1st Grade Unit 3 Overview and Standards

Use these links to access resources for this unit.

Before You Begin this Unit…

Unit at a

Glance

In Grade K, students had experience with addition and

subtraction situations within 10. In Grade 1, students work

with addition and subtraction situations within 20 (10+10=20)

to continue to better understand the operations and how to

apply the operations to problem solving. Students in Grade 1

are introduced to comparison subtraction. The modeling of

comparison subtraction is different from the other two types

of subtraction. Instead of finding part of one group as in

take-away or part-whole subtraction, students model the two

groups represented by the minuend and subtrahend and find

the difference between the two. Students are also introduced

to using a symbol as an unknown, though students have used

answer blanks or answer boxes as informal symbols for

unknowns in the past.

Throughout first grade, students work with the important idea

that quantities can be composed and decomposed in different

ways while the total quantity remains the same. Students

have repeated experiences breaking one number, a whole,

into two parts or combining two parts to form a whole. They

begin to notice that as one part increases, the other part

decreases, while the whole remains the same, i.e., if 3 + 6 = 9,

then 4 + 5 = 9 as well. Teachers need to assess students’

developing understanding of this concept and students’

strategies for solving problems like these.

As first grade students work with story problems, they should

visualize the action of story problems and solve the problems

in ways that make sense to them. Students use mathematical

tools and representations to model and solve addition and

subtraction problems and to clarify and communicate their

thinking. They are encouraged to represent their work on

paper and may use a combination of pictures, words,

numbers, and mathematical symbols. In this unit, students

move beyond solving addition story problems to problems

that involve subtraction or missing addends. Teachers need

Estimated Duration: 28 Days Investigation 1: 10 lessons

(include 1.10A) Investigation 2: 3 lessons Investigation 3: 5 lesson Investigation 4: 8 lessons

to assess students’ ability to interpret and solve addition,

subtraction, and missing addend story problems.

Also, students are introduced to Today’s Number in which

they generate many ways to make a given number. Students

can write expressions that have more than two addends and

that use addition, subtraction, or even addition and

subtraction.

Students may discover ways to use one expression to generate

another or find patterns that help them generate many

expressions. Teachers need to assess students’ flexibility in

composing and decomposing numbers, their ability to use

previous expressions and patterns to generate other

expressions, the size of the numbers students are comfortable

working with, and the operations they are comfortable using.

In investigation 4, students work on counting in a variety of

ways. They are expected to learn the rote counting sequence

to 100 and beyond, to read and write numbers to 105, and

strategies for counting groups of objects. By the end of this

unit, students are expected to be able to read, write, and

record numbers up to 65 and to count a set of 40 to 50 objects

accurately. Teachers need to assess how high students can

count, what numbers students can read and write, and

whether students can accurately count a set of 40 to 50

objects.

Standards Addressed in the Unit

Click here for the NCDPI CCSS Unpacking Document

Unit Goals:

• Find at least 5 combinations of 2 addends for a number up to 15.

• Combine 2 small quantities.

• Interpret (retell the action and sequence) and solve addition and subtraction story problems.

• Subtract one small quantity from another.

• Represent numbers by using equivalent expressions.

• Count a set off 40 – 50 objects.

• Rote count, read, and write numbers to 65.

This unit focuses on the Operations and Algebraic thinking strand. For more information about

this strand and how it should look in the classroom, please visit the Common Core State

Standards video series or the Link to unpacking document.

Represent and solve problems involving addition and subtraction.

1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of

adding to, taking from, putting together, taking apart, and comparing, with unknowns in all

positions, e.g., by using objects, drawings, and equations with a symbol for the unknown

number to represent the problem.

1.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less

than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the

unknown number to represent the problem.

Understand and apply properties of operations and the relationship between addition and

subtraction.

1.OA.3. Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 =

11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6

+ 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.

(Associative property of addition.)

1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8

by finding the number that makes 10 when added to 8. Add and subtract within 20.

Add and subtract within 20.

1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within

10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);

decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the

relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8

= 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the

known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Work with addition and subtraction equations.

1.OA.7. Understand the meaning of the equal sign, and determine if equations involving

addition and subtraction are true or false. For example, which of the following equations are

true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating

three whole numbers. For example, determine the unknown number that makes the equation

true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.

Unit Goals:

• Find at least 5 combinations of 2 addends for a number up to 15.

• Combine 2 small quantities.

