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.)