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Problem Set Lesson 26 Answers

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MODULE 4 Expressions and Equaons
Topic G: Solving Equaons
Lesson 27: One‐Step Equaons ―
Mulplicaon and Division
Student Outcomes
§ Students solve one‐step equaons by relang an equaon to a diagram.
§ Students check to determine if their soluon makes the equaon true.

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Classwork
Example 1
Solve 3z = 9 using tape diagrams and algebraically and then check your answer.
First draw two tape diagrams, one to represent each side of the equaon.
If 9 had to be split into three groups, how big would each group be?
Demonstrate the value of z using tape diagrams.

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How can we demonstrate this algebraically?
How does this get us the value of z?
How can we check our answer?

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Example 2
Solve using tape diagrams and algebraically. Then, check your answer.
First, draw two tape diagrams, one to represent each side of the equaon.
if the first tape diagram shows the size of y ÷4 , how can we draw a tape diagram to represent y?
Draw this tape diagram.

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What value does each y÷ 4 secon represent? How do you know?
How can you use a tape diagram to show the value of y?

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How can we demonstrate this algebraically?
How does this help us find the value of y?
How can we check our answer?

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Exercises
1. Use tape diagrams to solve the following problem: 3m = 21

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3. Calculate the soluon of the equaon using the method of your choice: 4 p = 36

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4. Examine the tape diagram below and write an equaon it represents. Then, calculate the
soluon to the equaon using the method of your choice.

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5. Write a mulplicaon equaon that has a soluon of 12. Use tape diagrams to
prove that your equaon has a soluon of 12.
6. Write a division equaon that has a soluon of 12. Prove that your equaon has
a soluon of 12 using algebraic methods.

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Closing
Please take out your exit ticket for Lesson 27, close your
binder, and complete the exit ticket. This will be collected.
§ How is solving addion and subtracon equaons similar and different to
solving mulplicaon and division equaons?
§ What do you know about the paern in the operaons you used to solve the
equaons today?
ú We used inverse operaons to solve the equaons today. Division was used
to solve mulplicaon equaons , and mulplicaon was used to solve division
equaons.

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