Lesson 5

Model Repeated Addition and Subtraction

Est. Class Sessions: 2–3

Developing the Lesson

Part 3: Solve Problems with Repeated Addition and Subtraction

When students have drawn 4 mice, pose questions similar to the following about the various features of the mice:

X
  • How many [eyes] on each Math Mouse? (2)
  • How many [eyes] on [four] mice? How do you know? (8 eyes; Possible response: I double 2 to make 4, and then double 4 to make 8.)
  • Do we have to count the [eyes] by ones? What can we count by? (twos)
  • What is a number sentence that describes the problem? (2 + 2 + 2 + 2 = 8)
  • Use the number line to show how to skip count to solve this problem. Let's count together. (2, 4, 6, 8)

Repeat with other features and numbers of mice. Then ask:

X
  • How can we keep track of all these numbers? Is there a tool that can help organize our work so that it is easy to see patterns? (a data table)

Display the Number of Math Mice Features Master. Ask students to help you fill in the data table, recording the number of features for one, two, three, and four mice. See Figure 3. As the table is filled in, ask students to look for patterns and relate them to skip counting. Have students demonstrate the patterns on the number line and a display of the 100 Chart from the Student Activity Book Reference section.

Ask:

X
  • Do you see a pattern in the column for Number of Brown Tails? What is the pattern? (Possible response: adding 1 for each math mouse)
  • Who can show that pattern on the number line? On the 100 Chart?
  • Look at the column for the Number of Blue Dots for Eyes. What pattern do you see? (Possible response: skip counting by 2s)
  • Who can show that pattern on the number line? On the 100 Chart?

After students are familiar with strategies for finding the number of features that are part of the mice in front of them, increase the number of mice to 5 and ask questions such as the following:

X
  • If you drew 5 mice, how many dots for the mouth would you have? (25)
  • Explain how you solved the problem. (Possible response: I skip counted by 5s five times: 5, 10, 15,
    20, 25.)
  • Does this match the pattern on the data table? (Possible response: Yes, the pattern skip counts by fives.)
X

It is best to avoid use of the term "multiplication" at this time, unless a student volunteers it. However, try to use a variety of words to describe these problems, including some language that implies multiplication. For example, have students say the addition number sentence, but also talk about having 3 fives in this sentence, or having 5 three times. In this way, students become accustomed to associating repeated addition with the language they will eventually know as the language of multiplication.

Fill in the data for the number of features on 5 mice.

Then ask questions about the features on
6 mice:

X
  • If you drew 6 mice, how many eyes would you have? (12)
  • Explain how you solved the problem. (Possible response: I added 2 + 2 + 2 + 2 + 2 + 2 = 12)
  • Does this match the pattern on the data table? (Possible response: Yes. Five mice had 10 eyes. 2 more eyes would be 12. The pattern on the table skip counts by twos, and all the numbers are even.)
  • Which is more efficient—drawing 6 mice or using another solution strategy? Why do you think so? (Possible response: It is more efficient to use patterns on the data table or to use repeated addition or skip counting. Drawing 6 mice takes longer.)

Fill in the data for the number of features on 6 mice. Use Sample Dialog 2 to guide your discussion for solving problems for multiple mice.

X

Use this dialog as a guide for discussing the number of eyes on 6 mice.

Teacher: What if we drew 6 mice? How many eyes would we have?

Jackie: I think it's 12 eyes.

Teacher: How did you get 12 eyes?

Jackie: I have 4 mice and I need 2 more so I pretended I had 2 more mice. [She points to her drawings of mice and then to two imaginary mice at the side of her paper.] I counted: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Teacher: So we'll write 1 + 1 for each mouse. That's 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 12. (Circling every two 1s to keep track of number of mice.) The answer is 12 eyes. Is there a faster way we could count the eyes?

Jackie: Tens?

Teacher: Try counting by tens.

Jackie: [Pointing to each mouse and two imaginary mice] 10, 20, 30, 40, 50, 60. Oh, that would be too many.

Teacher: Do we have 60 eyes?

Jackie: No.

Teacher: Let's look at the eyes. How are they grouped? Look at the first mouse. How many eyes does it have?

John: Two.

Teacher: So we say "2" for the first mouse. Then we go to the second mouse and we say…

John: Four.

Teacher: How are we counting?

John: We're counting by twos.

Teacher: Good. Now, let's all count by twos to find out how many eyes on 6 mice.

Class: 2, 4, 6, 8, 10, 12.

Teacher: So the answer is 12. Who can write a number

sentence?

Brian: My number sentence is 2 + 2 + 2 + 2 + 2 + 2 = 12.

Teacher: Explain why you wrote that number sentence.

Brian: I wrote 2 for each mouse and there's 6 mice, so that's
6 twos.

Teacher: Great explanation, Brian! If we had 7 mice, how many twos would you write in your number sentence?

Maria: 7 twos. That would be 2 + 2 + 2 + 2 + 2 + 2 + 2. If I count by twos, the answer is 14.


Next give students problems such as the following to give them practice with repeated addition and repeated subtraction:

X
  • A mouse has four feet. If you see four mice, how many feet do you see? (16 feet)
  • How did you solve it? (Possible response: I added
    4 + 4 + 4 + 4 = 16)
  • If you see 12 mice feet, how many mice are there? (3 mice)
  • How did you solve it? (Possible response: I started at 12 on the number line and went back 4 three times.)
  • You made 4 mice. If each mouse takes three bites of a piece of cheese, how many bites of cheese will there be? (12 bites)
  • How did you solve it? (Possible response: On the number line, I made 4 jumps of 3 and I landed on 12.)
  • Each mouse hole holds 4 mice. How many mouse holes would you need to hold 12 mice? (3 mouse holes)
  • Explain how you solved it. (Possible response: I drew 12 mice and drew a circle around every 4 and I made
    3 circles for the mouse holes.)
  • If a house had 4 mouse holes and there were
    4 mice in each one, how many mice would be in the house?     (16 mice)
  • Explain how you solved it. (Possible response: I found 4 on the 100 Chart, and counted 4 more, and then
    4 more, and 4 more. I got to 16.)
  • If you had 30 red dots for the mouth, how many mice would you have? How do you know? (6; Each mouse has 5 dots for a mouth. I counted by fives until I got to 30. It was 6 times.)
Adventure Book:
Student Activity Book:
Master: