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6-8 Accelerated 7 Unit 3 Lesson 4

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Lesson 1 Lesson 2 Lesson 3 •Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 3, Lesson 4

Reasoning about Equations and Tape Diagrams (Part 1)

Accelerated 7

Practice

Problem 1

Here are three stories:

A family buys 6 tickets to a show. They also pay a \$3 parking fee. They spend \$27 to see the show.
Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself.
Jada works for 6 hours preparing for the art fair. She spends 3 hours on a sculpture and then paints 27 picture frames. She spends the same amount of time painting each frame.

Here are three equations:

\(3x+6=27\)
\(6x+3=27\)
\(27x+3=6\)

Decide which equation represents each story. What does \(x\) represent in each equation?
Find the solution to each equation. Explain or show your reasoning.
What does each solution tell you about its situation?

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Lesson 4 Resources

Student Materials

Problem 2

Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning.

Tape diagram, 6 equal parts labeled x, 1 part colored blue and labeled 11, total 21.

\(6x+11=21\)

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Problem 3

ForLesson 3: Reasoning about Equations with Tape Diagrams

Select all the equations that represent the diagram.

Tape diagram, 3 equal parts each marked x + 5, total 18.

\(x+5=18\)
\(18\div3=x+5\)
\(3(x+5)=18\)
\(x+5 = \frac13\boldcdot 18\)
\(3x+5=18\)

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Problem 4

ForLesson 15: Meet Slope

Which line has a slope of 0.625, and which line has a slope of 1.6? Explain why the slopes of these lines are 0.625 and 1.6.

Two lines on a grid that intersect at a point. 2nd point on Top line is 8 up and 5 right from 1st point. 2nd point on bottom line is 5 up and 8 right from 1st point.

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Problem 5

ForLesson 9: Dilations

Jada claims that \(B’C’D’\) is a dilation of \(BCD\) using \(A\) as the center of dilation.

What are some ways you can convince Jada that her claim is not true?

<p>Point A, angle B C D and angle image B prime, C prime, D prime.</p>

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Problem 6

ForLesson 12: Alternate Interior Angles

The diagram shows two intersecting lines.

Find the missing angle measures.

Two intersecting lines, forming an X.

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