# Curriculum for Grade 1

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MODULE 1. Sums and Differences to 10

1A: Embedded Numbers and Decompositions

Students explore the composition of numbers 3-5 through visual models. They use objects, base-10 blocks, and equations.

- Decompose a set of 3-5 objects into two groups and identify as addends in an equation
- Match two addends, both visual and numeric, to reach a sum of 4
- Identify a missing addend, with and without visual support, in equations with a sum of 5
- Match two addends to reach a sum of 3 in a visual model
- Identify a missing addend in a visual model to reach a sum of 5
- Match two addends to reach a sum of 4 in a visual model
- Identify a missing addend in a visual model to reach a sum of 4
- Match two addends, both visual and numeric, to reach a sum of 5

1B: Counting On from Embedded Numbers

Students explore the composition of numbers 6-10 through visual models. They use objects, base-10 blocks, and equations. Base-10 models use a 5-group configuration to move students from counting all to counting on.

- Decompose a set of 6 objects into two groups and identify as addends in an equation
- Match two addends, both visual and numeric, to reach a sum of 6
- Identify a missing addend in equations with a sum of 6 given a model of base-10 blocks
- Match two addends to reach a sum of 6
- Decompose a set of 7 objects into two groups and identify as addends in an equation
- Match two addends, both visual and numeric, to reach a sum of 7
- Identify a missing addend in equations with a sum of 7 given a model of base-10 blocks
- Match two addends to reach a sum of 7
- Decompose a set of 8 objects into two groups and identify as addends in an equation
- Match two addends, both visual and numeric, to reach a sum of 8
- Identify a missing addend in equations with a sum of 8 given a model of base-10 blocks
- Match two addends to reach a sum of 8
- Decompose a set of 9 objects into two groups and identify as addends in an equation
- Match two addends, both visual and numeric, to reach a sum of 9
- Identify a missing addend in equations with a sum of 9 given a model of base-10 blocks
- Match two addends to reach a sum of 9
- Match two sets of uniform objects to reach a sum of 10
- Identify a missing addend in equations with a sum of 10 given a model of base-10 blocks
- Match two addends, both visual and numeric, to reach a sum of 10
- Match two addends, both visual and numeric, to reach a sum of 10
- Match two addends to reach a sum of 10
- Identify a missing addend in equations with a sum of 10 and their turnaround facts
- Identify a base-10 block model to represent an equation with a sum of 10 and identify the missing addend
- Record a number line scenario as an addition equation to 10 and its related subtraction equation
- Add or subtract by moving an object on a number line and solve a related equation that shows addition to or subtraction from 10

1D: Strategies for Counting On

Students count on to add 1, 2, or 3 in equations. They use manipulatives, visual models, and even fingers to solve equations.

1F: Development of Addition Fluency Within 10

Students reinforce thier understanding of addition within 10 and its underlying concepts as they build more efficient strategies to solve problems. They use addition scenarios with objects, base-10 block patterns, the number line, and equations to reinforce the relationships among fact families. They build upon existing knowledge of composition of numbers 6-10 as they move from the concrete to the abstract.

- Record a model of base-10 blocks as an addition equation
- Identify a set of base-10 blocks that represents an addition scenario based on objects or an equation
- Use base-10 blocks to represent an addition scenario based on objects
- Use base-10 blocks to represent an addition scenario based on objects and then record as an equation with a sum of 5, 6, or 7
- Use base-10 blocks to represent an addition scenario based on objects and then record as an equation with a sum of 6 or 7
- Count on by moving an object forward on a number line and identify the sum in an related equation
- Identify a number line model that represents an addition scenario explained in words
- Record a number line addition scenario as an equation
- Identify the missing addend in equations paired as turnaround facts with sums of 4, 5, and 6
- Identify the missing addend in equations paired as turnaround facts with sums of 5, 6, and 7
- Identify the missing addend in equations paired as turnaround facts with sums of 6, 7, and 8
- Use base-10 blocks to represent an addition scenario based on objects and then record as an equation with a sum of 8
- Identify the missing addend in equations paired as turnaround facts with sums of 7, 8, and 9
- Use base-10 blocks to represent an addition scenario based on objects and then record as an equation with a sum of 9
- Identify the missing addend in equations paired as turnaround facts with sums of 9 and 10
- Match two addends to reach a sum of 10
- Solve addition equations within 10

1I: Decomposition Strategies for Subtraction

Students reinforce thier understanding of subtraction within 10 and its underlying concepts as they build more efficient strategies to solve problems. They explore the relationship between addition and subtraction and work increasingly with 0 as a subtrahend and difference. They use subtraction scenarios with objects, base-10 block patterns, the number line, and equations to reinforce the relationships among fact families. They build upon existing knowledge of composition of numbers 6-10 as they move from the concrete to the abstract.

