# Curriculum for Grade 1

Students look under the hood of addition and subtraction, applying place value understanding to 2-digit operations.

## MODULE 1. Sums and Differences to 10

### Topic A: Embedded Numbers and Decompositions

Students learn addition to 5 using concrete objects, abstract objects and equations. They learn the meaning and proper use of + and = signs, as well as the terms "addend" and "sum."

#### Count two addends and determine the total

#### Determine total number of objects and determine its two addends

#### Use the + and = signs in an equation

#### Identify addends and sum in an equation

#### Compose an addition equation based on a picture

#### Represent objects with cubes

#### Compose addition equations based on cubes, and solve equations with and without cubes

#### Solve addition equations

### Topic B: Counting On from Embedded Numbers

Students learn addition to 10 using concrete objects, abstract objects, equations and number bonds. They solve for missing addend problems and begin to represent and solve word problems.

#### Add 0 to a number

#### Use the + sign in an equation and find the sum

#### Model and solve an addition equation

#### Record an addition equation based on a model to show more than one way to reach a given sum

#### Show more than one way to reach a given sum

#### Solve an addition equation (totals to 7)

#### Identify parts of an addition equation

#### Record an addition equation based on a model and create a model to show more than one way to reach a given sum

#### Solve addition equations to 10 with or without a model

#### Solve an addition equation (totals to 10)

#### Model and solve an addition word problem with objects

#### Model and solve an addition word problem with cubes

#### Write and solve an addition equation based on a word problem

#### Determine the missing addend based on a model of cubes

#### Determine the missing addend based on a cubes model

#### Counting on with cube models

#### Determine the missing addend in an equation (Part 1)

#### Determine the missing addend in an equation (Part 2)

#### Use a cube model to determine the missing addend

#### Determine the missing addend in an equation (Part 3)

#### Determine the missing addend in an equation

#### Choose two addends to reach a given total

#### Solve missing addend addition equations

#### Identify addends with a sum of 10

#### Identify a number bond

#### Build a number bond based on a model of cubes

#### Build a number bond based on a model of cubes and complete its addition equation

#### Build a model, number bond, and equation

#### Complete a number bond

#### Complete a number bond to show more than one way to reach a given total

#### Determine the missing addend in a number bond

### Topic C: Development of Addition Fluency Within 10

Students reinforce their 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.

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

#### Record a model of base-10 blocks as an addition equation

#### Identify the missing addend in equations paired as turnaround facts with sums of 4, 5, 6 and 7

#### Solve for a missing addend in an equation

#### Identify the missing addend in equations paired as turnaround facts with sums of 6, 7, 8 and 9

#### Choose the correct sum for an addition expression

#### Identify the missing addend in equations paired as turnaround facts with sums of 9 and 10

### Topic D: The Commutative Property of Addition and the Equal Sign

Students learn about the commutative property of addition by comparing addition expressions with the same addends, but in a different order. In addition, students practice making expressions equal to each other by filling in the missing addend. Finally, students are introduced to the equal sign as a way to show that two expressions are equal or the same.

#### Solve simple addition equations and observe that changing the order of the addends doesn't change the sum

#### Explore expressions and reinforce the commutative property of addition

#### Make equal expressions and solve equations with the same addends in a different order

#### Identify and create equal and non equal addition expressions

#### Use the equal sign to show and create equal expressions (Part 1)

#### Use the equal sign to show and create equal expressions (Part 2)

#### Identify whether number sentences are true and false

### Topic E: Subtraction as an Unknown Addend Problem

Students build their understanding of subtraction as its relate to addition. They move from the concrete to the abstract to solve problems. They use number bonds to relate addition and subtraction facts.