• Interpret (retell the action and sequence) and solve addition and subtraction story problems.

• Subtract one small quantity from another.

• Represent numbers by using equivalent expressions.

• Count a set off 40 – 50 objects.

• Rote count, read, and write numbers to 65.

This unit focuses on the Operations and Algebraic thinking strand. For more information about

this strand and how it should look in the classroom, please visit the Common Core State

Standards video series or the Link to unpacking document.

Represent and solve problems involving addition and subtraction.

1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of

adding to, taking from, putting together, taking apart, and comparing, with unknowns in all

positions, e.g., by using objects, drawings, and equations with a symbol for the unknown

number to represent the problem.

1.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less

than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the

unknown number to represent the problem.

Understand and apply properties of operations and the relationship between addition and

subtraction.

1.OA.3. Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 =

11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6

+ 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.

(Associative property of addition.)

1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8

by finding the number that makes 10 when added to 8. Add and subtract within 20.

Add and subtract within 20.

1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within

10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);

decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the

relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8

= 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the

known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Work with addition and subtraction equations.

1.OA.7. Understand the meaning of the equal sign, and determine if equations involving

addition and subtraction are true or false. For example, which of the following equations are

true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating

three whole numbers. For example, determine the unknown number that makes the equation

true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.

1st Grade Unit 3 Planning Differentiation

Students Who Struggle...

Behaviors Resources How to Use

Student cannot find

identify

combinations of 9

Toss the

Chips

You can have the students play the Kindergarten game

Toss the Chips (KG unit 4, session 4.4). Make the

connection apparent for them that this activity is similar

to the How Many of Each? problems.

Students struggle

solving problems

with larger numbers

Continue to allow struggling students to work with

smaller numbers (within 5, then 7, then 10) and

emphasize using counters to act out and represent the

problem situation.

Students who

experience difficulty Unifix Cubes

Students build 5s with Unifix cubes, using two different

colors. As students connect the cubes, encourage them

with decomposing

numbers

to say the addition problem aloud. For example, 3 plus

2 equals 5. Assist students as they record the

equations. Encourage them to record the equations with

the addends in different orders. As students become

comfortable writing the equations, use the same trains to

work with the corresponding subtraction

equations. Repeat with larger sums.

Students who

experience difficulty

with subtracting

Ten Frame

Students work with 10 counters arranged in a ten frame

to write subtraction equations. Students begin by

placing all ten counters in the ten frame. Prompt

students to subtract a number of counters and write the

subtraction equation. Challenge students to write five

different “10 minus” equations.

Students Who Have Mastery...

Behaviors Resources How to Use

Students who

understand and apply

the relationship

between addition and

subtraction

Cooperative

Groups

Students work with partners or in small

groups. Students spin a 0-10 spinner four times to

generate 4 numbers. Students use these numbers to

compose word problems that combine both addition and

subtraction. For example, the numbers are 4, 6, 2, and

10, a word problem could be:

Sally has 10 marbles. She loses 4 marbles. Then Jim

gives her 6 marbles and Leah gives her 2 marbles. How

many marbles does Sally have now?

Students exchange problems and challenge classmates

to find the answers.

Students who

understand and apply

the relationship

between addition and

subtraction

Compare

Favorites

Students tally whether their classmates prefer grape

juice or orange juice. Students make a bar graph to

show the findings. Then they use comparison

subtraction to find out how many more students prefer

one juice than the other.

Students who

understand and apply

the relationship

between addition and

subtraction

Figure It!

Students play the game Figure It! in groups of

3. Provide cards numbered 1 through 20. One student

is the dealer, and the other two are players. The dealer

places the cards face down and gives each player one

card. Players may not look at the cards. Dealer says,

“Figure It” and players hold their cards face out on their

foreheads. The dealer then states the total of the two

players’ cards. Players determine the value of their

cards (the missing addend). Increase numbers on the

cards as well as the number of players to 3, depending

on students’ abilities.

Student who

demonstrate mastery

with combinations to

10

Make the

Number

Give students two decks of cards, one which has four

sets of the numbers 0 through 9 and a second that has

one set of the numbers10 through 20. Students deal 5

cards from the first deck and 1 card from the second

deck. Then they try to make the number from the

second deck using at least 2 cards from the first

deck. Students use addition, subtraction, or both. For

example, if the numbers 3, 6, 8, 9, and 2 are dealt, and

the target number is 17, students could say

6+8=14+3=17. The first student to make the number

keeps all cards. The student with the most cards at the

end of play is the winner.

