Lesson 1

Sums and Differences Within 20

Warm-up: Number Talk: Subtract Within 20 (10 minutes)


This Number Talk encourages students to think about how they may use known sums and differences to find the value of other sums and differences. This understanding will be helpful as students continue building fluency with addition and subtraction within 20.


  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time


  • Record answers and strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Facing

Find the value of each expression mentally.

  • \(10 - 5\)
  • \(11 - 5\)
  • \(12 - 6\)
  • \(13 - 6\)

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • “How did the third expression help you find the value of the last expression?”

Activity 1: Check Yourself (20 minutes)


The purpose of this activity is for students to identify the addition facts within 20 that they do not yet know from memory. They write these sums on index cards which can be used to help students build fluency throughout the section. Students should store these cards to use again in an upcoming lesson. The number choices in this activity include some of the facts that students may still be working to recall from memory at this point in the school year. If desired, the inventory of sums that students complete at the beginning of the activity could be replaced with a list of all sums within 20 or a smaller set of sums that best fit the needs of your students.


  • Groups of 2
  • Give students access to index cards.


  • “Find the value of each sum mentally.”
  • 2 minutes: independent work time
  • “Circle any sums that you did not remember right away.”
  • Share answers. Prompt students to also circle any sums that they did not find correctly.
  • “Write each expression that you circled on one side of an index card. Write the value of the expression on the other side. Then you can use the cards to practice these sums.”
  • “If you did not circle any expressions, make cards for some of the expressions that are the trickiest to remember. Make cards for these sums and think about what methods you use to remember these sums quickly. Be prepared to share.”
  • 6 minutes: independent work time
  • Monitor for the sums that several students identify as a sum they need to work on.
  • “Share your thinking with your partner.”
  • 2 minutes: partner discussion

Student Facing

  1. Find the value of each sum mentally.

    \(6 + 6\)

    \(9 + 9\)

    \(7 + 7\)

    \(8 + 8\)

    \(5 + 5\)

    \(9 + 8\)

    \(7 + 8\)

    \(8 + 5\)

    \(6 + 5\)

    \(7 + 6\)

    \(7 + 9\)

    \(6 + 8\)

    \(9 + 2\)

    \(7 + 5\)

    \(8 + 4\)

    \(2 + 9\)

    \(9 + 7\)

    \(6 + 9\)

    \(8 + 3\)

    \(9 + 4\)

    \(8 + 6\)

    \(3 + 9\)

    \(5 + 6\)

    \(9 + 5\)

    \(5 + 9\)

    \(9 + 6\)

    \(8 + 9\)

    \(6 + 7\)

    \(5 + 7\)

    \(8 + 7\)

  2. Circle any sum that you did not remember right away.

    Write each sum you circled on an index card.

    Use the index cards to work on building fluency with these sums.

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • Display a list of sums that many students are still working on.
  • “A lot of students wrote these sums on their cards. Choose one of the expressions and be ready to explain how you can remember the sum.”
  • Share and record responses.

Activity 2: Spin and Find the Missing Number (15 minutes)


The purpose of this activity is for students to practice finding unknown addends within 20. Students use spinners to determine the total and one of the addends. They write addition equations or subtraction equations to represent how they found the unknown addend. Students connect the different equations in the synthesis and compare different methods for finding the unknown addend mentally.

This activity uses MLR8 Discussion Supports. Advances: listening, speaking, conversing

Action and Expression: Develop Expression and Communication. Give students access to a number line or a number bond mat with base ten blocks. Allow students to recreate the problems in a concrete manner and continue to build a deeper understanding if needed.
Supports accessibility for: Conceptual Processing, Memory, Organization

Required Materials

Materials to Gather

Materials to Copy

  • Spin and Find the Missing Number Spinners


  • Groups of 2
  • Give each group the spinners and a paper clip.
  • “Let’s play a game to practice our addition and subtraction facts.”
  • “Spin the first spinner to get your total. Spin the second spinner to get one addend.”
  • Demonstrate spinning both spinners and naming your total and first addend.
  • “Both players mentally find the missing addend.”
  • Think aloud, finding the missing addend.
  • “Share your thinking with your partner. If you both agree on the missing addend, write and share equations that show how you found the missing number.”

MLR8 Discussion Supports

  • Display sentence frames to support small-group discussion:
    • “I agree because . . . .”
    • “I disagree because . . . .”
  • Demonstrate writing an equation that best matches the method you used to find the missing addend.


  • 10 minutes: partner work time
  • Monitor for students who:
    • decompose to get to a ten
    • use known addition or subtraction facts
    • make equivalent but easier sums

Student Facing

  • Spin the top spinner to get your total.
  • Spin the bottom spinner to get one addend.
  • Find the unknown addend.
  • Write an equation to show how you found the unknown addend.
my equations my partner’s equations

Student Response

For access, consult one of our IM Certified Partners.

Advancing Student Thinking

If students disagree about the unknown number, encourage students to use the sentence frames and create drawings or diagrams to explain why they think their number would make the equation true.

Activity Synthesis

  • “Read your equations. Which equations did you know right away?”
  • “What did you do when you did not know the unknown number?”
  • Invite previously identified students to share methods.

Lesson Synthesis

Lesson Synthesis














“Which expressions would you group together? Why?” (A and E because you could use \(9 + 8 = 17\) to find \(17 - 9\). B and F because you could use \(7 + 7\) to find the value of \(14 - 7\). B, D, and E because they are all addition.)

Cool-down: Add and Subtract with Fluency (5 minutes)


For access, consult one of our IM Certified Partners.