#### Explore the concept of "taking away" with concrete objects

#### Use minus and equal signs to rewrite "taking away" as subtraction

#### Complete subtraction number sentences using concrete objects

#### Match sets of cubes to real objects to model "taking away"

#### Complete subtraction number sentences using a cube model

#### Compose and solve subtraction equations

#### Take away cubes to match and solve a subtraction equation

#### Solve subtraction equations within 7

#### Write a full subtraction equation to match a cube model

#### Use cubes to model subtraction from 8, 9, and 10

#### Solve subtraction equations from 8, 9, and 10

#### Solve subtraction equations within 10

#### Addition and subtraction as types of expressions

#### Sort expressions into addition and subtraction

#### Complete number bonds and relate them to subtraction number sentences

#### Explore how addition and subtraction equations are related through number bonds

#### Identify the missing parts of related addition and subtraction facts

#### Identify members of a fact family from a given set of equations

### Topic F: Decomposition Strategies for Subtraction

Students reinforce their 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 (Part 1)

#### 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

#### Record a scenario based on objects as a subtraction equation with a difference of 0 (Part 2)

#### Use base-10 blocks to represent subtraction scenarios with objects within 5 and identify base-10 block patterns that represent subtraction scenarios with objects within 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

#### Record a model of base-10 blocks as two related equations that show subtraction from 7 or 8

#### Subtract by moving an object backward on a number line and solve a related equation that shows subtraction within 7

#### Record a model of base-10 blocks as two related equations that show subtraction from 9 or 10

#### Identify missing numbers in subtraction equations from 9

### Topic G: 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.

#### 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

#### Choose matching subtraction expression and difference

#### Identify missing numbers in subtraction equations from 7 and 8

#### Identify missing numbers in subtraction equations from 8 and 9

#### Determine the missing element in a subtraction equation

#### Identify missing numbers in subtraction equations from 9 and 10

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

### Topic A: 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.

#### Reinforce knowledge of numbers 11-20 by adding a single digit to the number ten

#### Discover the addends to make ten

#### Determine the missing addend

#### Practice with ten frames

#### Use ten frames to explore equations and determine the sum

#### Use base ten blocks to make ten then find the sum

#### Use base ten blocks to determine the sum

#### Introduction to equations with three addends

#### Making 10 to solve three-addend equations

#### Decomposing addends in order to make ten then adding to find the sum

#### Continued practice decomposing addends to solve an equation

#### Demonstrate knowledge of missing addend to make ten

#### Use the strategy of making ten to solve addition equations

#### Solving using a number bond

#### Using number bonds to solve addition equations

#### Continued practice using number bonds to solve addition equations

#### Demonstrate proficiency or practice with assistance

#### Solve the addition equations with sums of 11-16 to combine objects

#### Solve the addition equations with sums of 11-16

#### Solve the addition equations with regrouping

### Topic B: Counting On or Taking from Ten to Solve Result Unknown and Total Unknown Problems

Students will use the strategy of making 10 to solve subtraction problems. They will use number bonds to break elements of subtraction equations into useful parts. Then, students will adapt these strategies to solving subtraction problems mentally.

#### Solve subtraction problems taking from 10

#### Subtract single digits from numbers 11-19 to make 10

#### Subtract the digit in the ones place from numbers 11-19 to make 10

#### Find the unknown number in subtraction problems to make 10

#### Solve subtraction problems beginning with a number from 11-15 and crossing 10

#### Use the strategy of making 10 to solve subtraction equations

#### Introduce subtraction across 10 using base-ten blocks

#### Model subtraction across 10 using base-ten blocks and knowledge of number bonds

#### More practice subtracting across 10 with base-ten blocks

#### Use number bonds to break down components of subtraction equations; use two equations to solve

#### Use number bonds to break down components of subtraction equations; use one equation to solve

#### Solve subtraction equations by using the strategy of making 10

#### Solve subtraction equations that cross 10

### Topic C: 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.

#### Solve substraction equations that include the number 10

#### Complete equations that add or subtract all tens or all ones with and without a model of base-10 blocks

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

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

#### Solve +/- equations that use numbers in the second ten and a single-digit number (Part 1)

## MODULE 3. Ordering and Comparing Length Measurements as Numbers

### Topic A: Indirect Comparison in Length Measurement

Students use familiar, real objects to build their sense of length comparison. They determine the longest, shortest, longer, and shorter among objects, even when not aligned.

