# 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 in an equation (Part 1)

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

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

#### 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

### 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: 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 (Part 2)

#### 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 1)

#### 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 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 9 or 10

#### Solve addition and subtraction equations based on a number line model

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

### Topic E: 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.

#### 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 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 or base-10 blocks grouped into a ten and ones

#### Determine the total number of objects by filling a ten-frame

#### Represent numbers in the second ten using a rod and cubes

#### Determine missing numbers in the second ten on a number line and identify their written name

#### Position numbers to 19 on a number line

#### Determine the 2-digit total of aligned objects

#### Add to or subtract from numbers 11-20 with and without a number line model

#### Solve +/- equations that include the number 10

#### 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

#### Add three addends by first matching two addends to make a 10 based on a model of base-10 blocks (Part 1)

#### Add three addends by first matching two addends to make a 10 based on a model of base-10 blocks (Part 2)

#### Model and solve addition equations across 10 using base-10 blocks by making a ten

#### Solve +9 equations with and without a model of base-10 blocks

#### Solve equations with 9 across 10 using a number line

#### Add to numbers 11-20 across ten

#### Solve +8 equations with and without a model of base-10 blocks

#### Solve +8 equations with and without a model of base-10 blocks

#### Solve equations with 8 across 10 using a number line

#### Solve +6 and +7 equations with and without a model of base-10 blocks

#### Identify addends to reach a given sum of 11, 12, or 13

#### Solve addition equations across 10 using a number line

#### Split an addend to make a 10 and solve an addition equation

#### Split an addend to make a 10 based on a model of base-10 blocks and solve an addition equation

#### Identify addends to reach a given sum of 14, 15, or 16

#### Identify addends to reach a given sum of 17, 18, or 19

#### Solve addition equations across 10 (Level 1)

#### Solve addition equations across 10 (Level 2)

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

Students learn strategies for adding and subtracting across ten. They use familiar models of base-10 blocks, the number line, and ten frames to illustrate the meaning behind the operations.

#### 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

#### 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

#### Solve 2-digit minus 1-digit subtraction equations across 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

#### 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

#### 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)

#### Identify a missing addend to reach a sum of 20 with and without a model of base-10 blocks

#### Solve +/- equations that use numbers in the second ten and a single-digit number (Part 2)

## 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

#### Count distances in blocks on a map and compare

#### Count distances in blocks on a map and create a path that is longer or shorter than given paths

### 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 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 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 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 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

#### Identify names of numbers to 40 on a number line

#### 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

#### Solve equations that add or subtract 1 or 10 with and without modeling with base-10 blocks (Part 1)

#### Solve equations that add or subtract 1 or 10 with and without modeling with base-10 blocks (Part 2)

#### Solve equations that add or subtract 1 or 10 with and without modeling with base-10 blocks (Part 3)

#### Solve equations that add or subtract 1 or 10 with and without modeling with base-10 blocks (Part 4)

#### Solve equations that add or subtract 1 or 10 with and without modeling with base-10 blocks (Part 5)

### 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.

#### 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

#### Place 2-digit numbers on a number line

#### Compare 2-digit numbers using <, =, or > with and without a number line model

#### Compare 2-digit numbers using <, =, or >

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

#### Solve equations that add or subtract 1 or 10 with and without modeling with base-10 blocks

#### Model and solve addition equations that add a single-digit number to a two-digit number using a number line

#### Solve equations that add a single-digit number to a two-digit number (Part 1)

#### Choose matching addition expression and sum

#### Determine a missing addend to add up to the next round number with and without a model of base-10 blocks

#### Determine a missing addend to add up to the next round number and solve the equation (Part 1)

#### Determine a missing addend to add up to the next round number and solve the equation (Part 2)

#### Determine a missing addend to add up to the next round number and solve the equation (Part 3)

#### Model and solve 2-digit addition equations with exchanging using base-10 blocks

#### Solve addition equations across 10 using a number line

#### Solve addition equations across a 10 by splitting an addend to make a ten

#### Solve equations that add a single-digit number to a two-digit number (Part 2)

### 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 two-digit number. They are supported by the familiar model of base-10 blocks and step-by-step guidance.

#### 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

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

#### Solve 2-digit addition equations

#### Model and solve 2-digit addition equations with exchanging using base-10 blocks (Part 1)

#### Model and solve 2-digit addition equations with exchanging using base-10 blocks (Part 2)

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

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

## 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 and use associated language

#### 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 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 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 across 10 using a ten-frame (within 100)

#### 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

### 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.