Lesson 18

Patterns in Addition

Warm-up: How Many Do You See: More Double 10-frames (10 minutes)

Narrative

The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. This warm-up is similar to the warm-up in the previous lesson. The teacher can notice if the students’ approach to the warm-up is different after the activities in the previous lesson. When students use grouping strategies to visualize the quantities in the \(10 + n\) structure they come to see that some can be taken from one group and added to the other to make a ten and some more (MP7).

Launch

  • Groups of 2
  • “How many do you see? How do you see them?”
  • Flash the image.
  • 30 seconds: quiet think time

Activity

  • Display the image.
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Record responses.
  • Repeat for each image.

Student Facing

How many do you see?
How do you see them?

Double ten frame. 9 red counters. 5 yellow counters.

Two ten frames. Top, 3 counters. Bottom, 9 counters.  
Double ten frame. Red, 8 counters. Yellow, 6 counters.

Student Response

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Activity Synthesis

  • “What do these images have in common?” (You can take some dots from one 10-frame and add them to the other. None of the 10-frames are full.)
  • “The first image shows \(9 + 5\), but if we share one yellow with the top 10-frame we could write \(10 + 4\).”
  • Write \(9 + 5 = 10 + 4\).
  • “What expressions could we write for the second image?” (\(3 + 9 = 2 + 10\))

Activity 1: Expression Match (10 minutes)

Narrative

The purpose of this activity is for students to use what they know about making a ten to identify which addition expressions are equivalent to \(10 + n\) expressions. Students should have access to double 10-frames and connecting cubes or two-color counters.

The Compare Stage 2 Addition Cards will be used again in a later lesson.

Required Materials

Materials to Gather

Materials to Copy

  • Compare Stage 2 Addition Cards to 20

Required Preparation

  • Create a set of Compare Stage 2 Addition Cards to 20 from the blackline master for each group of 3.

Launch

  • Groups of 3
  • Give each group a set of cards and access to double 10-frames and connecting cubes or two-color counters.

Activity

  • Read the task statement.
  • 8 minutes: small-group work

Student Facing

  1. Take out all the expression cards that have the number 10. 
  2. Mix up the rest of the cards.
  3. Pick a card.
  4. Place the card under the expression with 10 that it is equal to.

small group at a table

Student Response

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Activity Synthesis

  • “We are going to create a poster and do a Gallery Walk.”

Activity 2: Compare and Connect: Gallery Walk (15 minutes)

Narrative

The purpose of this activity is for students to create a poster to show all the expressions equivalent to their assigned \(10 + n\) expression. Before the activity, assign each group an expression for which they will make a poster. Then, students get into new groups of three and each group visits three posters. Students consider what patterns they notice between the expressions on the poster. Students may notice there is a relationship between the addends of equivalent expressions. For example, when one addend decreases by 1, the other addend in the sum increases by 1 (MP7).

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing

Action and Expression: Develop Expression and Communication. Provide students with alternatives to writing their observations on paper: students can share their observations verbally, or through drawings.
Supports accessibility for: Language, Conceptual Processing

Required Materials

Launch

  • Groups of 3
  • Give each group tools for creating a visual display.
  • Assign each group an expression.

Activity

MLR7 Compare and Connect
  • “Create a visual display that shows the expressions equal to the expression with 10 I assigned you.”
  • 3 minutes: small group work
  • 7 minutes: gallery walk
  • During the gallery walk, consider asking:
    • “What do you notice about the expressions on the poster?”
    • “What patterns do you notice?”
    • “Are the patterns the same across all of the posters?”

Activity Synthesis

  • Display posters for \(10 + 1\), \(10 + 3\), and \(10 + 5\).
  • “What patterns did you notice as you went from poster to poster?” (I saw that there was an expression with 9 on every poster. For example, \(10 + 3\) is equivalent to \(9 + 4\). This is because I can take 1 from the 4 and give it to the 9.) To amplify student language and illustrate connections, follow along and point to the relevant parts of the displays as students speak.
  • Record responses as equations (for example, \(10 + 3 = 9 + 4\)). 
  • Record \(10 + 3 = 9 + 4\). “Is the same pattern on other posters?” (Yes, it happened on \(10 + 2\). If I have \(9 + 3\), I can take one from the 3 and give it to the 9. Then I have \(10 + 1\).)

Activity 3: Centers: Choice Time (15 minutes)

Narrative

The purpose of this activity is for students to choose from activities that offer practice adding and subtracting within 10. Students choose from any stage of previously introduced centers.

  • Shake and Spill
  • Compare
  • Number Puzzles

Required Materials

Materials to Gather

Required Preparation

  • Gather materials from previous centers:
    • Shake and Spill, Stages 3–5
    • Compare, Stage 1
    • Number Puzzles, Stages 1 and 2

Launch

  • Groups of 2
  • “Now you are going to choose from centers we have already learned.”
  • Display the center choices in the student book.
  • “Think about what you would like to do.”
  • 30 seconds: quiet think time

Activity

  • Invite students to work at the center of their choice.
  • 10 minutes: center work time

Student Facing

Choose a center.

Shake and Spill

Center activity. Shake and Spill.

Compare

Center. Compare.

Number Puzzles

Center activity. Number Puzzles.

Activity Synthesis

  • Display nine red counters and cover five yellow counters with a cup.
  • “We are playing with 14 counters. How many yellow counters are under the cup? How do you know?”

Lesson Synthesis

Lesson Synthesis

Display a double 10-frame with eight counters on the top frame and four on the bottom, and  \(8 + 4 = 10 + 3\).

“Today we matched addition expressions to equivalent expressions with a 10. Is this equation true or false? How do you know?” (It’s false, because if I move two counters to the top 10-frame then it shows \(10 + 2\).)

Cool-down: Unit 3, Section C Checkpoint (0 minutes)

Cool-Down

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