#### Identify the longer or shorter of two objects and align objects to compare length

#### Identify the statement that correctly compares the length of two objects

#### Identify the shortest or longest object in an unaligned set of three objects

#### Arrange a set of aligned objects according to length

### Topic B: Non-Standard Length Units

Students use paper clips as a non-standard unit of length to measure objects. They learn that units must measure from endpoint to endpoint with no gaps or overlaps.

#### Count to measure lengths of objects

#### Measure lengths of objects from endpoint to endpoint with no gaps or overlaps

#### Identify which of two objects is measured correctly

#### Measure lengths of objects by laying units correctly

### Topic C: Data Interpretation

Students count real objects and use tally marks or bar graphs to represent them. They interpret data presented in tables and graphs, and use it to find total, how many more, and how many fewer.

#### Make tally marks to count up to 5 objects

#### Identify totals of tally marks (Part 1)

#### Identify totals of tally marks (Part 2)

#### Interpret data in a table using tally marks (Level 1)

#### Interpret data in a table using tally marks (Level 2)

#### Interpret data in a 1-category bar graph

#### Create a 2-category bar graph and use it to interpret data

#### Interpret data in 2-category bar graphs

#### Interpret horizontal bar graphs and find the difference between 2 categories

#### Interpret vertical bar graphs and find the difference between 2 categories

#### Interpret vertical bar graphs to find "how many fewer" between 2 categories

#### Write and solve subtraction equations to find the difference between 2 categories

#### Interpret data in a 3-category bar graph (Part 1)

#### Interpret data in a 3-category bar graph (Part 2)

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

### Topic A: Tens and Ones

Students will explore the concept of 2-digit numbers and place value. Students will begin to understand that 2-digit numbers represent a value of tens and some ones. They will have the support of base-10 blocks, number lines, and 10-frames.

#### Decompose numbers 11-19 into a group of 10 and some ones

#### Practice with number words 0-50

#### Practice with number lines showing 10-100

#### More practice with number lines showing 0-50

#### Review the difference between letters and digits. Learn about 1- and 2-digit numbers

#### Learn about the concept of 10-frames

#### Represent groups of ten as 2-digit numbers

#### Review the concept of tens written as a 2-digit number

#### Represent 2-digit numbers as groups of ten and some ones

#### More practice making equivalencies between groups of ten and some ones and 2-digit numbers

#### Write a 2-digit number to represent tens and ones

#### Identify place value within a 2-digit number

#### More practice identifying place value within 2-digit numbers

#### Complete number sentences breaking 2-digit numbers into tens plus some ones

### Topic B: 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.

#### Count and compare sets of objects

#### Explore with > and < signs when counting and comparing objects

#### Use >, =, and < to compare two single-digit numbers

#### Use >, =, and < to compare at the ones and tens place, using base-10 blocks for support

#### Use >, =, and < to compare one- and two-digit numbers, without additional supports

#### Use >, =, and < to compare two-digit numbers (Part 1)

#### Use >, =, and < to compare two-digit numbers (Part 2)

#### Use >, =, and < to compare two-digit numbers, without additional supports

#### Select the correct < or > sign to compare a pair of two-digit numbers

#### Select the number from a set that is the least or greatest

#### Order a set of one- and two-digit numbers from least to greatest

### Topic C: 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.

#### Solve addition equations that add round numbers to 40

#### Count backward by 10 on a number line (Part 1)

#### Count backward by 10 on a number line (Part 2)

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

Students begin to develop strategies to add ones or tens to a 2-digit number. They utilize base-10 models, making ten, and number bonds to solve addition equations.

#### Use base-10 models to add ones to a 2-digit number

#### Add ones to a 2-digit number

#### Use base-10 blocks to add a tens to a 2-digit number

#### Solve addition equations adding tens or ones to a 2-digit number

#### Identify tens numbers from a set

#### Given a number along a number line, identify the next ten

#### Identify the next ten from a given number, without models

#### Use base-10 blocks to practice adding to make a next ten

#### Identify the next ten and find the missing addend

#### Find the missing addend to make the next ten from a given number

#### Use base-10 blocks to solve addition equations with exchanging

#### Use number bonds to solve addition equations with exchanging (Level 1)

#### Use number bonds to solve addition equations with exchanging (Level 2)

#### Solve addition equations with exchanging, using a number bond if needed

#### Add ones to a 2-digit number

#### Add ones to a 2-digit number, with and without exchanging

### Topic E: Addition of Tens and Ones to a Two-Digit Number

Students synthesize their learning from the previous topic to add tens and ones to a 2-digit number. They are supported by the familiar model of base-10 blocks, place value charts, and step-by-step guidance.