- Record a scenario based on objects as a subtraction equation with a difference of 0
- Record a number line scenario as a -0 subtraction equation
- Record a number line scenario as a subtraction equation with a difference of 0
- Identify missing numbers in subtraction equations with a difference of 0
- Subtract by moving an object backward on a number line and solve a related equation that shows subtraction from 3, 4, or 5
- Record a number line scenario as an equation that shows subtraction from 3, 4, or 5
- Solve equations based on a model of base-10 blocks to subtract 1 or all but 1
- Record a model of base-10 blocks as two related equations that show subtraction from 6
- Subtract by moving an object backward on a number line and solve a related equation that shows subtraction from 4, 5, or 6
- Record a number line scenario to 6 as related addition and subtraction equations
- Record a model of base-10 blocks as two related equations that show subtraction from 7
- Subtract by moving an object backward on a number line and solve a related equation that shows subtraction within 7
- Record a number line scenario as an equation that shows subtraction from 7
- Record a model of base-10 blocks as two related equations that show subtraction from 8
- Subtract by moving an object backward on a number line and solve a related equation that shows subtraction from 8
- Record a number line scenario as equations that show addition to 8 and then subtraction from 8
- Record a model of base-10 blocks as two related equations that show subtraction from 9
- Subtract by moving an object backward on a number line and solve a related equation that shows subtraction from 9
- Identify missing numbers in subtraction equations from 9
- Record a number line scenario as equations that show addition to 9 and then subtraction from 9
- Record a model of base-10 blocks as two related equations that show subtraction from 10

1J: Development of Subtraction Fluency Within 10

Students reinforce the relationship between addition and subtraction and the relationships among fact families. They use familiar objects, base-10 blocks, the number line, and equations to explore the composition of numbers 3-10. They build speed and accuracy with all +/- facts within 10.

- Record a model of base-10 blocks as an equation that show subtraction from 7, 8, or 9
- Identify a set of base-10 blocks that represents a subtraction scenario based on objects or an equation
- Use base-10 blocks to represent a subtraction scenario based on objects and record it as an equation that shows subtraction from 3, 4, or 5
- Identify a number line model that represents a subtraction scenario given in words
- Identify missing numbers in subtraction equations from 4, 5, and 6
- Identify missing numbers in subtraction equations from 6 and 7
- Identify missing numbers in subtraction equations from 7 and 8
- Identify missing numbers in subtraction equations from 8 and 9
- Identify missing numbers in subtraction equations from 9 and 10
- Solve subtraction equations within 10
- Record number line scenarios as addition or subtraction equations that use 0

MODULE 2. Introduction to Place Value Through Addition and Subtraction Within 20

2A: Counting On or Making Ten to Solve Result Unknown and Total Unknown Problems

Students reinforce their understanding of “tens” and “ones” while sorting, counting, adding, and subtracting. They use objects, base-10 blocks, the number line, and a ten-frame. They practice various strategies to add across 10 and increase fluency with +/- facts within 20.

- Group base-10 rods and cubes into a ten and ones and determine totals
- Determine the number of tens and ones using objects or base-10 blocks grouped into a ten-frame or a rod
- Determine the total number of objects or base-10 blocks grouped into a ten and ones
- Determine the number of tens and ones using objects or base-10 blocks grouped into a ten-frame or a rod and then determine the total
- Determine the total number of objects by filling a ten-frame
- Represent a teen number using a rod and cubes
- Determine a missing teen number on a number line and identify its written name
- Position numbers to 19 on a number line
- Solve +/- 1 equations in the teens with and without a number line model
- Determine the 2-digit total of aligned objects
- Complete a series of related equations to add across 10 based on a model of base-10 blocks
- Solve addition equations across 10 using a number line
- Add three addends by first matching two addends to make a 10 based on a visual model
- Solve +/- equations in the teens
- Add three addends by first matching two addends to make a 10 based on a model of base-10 blocks
- Solve +9 equations with and without a model of base-10 blocks
- Solve +8 equations with and without a model of base-10 blocks
- Model and solve addition equations across 10 using base-10 blocks by making a ten
- Model and solve addition equations across 10 using base-10 blocks by splitting an addend into two components
- Model and solve addition equations across 10 using base-10 blocks by adding on to a 10
- Solve addition equations in the teens and across 10
- Solve addition equations across 10 using a number line
- Identify addends to reach a given sum of 11, 12, or 13
- Solve addition equations across 10 using a number line
- Solve addition equations across 10 by splitting an addend into two components with and without a number line model
- Solve addition equations across 10
- Identify addends to reach a given sum of 14, 15, or 16
- Solve "almost doubles" addition equations by adding doubles plus 1 more
- Identify equations with “almost doubles” addends and solve
- Determine a missing addend to reach a sum of 20 with and without a model of base-10 blocks
- Identify addends to reach a given sum of 17, 18, or 19

