Lesson 1
One of These Things Is Not Like the Others
Let’s remember what equivalent ratios are.
Problem 1
Which one of these shapes is not like the others? Explain what makes it different by representing each width and height pair with a ratio.
![Three ovals, A, B and C on a grid.](https://cms-im.s3.amazonaws.com/E6ikyddgY7wwTgTqBVLvQdo1?response-content-disposition=inline%3B%20filename%3D%227-7.2.B.PP.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.B.PP.Image.04.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=20240630T211348Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0c859aa22344bbc967e830e14711b90c7da1f62b1a96c0806e0608a78c31cf3f)
Problem 2
In one version of a trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another version of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. Are the ratios equivalent for the two mixes? Explain your reasoning.
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
Which scale is equivalent to 1 cm to 1 km?
A:
1 to 1000
B:
10,000 to 1
C:
1 to 100,000
D:
100,000 to 1
E:
(From Unit 1, Lesson 11.)
1 to 1,000,000
Problem 5
- Find 3 different ratios that are equivalent to \(7:3\).
- Explain why these ratios are equivalent.