reach a sum of 100
- Identify 2-digit addends to reach a given round number sum
- Identify 2-digit addends to reach round number sums and solve
- Identify 2-digit addends to make a round number and add on a third addend
- Add a single-digit number to a two-digit number with exchanging based on a model of objects in ten-frames
- Model and solve 2-digit addition equations with and without exchanging using base-10 blocks
- Model and solve 2-digit addition equations with and without exchanging using base-10 blocks
- Solve 2-digit addition equations with and without exchanging by adding tens and ones separately using base-10 blocks
- Solve 2-digit addition equations with and without exchanging by adding tens and ones separately using place value cards
- Solve 2-digit addition equations with exchanging based on a model of base-10 blocks
- Solve 2-digit addition equations with and without exchanging by decomposing each number into tens (with placeholder zeros) and ones
- Solve 2-digit addition equations without exchanging by decomposing each number into tens (without placeholder zeros) and ones
- Solve 2-digit addition equations with exchanging by decomposing each number into tens (without placeholder zeros) and ones
- Solve 2-digit addition equations by determining whether or not an exchange is necessary

4C: Strategies for Decomposing a Ten

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.

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