2D: Varied Problems with Decompositions of Teen Numbers as 1 Ten and Some Ones

Students explore place value as they add and subtract across 10. They use multiple representations (objects, ten-frame, number line, base-10 blocks, and equations) to move from the concrete to the abstract. Students build their fluency with +/- facts within by reinforcing the underlying concept of exchanging and using the strategy of "resting" on 10. They also solve +/- problems in which all ones or all tens are added or subtracted.

- Complete a series of related equations to subtract across 10 based on a model of base-10 blocks
- Solve subtraction equations across 10 using a number line
- Model and solve subtraction equations across 10 using objects in a ten-frame
- Solve +/- equations within 20 with and without a model of base-10 blocks
- Record a model of objects or base-10 blocks as an equation that adds or subtracts all tens or all ones
- Complete equations that add or subtract all tens or all ones with and without a model of base-10 blocks
- Model and solve addition equations in the teens by adding ones to ones using base-10 blocks
- Model and solve subtraction equations in the teens by subtracting ones from ones using base-10 blocks
- Solve +/- equations that use a teen number and a single-digit number
- Model and solve +/- equations across 10 using base-10 blocks
- Model and solve subtraction equations across 10 using base-10 blocks (part 1)
- Model and solve subtraction equations across 10 using base-10 blocks (part 2)
- Solve subtraction equations within 20
- Solve subtraction equations across 10 by splitting a subtrahend into two components with and without a number line model
- Solve subtraction equations across 10
- Solve addition equations across 10 by splitting an addend into two components based on a model of base-10 blocks
- Model and solve subtraction equations across 10 using base-10 blocks
- Solve addition equations across 10
- Solve subtraction equations across 10
- Solve subtraction equations across 10

MODULE 4. Place Value, Comparison, Addition and Subtraction to 40

Students further explore the concept that a two-digit number is composed of a round number (tens) plus ones. They determine totals, decompose numbers, add, and subtract. Students use familiar objects, base-10 blocks, ten-frames, equations, and number names along with place value cards. Note that the “coins” used are to reinforce the concept of tens, fives, and ones, not coin recognition.

- Add tens to 40 based on a model of base-10 blocks
- Determine totals to 90 by counting objects in ten-frames
- Determine totals to 90 by counting base-10 rods
- Determine totals by counting objects with or without filling ten-frames
- Identify 2-digit round numbers
- Determine totals to 40 by counting tens and ones using base-10 blocks
- Determine totals to 40 by counting tens and ones using base-10 blocks
- Determine totals to 40 by counting tens and ones using objects in ten-frames
- Determine totals by counting tens and ones using scattered and dissimilar objects in ten-frames
- Determine the total of a set of "coins" using 10s, 5s, and 1s
- Represent numbers to 40 using base-10 rods and cubes
- Determine a missing number to 40 on a number line and identify its written name
- Decompose 2-digit numbers to 40 into tens and ones with and without a model of base-10 blocks
- Decompose 2-digit numbers to 40 into a round 2-digit number plus ones
- Identify names of numbers to 40 on a number line
- Solve equations that add or subtract 1 or 10 with and without modeling with base-10 blocks

4B: Comparison of Pairs of Two-Digit Numbers

Students compare and order numbers, reinforcing their understanding of place value and sequence. They use familiar base-10 blocks, number line, and begin using inequality signs.

- Align a scattered set of numbered, non-sequential objects in ascending order
- Compare two sets of scattered objects using > or < with a visual aid
- Align a scattered set of numbered, non-sequential objects in descending order
- Determine missing round numbers on a number line numbered by tens
- Compare two 2-digit numbers using >, <, or = with and without a model of base-10 blocks
- Position 2-digit numbers on a number line
- Compare two 2-digit numbers using >, <, or = with and without a number line

4C: Addition and Subtraction of Tens

Students work with round numbers to reinforce place value understanding of 10 more and 10 less. They use equations and the number line to solve addition problems and counting patterns.

4D: Addition of Tens or Ones to a Two-Digit Number

Students rely on growing understanding of exchanging to model and solve two-digit addition problems with exchanging using familiar models and new strategies.

