Lesson 1

One of These Things Is Not Like the Others

The practice problem answers are available at one of our IM Certified Partners

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.

 

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

  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 Grade7, Unit 1, Lesson 12.)

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:

1 to 1,000,000

(From Grade7, Unit 1, Lesson 11.)

Problem 5

  1. Find 3 different ratios that are equivalent to \(7:3\).
  2. Explain why these ratios are equivalent.