1st Grade Unit 3 Planning Each Investigation

and Classroom Routines

Notes About Each Investigation

Unit Summary:

This unit focuses on counting and comparing larger quantities and on composing and

decomposing numbers into several parts. There is also the added challenge of finding all of the

2-addend combinations of a number. Students revisit familiar addition activities with variations

that encourage counting on, and are introduced to the operation of subtraction. Students’ work

focuses on developing an understanding of the operations and on developing strategies for

solving addition and subtraction problems.

INVESTIGATION 1

As students are working with the equals sign, emphasize that the equals sign means that the

value on the left is “the same as” or “equal to” the value on the right. Increase flexibility by

writing equations in a variety of ways, e.g., 6+3 = 9 or 9 = 6+3. Look for opportunities to do

teacher think-alouds or facilitate class discussions to help students make sense of various

problem situations.

INVESTIGATION 2

In this Investigation, students begin their formal work with subtraction. Subtraction gets

introduced in line with 1.OA.4 as a missing addend problem. Students should be encouraged to

reason about and use a variety of strategies, such as counting up from the smaller number,

counting back from the larger number, drawing pictures, using a number line, or using counters

to find their answers. Make sure to provide opportunities for students to discuss the reasoning

that they used as they solve the problems.

INVESTIGATION 3

As students solve more story problems in this Investigation, provide opportunities for them to

reason about whether they add or subtract and why they chose a certain operation. Avoid the

emphasis of key words, but rather have them think about the problem situation and the action in

the problem. Refer to the problem type table, Table 1 from the Common Core, in the

Unpacking Document. This document has the various problem types for addition and

subtraction and will provide you more ideas for additional tasks that you can pose to students.

INVESTIGATION 4

Make sure to provide students with opportunities to work with hundreds boards to emphasize

the patterns in the counting sequence. Some students may recognize that all of the numbers in

one column may have the same number of ones, while numbers in the same row may have the

same number of tens. Emphasizing the counting sequence and simultaneously representing

numbers with base-10 blocks and/or ten frames will help students gain a deeper understanding

of these numbers.

Classroom Routines

Activity Note Standard

Morning

Meeting

Students continue to use the calendar to keep

track of time and events, collect and analyze data

about the weather, and count the number of

students on the class. Variations focus on the days

of the week, different times of day, and solving

problems on the number of students in class.

1.NBT.1, 1.NBT.2 Students

complete a variety of

activities involving number

sense, the calendar, and

patterns.

Start

With/Get

To

Students continue to practice counting forward and

back with numbers to 30. Then, students count

from a number between 0 and 30 to a number

between 31 and 60. Later, they count from a

number between 31 and 60 to a number between 0

and 30.

1.NBT.1, 1.OA.1-

1.OA.8 Students extend their

work with the counting

sequence by counting

forwards and backwards.

Quick

Images

Students see two or three images and determine

the total number of dots, practicing the single-digit

addition combinations and considering

relationships among combinations (e.g., 2+2, 2+3,

3+3). They also see and combine equal groups as

they use cubes or square tiles to recreate images of

groups of squares.

1.OA.1-1.OA.8 Students

work with Dot Addition

Cards to decompose and

compose numbers.

1st Grade Unit 3 Teaching Standards for

Math Practice

Standards for Mathematical Practice

(behaviors of mathematically proficient students)

Building the Language of

Mathematics

Increasing accountable talk is the

goal for ALL students in our

district.

The following activities are

provided to help ensure your

students are engaging in

mathematical conversations that

address SMP 3 (Construct Viable

Arguments) and SMP 6 (Attend

to Precision)

Words you should hear

students use in mathematical

conversations:

sum, difference, equation,

combination, greater than, less

than

Students must "start by explaining to themselves the

meaning of a problem and look for entry points to its

solution." Many sessions in this unit begin by reading story

problems aloud as a class. Introduce the First Grade Story

Problem Routine to help students identify strategies to

solve a variety of problems.

How can we use the information in the story to solve the

problem? What strategies can we use to solve this

problem?

As students solve story problems

in this unit, encourage them to be

precise when sharing

solutions. For example, a student

might say, “I plussed six”. The

teacher then can re-voice and say,

“So you added 6?” Further

prompt students by asking,

“where did the 6 come from?”

