Lesson 4

Reasoning about Equations and Tape Diagrams (Part 1)

Let’s see how tape diagrams can help us answer questions about unknown amounts in stories.

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?

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.

\(6x+11=21\)

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
(From Unit 2, Lesson 7.)

Problem 4

The diagram shows two intersecting lines.

Find the missing angle measures.

Two intersecting lines, forming an X. 
(From Unit 1, Lesson 12.)