#### Review adding ones to 2-digit numbers

#### Review adding tens to 2-digit numbers

#### Identify tens from a group of numbers and label place value of 2-digit numbers

#### Break down 2-digit numbers into tens and ones

#### Use place value charts with base-10 blocks to add two 2-digit numbers

#### Solve 2-digit addition equations by adding tens and ones separately

#### Mentally solve 2-digit addition problems

#### Use place value charts with base-10 blocks to add 2-digit numbers, including regrouping

#### Review adding 1- and 2-digit numbers

## MODULE 5. Identifying, Composing, and Partitioning Shapes

### Topic A: Attributes of Shapes

Students learn the basic attributes of shapes: lines, closed figures, sides, and corners. They learn to identify triangles, rectangles, squares, trapezoids, and hexagons.

#### Identify the lines

#### Identify curved lines

#### Identify closed shapes

#### Identify shapes with a given number of sides

#### Count the number of sides and corners of shapes

#### Identify hexagons

#### Identify triangles, rectangles, squares, and hexagons

#### Identify a trapezoid

#### Draw given shapes

#### Identify given shapes

#### Identify shapes of everyday objects

### Topic B: Halves and Quarters of Rectangles and Circles

Students learn to identify and count equal parts in a partitioned shape. They learn the names for halves and quarters, and use these names in identifying shapes partitioned as such.

#### Identify a shape that is partitioned into halves (Level 1)

#### Identify a shape that is partitioned into halves (Level 2)

#### Determine the number of equal parts in a partitioned shape

#### Identify a shape that is partitioned into quarters

### Topic C: Application of Halves to Tell Time

Students explore digital and analog clocks to understand the passage and identification of time. They learn parts of the clock and different types of time notation: X:XX, X o'clock, X-thirty, and half past X.

#### Identify clock parts and time to the hour on a clock

#### Identify daily and hourly passage of time

#### Identify time to the hour on a digital and analog clock

#### Determine time to the hour on an analog clock

#### Identify passage of minutes on an analog clock

#### Identify time to the half hour on an analog clock and use associated language (Part 1)

#### Identify time to the half hour on an analog clock and use associated language (Part 2)

#### Identify time to the half hour on a digital and analog clock

#### Identify time on a clock

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

### Topic A: Numbers to 120

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

#### 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

#### Adding round numbers using blocks and bars

#### Addition and subtraction of round numbers

#### Solve equations that add two-digit numbers across a 10

#### Solve equations that add or subtract a round number using a hundred chart

#### Identify missing numbers in columns on a hundred chart with limited numbering

#### Identify 1 more and 10 more on a hundred chart with limited numbering

#### 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

### Topic B: Addition to 100 Using Place Value Understanding

Students use place value charts and base-10 blocks to solve 2-digit addition and subtraction equations. They also practice solving these problems mentally. Students begin to learn when to regroup in equations with 2-digit numbers.

#### Add tens numbers (Level 1)

#### Add tens numbers (Level 2)

#### Subtract tens numbers (Level 1)

#### Subtract tens numbers (Level 2)

#### Solve addition problems with 2-digit numbers and tens numbers (Level 1)

#### Solve addition problems with 2-digit numbers and tens numbers (Level 2)

#### Solve addition problems with two 2-digit numbers (Level 1)

#### Solve addition problems with two 2-digit numbers (Level 2)

#### Solve addition problems with two 2-digit numbers (Level 3)

#### Solve addition problems with two 2-digit numbers, including regrouping

### Topic C: Coins and Their Values

Students explore the heads and tails sides of the penny, nickel, dime, and quarter. They learn the value of each coin, how to count a collection of them, and how to count a mixed collection of coins. Students match coin image, name, and value.