Building Mathematically Proficient Students

MP4. Model with Mathematics. Students begin the work

of representing everyday situations with equations and

models in the early grades. In this unit, students discuss

and represent strategies for subtraction (Sessions 2.1-2.3),

strategies for addition (Session 3.4), and today's number

(Session 3.2). Post the story problem situations so students

can refer back to the question and identify what each

number or drawing in their mathematical representation

means within the context of the story problem.

Describe how you solved this

problem to a partner.

MP8. Look for and express

regularity in repeated

reasoning.

Can you use information from

another problem to help you

solve this problem?

1st Grade Unit 3 Assessing Student

Understanding

Resource:

Teaching Suggestion:

AMC Anywhere

Hiding Assessment

Give the Hiding Assessment to students to determine what

combinations they know, and what they are working on. Start with

combinations of 4, continue to assess until you reach 2 P’s, or an N.

This information will help you guide students through the work in

this unit. For more information on these assessments, click here.

Exit Tickets and

Journal Prompts

Utilize the exit tickets to inform future instruction and immediate

feedback. The exit tickets have the session labeled in parenthesis to

let you know which session to administer. The journal prompts need

to be given at the conclusion of each investigation.

Checkpoints

1. Find at least five combinations of two addends for a number

up to 15.

2. Interpret (retell the action and sequence) and solve addition

and subtraction story problems.

3. How students combine two small quantities.

4. Represent numbers by using equivalent expressions.

5. Subtract one small quantity from another.

6. Count a set of 40-50 objects.

7. Rote count, read, and write numbers to 65 (1s, 2s, 5s, and 10s)

Exit Tickets

Investigation 1

Exit Tickets:

Describe your strategy for finding all the pairs of addends that add up to 10 .

How do you know when you have them all? (1.4)

Explain how you can use the strategy of “counting on” to add. (1.7)

Journal Prompt/Reflection:

Write an addition story problem. Solve the problem and show the equation

for the problem.

Investigation 2

Exit Tickets:

Explain the strategy you used to solve a subtraction problem. (2.3)

Journal Prompt/Reflection:

Write a subtraction story problem. Solve and then show the equation for the

story problem.

Investigation 3

Exit Tickets:

Describe a strategy for figuring out “Today’s Number”. (3.4)

Journal Prompt/Reflection:

Describe at least 2 strategies for solving addition problems (counting all,

counting on, using a number relationship they know).

Investigation 4

Exit Tckets:

Describe the patterns you see on the 100 chart. (4.4)

Journal Prompt/Reflection:

Explain your strategy for finding missing numbers on the hundred chart.

1st Grade Unit 3 Digital Resources

Interactive Student Resources

Resource Suggestion for Use: What standard(s) are addressed?

Breakapart

Choose

“Make 10”

Easy

This game would need to be taught

to students before use. Students are

asked to apply the skill of making a

ten to add. For example, if the

equation is 9+8, students must solve

the problem with 10+7.

1.OA.6. Add and subtract within 20,

demonstrating fluency for addition and

subtraction within 10. Use strategies such

as counting on; making ten (e.g., 8 + 6 = 8

+ 2 + 4 = 10 + 4 = 14); decomposing a

number leading to a ten (e.g., 13 – 4 = 13

– 3 – 1 = 10 – 1 = 9); using the

relationship between addition and

subtraction (e.g., knowing that 8 + 4 = 12,

one knows 12 – 8 = 4); and creating

equivalent but easier or known sums (e.g.,

adding 6 + 7 by creating the known

equivalent 6 + 6 + 1 = 12 + 1 = 13).

How Many

Under the

Shell

This game helps students solidify

their combinations. Use the Hiding

Assessment data to help students

choose the correct number to start

with.

1.OA.8. Determine the unknown whole

number in an addition or subtraction

equation relating three whole numbers.

For example, determine the unknown

number that makes the equation true in

each of the equations 8 + ? = 11, 5 = _ – 3,

6 + 6 = _.

1.NBT.1 Develop fluency with addition

and subtraction facts.

Numbers

When students engage in this

activity, they will quickly encounter

problems with the unknown in all 3

places (addition). This game is

particularly helpful because it

provides a visual representation of

the problems.

1.OA.8. Determine the unknown whole

number in an addition or subtraction

equation relating three whole numbers.

For example, determine the unknown

number that makes the equation true in

each of the equations 8 + ? = 11, 5 = _ – 3,

6 + 6 = _.

