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6-8 Grade 7 Unit 6 Lesson 3

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Lesson 3

3.1 Warm-up 3.2 Activity 3.3 Activity Student Lesson Summary Glossary

Unit 6, Lesson 3

Reasoning about Equations with Tape Diagrams

Grade 7

3.1

Warm-up

Find Equivalent Expressions

Select all the expressions that are equivalent to . Explain how you know each expression you select is equivalent.

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3.2

Activity

Matching Equations to Tape Diagrams

Match each equation to one of the tape diagrams. Be prepared to explain how the equation matches the diagram.

Tape diagram A, 3 parts, 5, x, x, total 19. — A

Tape diagram B, 3 parts, x, x, 5, total 19. — B

Tape diagram C, 6 parts, 2, x, x, x, x, x, total 19. — C

Tape diagram D, 2 parts, x + 5, x + 5, total 19. — D

Tape diagram E, 5 parts, x + 2, x + 2, x + 2, x + 2, x + 2, total 19. — E

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3.3

Activity

Drawing Tape Diagrams to Represent Equations

Draw a tape diagram to match each equation.
Use any method to find values for and that make the equations true. Explain your reasoning.

Student Lesson Summary

We have seen how tape diagrams represent relationships between quantities. Because of the meaning and properties of addition and multiplication, more than one equation can often be used to represent a single tape diagram.

Let’s take a look at two tape diagrams.

Tape diagram, one large part labeled 26, four small equal parts labeled x, total 46.

We can represent this diagram with several different equations. Here are some of them:

, because the parts add up to the whole.
, because addition is commutative.
, because if two quantities are equal, it doesn’t matter how we arrange them around the equal sign.
, because one part (the part made up of 4 ’s) is the difference between the whole and the other part.

Tape diagram, four equal parts labeled, x + 9, total 76.

Here are some equations that represent this diagram:

, because multiplication means having multiple groups of the same size.
, because multiplication is commutative.
, because division tells us the size of each equal part.

Glossary

equivalent expressions

Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.

For example, is equivalent to .

When is 3, both expressions equal 21.
When is 10, both expressions equal 70.
When is any other number, both expressions still have equal value.

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