Lesson 8

Multiplication Number Sentences

Est. Class Sessions: 2

Developing the Lesson

Part 2. Function Machines

Review Function Machines. Students were introduced to Function Machines in second grade. See Content Note. Display the Doubling Function Machine Master. See Figure 3. Briefly review how Function Machines work by telling students to imagine a machine that takes numbers in, does something to them, and then gives you the results. Point out the rule on the Function Machine, double the number.

Ask student volunteers to fill in the output and write a number sentence for the first two numbers while explaining their thinking. Encourage students to write both an addition number sentence and a multiplication number sentence.

Next, ask students if they can do the operation backwards—if they know the output, can they figure out the input number? Have student volunteers fill in the last three rows of the table and explain their thinking. See the Content Note.

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Functions. The concept of a function is an important one. Students will study it formally when they study algebra in later years. We introduce the basic concept of function in an informal way, without ever giving students a definition. One way of defining a function is to say that it is a rule that assigns to every input number exactly one number, the output number. In this lesson, students use patterns in the tables for Function Machines to solve multiplication and division problems. For every input number, there is exactly one output number on the table.

Practice Multiplication with Function Machines. Assign the Function Machines pages in the Student Activity Book to student pairs. Students will work with partners to complete several function tables involving multiplication with 0, 5, and 10 and one involving division by 2.

When students have finished, choose several students to share their solutions and thinking for a few problems.

Then ask:

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  • What is special about the Function Machine table for Question 6? Why? (All of the output numbers equal 0. The rule is multiply by 0, and any number times 0 is 0.)
Student Guide:
Student Activity Book: 305 306
Answers
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SG_Mini
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SG_Mini
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Master:
Completed doubling Function Machine table
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