- Determine the closest round numbers (greater than and less than) to a given 2-digit number
- Determine a missing addend to add up to the next round number with and without a model of base-10 blocks
- Model and solve 2-digit addition equations within 40 using base-10 blocks
- Model and solve 2-digit addition equations within 40 using base-10 blocks
- Solve 2-digit addition equations within 40 with and without modeling with base-10 blocks
- Determine a missing addend to add up to the next round number and solve the equation
- Model and solve 2-digit addition equations with exchanging using base-10 blocks
- Model and solve 2-digit addition equations with exchanging using base-10 blocks
- Model and solve 2-digit addition equations with exchanging by adding on a ten and then ones using base-10 blocks
- Solve 2-digit addition equations with exchanging by adding tens and ones separately
- Model and solve 2-digit addition equations with exchanging by adding tens and ones separately using base-10 blocks
- Model and solve 2-digit addition equations with exchanging using base-10 blocks

MODULE 6. Place Value, Comparison, Addition and Subtraction to 100

Students use familiar representations (objects, ten-frames, base-10 blocks, number line, place value cards, number names, and equations) to extend their place value understanding to higher numbers within 100. They begin building their mental model of the hundred chart by understanding the relationship between numbers in columns and rows. They reinforce the understanding that 2-digit numbers are composed of a round number (or tens) plus ones.

- Determine a missing round number to 100 on a number line and identify its written name
- Position round numbers, in both digits and words, on a vertical number line
- Determine 2-digit totals based on base-10 blocks and place value cards
- Determine 2-digit totals of objects in ten-frames or base-10 blocks
- Determine totals by counting objects with or without filling ten-frames
- Represent a given two-digit number with base-10 blocks
- Identify 2-digit round numbers
- Decompose 2-digit numbers into a round number plus ones
- Determine 2-digit totals of base-10 blocks by counting tens and ones
- Determine totals by counting tens and ones using scattered and dissimilar objects in ten-frames
- Decompose 2-digit numbers into tens and ones with and without a model of base-10 blocks
- Solve +/- 1 and +/- 10 equations with and without a model of base-10 blocks
- Count forward and backward within a ten on a number line
- Align a scattered set of numbered, non-sequential objects in ascending order
- Count forward and backward across a ten on a number line
- Determine the closest round numbers to a given 2-digit number and identify the one that is closer with and without a number line
- Align a scattered set of numbered, non-sequential objects in descending order
- Compare 2-digit totals with a set of 10, 5, and 1 "coins"
- Identify missing numbers on a hundred chart
- Identify 10 less, 10 more, 1 less, and 1 more on a hundred chart with limited numbering
- Identify missing numbers in columns on a hundred chart with limited numbering
- Identify 10 more or 1 more on a hundred chart with limited numbering
- Solve equations that add or subtract a round number using a hundred chart
- Complete and solve equations that add or subtract a round number using a hundred chart
- Identify missing numbers on a hundred chart and decompose into tens and ones
- Count forward across 100 and beyond 100 on a number line
- Count backward across 100 and beyond 100 on a number line
- Identify a missing three-digit number on a number line and its written name
- Determine totals of objects in ten-frames beyond 100
- Count base-10 rods beyond 100
- Determine totals beyond 100 using a base-10 flat, rods, and cubes
- Determine totals beyond 100 using objects in ten-frames

6C: Addition to 100 Using Place Value Understanding

Students use familiar base-10 blocks, number line, and equations to work with round numbers. They rely on counting, place value, and addition/subtraction skills to solve problems. Students use familiar manipulatives to solve two-digit addition problems with and without exchanging. They also solve two-digit subtraction problems without exchanging.

- Solve equations by adding or subtracting 10 to or from a round number
- Add and subtract round numbers with and without a model of base-10 blocks
- Record and solve equations that add a round number to a 2-digit number based on a model of base-10 blocks
- Record and solve equations that subtract a round number from a 2-digit number based on a model of base-10 blocks
- Model and solve equations that add a round number to a 2-digit number using base-10 blocks
- Model and solve addition equations that add a single-digit number to a two-digit number using a number line
- Model and solve equations that add two 2-digit numbers using base-10 blocks
- Model and solve equations that add two 2-digit numbers using base-10 blocks
- Model and solve equations that add two 2-digit numbers using base-10 blocks
- 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 based on a model of base-10 blocks
- Solve 2-digit addition equations with and without exchanging by adding tens and ones separately
- Solve 2-digit addition equations with and without exchanging by adding tens and ones separately using base-10 blocks