Section C Section C Checkpoint

Problem 1

Kansas and South Dakota both have rectangular shapes. Kansas is 660 kilometers long and 343 kilometers wide. South Dakota is 610 kilometers long and 340 kilometers wide.

Is the area of Kansas greater than or less than 200,000 square kilometers? Explain or show your reasoning.
Explain why 200,000 square kilometers is a good estimate for the area of South Dakota.

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Solution

Sample responses:

Greater. I know $600 \times 300 = 180,000$ and then $600 \times 40$ is more than 20,000 so that's already more than 200,000.
South Dakota is a little more than 600 km long and 300 km wide. I know $3 \times 600 = 1,800$ and then 100 times more is $180,000$ so $200,000$ is a good estimate.

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Sample Response

Sample responses:

Greater. I know $600 \times 300 = 180,000$ and then $600 \times 40$ is more than 20,000 so that's already more than 200,000.
South Dakota is a little more than 600 km long and 300 km wide. I know $3 \times 600 = 1,800$ and then 100 times more is $180,000$ so $200,000$ is a good estimate.

Problem 2

The back of a garbage truck is 23 feet long, 8 feet wide, and 12 feet tall. How many loads of trash from the garbage truck will it take to fill a 40-foot-by-9-foot-by-8-foot storage container? Explain or show your reasoning.

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Solution

2 loads. Sample response: Each set of side lengths has an 8 so I can compare $23 \times 12$ to $40 \times 9$ . I know $23 \times 12 = 276$ and $40 \times 9 = 360$ . So one load of trash is not enough, but two loads are.

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Sample Response