1.OA.5. Relate counting to addition and

subtraction (e.g., by counting on 2 to add

2).

Busy Bees Students solve Change Unknown-

Take From problems (“There were

1.OA.8. Determine the unknown whole

number in an addition or subtraction

10 bees, some went inside the hive,

how many bees went inside?”)

equation relating three whole numbers.

For example, determine the unknown

number that makes the equation true in

each of the equations 8 + ? = 11, 5 = _ – 3,

6 + 6 = _.

Can You

Balance

In this activity, students must move

cubes to balance the equation. The

written equation at the end of each

round will help students make

connections between the concrete

and abstract forms of representation.

1.OA.7. Understand the meaning of the

equal sign, and determine if equations

involving addition and subtraction are true

or false. For example, which of the

following equations are true and which are

false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1

= 5 + 2.

Digital Resources for Teachers

Resource Suggestion for Use:

What

standard(s) are

addressed?

Brainpop Jr.

In this movie, you’ll get an overview of different

strategies for adding two numbers together. You’ll

explore how to count on and how to add ten to find the

sum. You'll also learn how to use doubles to add numbers

together. You'll find out how to use a number line, draw

pictures, or use tally charts and other graphic organizers to

find totals. Annie and Moby will show you how to write

and solve addition number sentences using addends, the

plus sign, and the equal sign.

1.OA.1-1.OA.8

Dot Addition

Video

Watch a teacher interact with struggling and strong math

students while playing the game. Notice questions they

ask as they play, as well as explanations of their teacher

moves.

1.OA.1, 1.OA.2,

1.OA.3, 1.OA.5,

1.OA.6, 1.OA.7

Five-in-a-Row

Addition

Video

Watch a teacher interact with struggling and strong math

students while playing the game. Notice questions they

ask as they play, as well as explanations of their teacher

moves.

1.OA.1, 1.OA.5,

1.OA.6, 1.OA.7,

1.NBT.1

Five-in-a-Row

Subtraction

Video

Watch a teacher interact with struggling and strong math

students while playing the game. Notice questions they

ask as they play, as well as explanations of their teacher

moves.

1.OA.1, 1.OA.3,

1.OA.4, 1.OA.5,

1.OA.6, 1.OA.7,

1.NBT.1

Printable Resources for Teachers

Resource Suggestion for Use: What standard(s) are addressed?

Combinations

to 20

This is a printable ten

frame that students can

use as to support

combinations of 20

story problems.

1.OA.6. Add and subtract within 20, demonstrating

fluency for addition and subtraction within 10. Use

strategies such as counting on; making ten (e.g., 8 +

6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a

number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 =

10 – 1 = 9); using the relationship between addition

and subtraction (e.g., knowing that 8 + 4 = 12, one

knows 12 – 8 = 4); and creating equivalent but

easier or known sums (e.g., adding 6 + 7 by

creating the known equivalent 6 + 6 + 1 = 12 + 1 =

13).

Number

Sentence

Match

In this activity, students

create a number

sentence, then must find

the ten frame that

matches the equation.

1st Grade Unit 3 Professional Learning for

Teachers

Professional

Learning

Activities

Things to Discuss with Your

Team

Before beginning the unit,

read page 225 “Does This

Show Paula’s Strategy?”

Students in 1st grade often struggle to share the strategy they

actually used. Oftentimes, students say one thing, and record

another. First grade teachers play a vital role in helping

students develop proficiency in explaining, and recording

their strategies. After reading the selection brainstorm a list

of ways teachers on your team can help students match the

strategy they used with the strategy they share.

Introducing Notation, Part 2,

page 182

Many students have a misunderstanding of the equal sign

and believe it means, “Here comes the answer”. Read

Introducing Notation, Part 2 with your team mates and

discuss how this relates to standard

1.OA.7. Understand the meaning of the equal sign, and

determine if equations involving addition and subtraction are

true or false. For example, which of the following equations

are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4

+ 1 = 5 + 2.

Quick Images Video

Click the link and watch the video with your team. (It’s the

first one on the page). After watching, discuss with your

team:

What part of the quick image routine would you like

to improve in your classroom?

How does the quick image routine help students build

number sense and fluency?

1st Grade Unit 3 Teacher to Teacher Files

Teacher to Teacher Files

Smart Board/Promethean Files

Teacher Made Work

Daily Weather

Unit 3 Smart Board File (with Common Core Additions)