Lesson 4

Reasoning about Equations and Tape Diagrams (Part 1)

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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.

Here are three equations:

  • 3x+6=27
  • 6x+3=27
  • 27x+3=6
  1. Decide which equation represents each story. What does x represent in each equation?
  2. Find the solution to each equation. Explain or show your reasoning.
  3. 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 part colored blue and labeled 11, total 21.

6x+11=21

Solution

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Problem 3

For each object, choose an appropriate scale for a drawing that fits on a regular sheet of paper. Not all of the scales on the list will be used.

Objects

  1. A person
  2. A football field (120 yards by 53\frac{1}{3} yards)
  3. The state of Washington (about 240 miles by 360 miles)
  4. The floor plan of a house
  5. A rectangular farm (6 miles by 2 mile)

Scales

  • 1 in : 1 ft
  • 1 cm : 1 m
  • 1: 1000
  • 1 ft: 1 mile
  • 1: 100,000
  • 1 mm: 1 km
  • 1: 10,000,000

Solution

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(From Unit 2, Lesson 7.)

Problem 4

The diagram shows two intersecting lines.

Find the missing angle measures.

Two intersecting lines, forming an X. 

Solution

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(From Unit 1, Lesson 12.)