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.
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Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself.
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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:
- \(3x+6=27\)
- \(6x+3=27\)
- \(27x+3=6\)
- 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?
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.](https://cms-im.s3.amazonaws.com/Ne5Ni35nZTAHXdN15xTgrWn1?response-content-disposition=inline%3B%20filename%3D%227-7.6.A4.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A4.newPP.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182425Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=980adfe3ce5244e905e1a6cc6b3f53bdc5c80e1799169dac5dda0e1f31aebb2e)
\(6x+11=21\)
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
- A person
- A football field (120 yards by 53\(\frac{1}{3}\) yards)
- The state of Washington (about 240 miles by 360 miles)
- The floor plan of a house
- 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
Problem 4
The diagram shows two intersecting lines.
Find the missing angle measures.
![Two intersecting lines, forming an X.](https://cms-im.s3.amazonaws.com/H8WVUfQkpBy1WX9Z7aSBCXP2?response-content-disposition=inline%3B%20filename%3D%228-8.1.D14.newPP.01b.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.D14.newPP.01b.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182425Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4fcbe6d36cceb66b674daf3f9bb784b92436c22eb68a7c5249f6d6d565ddbe35)