Lesson 5

Reasoning about Equations and Tape Diagrams (Part 2)

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Problem 1

Here are two stories:

  • A family buys 6 tickets to a show. They also each spend $3 on a snack. They spend $24 on the show.
     
  • Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends, and then adds 6 more ounces for each.

Here are two equations:

  • \(3(x+6)=24\)
  • \(6(x+3)=24\)
  1. Which equation represents which story?
  2. What does \(x\) represent in each equation?
  3. Find the solution to each equation. Explain or show your reasoning.
  4. What does each solution tell you about its situation?

Solution

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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, total 24

\(\displaystyle 6(x+1)=24\)

Solution

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Problem 3

Find a sequence of rotations, reflections, translations, and dilations showing that one figure is similar to the other. Be specific: give the amount and direction of a translation, a line of reflection, the center and angle of a rotation, and the center and scale factor of a dilation.

polar coordinate plane with center at A. quadrilateral BCDE and quadrilateral B prime prime, C prime prime, D prime prime, E prime prime graphed.

 

Solution

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(From Unit 2, Lesson 11.)

Problem 4

Suppose Quadrilaterals A and B are both squares. Are A and B necessarily scaled copies of one another? Explain.

Solution

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(From Unit 2, Lesson 2.)