Eligible Content - M05.A-F.2.1.3 Demonstrate an Understanding of Multiplication As Scaling

Unit 2 LEQ #2:

Eligible Content - M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing the size of a product to the size of one factor on the basis of the size of the other factor without performing the indicated multiplication. Example 2: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

1. Students are adding some rocks to the school’s fish tank. After they add the rocks, less water is needed in the fish tank than was needed before the rocks were added. Which number could the students multiply by the number of gallons of water in the fish tank before the rocks were added to show how much water is needed in the fish tank after the rocks are added?

(A)(B)(C)(D)

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2. The table below lists the number of pints of blueberries that are needed for two different recipes.

Each recipe makes one batch. A cook decides to make a half batch of each recipe. Which pair of statements about the recipes is true?

(A) Both recipe L and recipe M use less than 1 pint each.
The cook needs less than 1 pint of blueberries to make both half batches.

(B) Both recipe L and recipe M use more than 1 pint each.
The cook needs more than 1 pint of blueberries to make both half batches.

(C) Recipe L uses less than 1 pint and recipe M uses more than 1 pint.
The cook needs less than 1 pint of blueberries to make both half batches.

(D) Recipe L uses less than 1 pint and recipe M uses more than 1 pint.
The cook needs more than 1 pint of blueberries to make both half batches.

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3. The product of and any whole number is less than the whole number. Which statement about the fraction is a reason why this is true?

(A) The numerator is greater than 1.

(B) The denominator is greater than 1.

(D) The difference between the denominator and the numerator is greater than the numerator.

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4. Kaitlin walked the length of a path in a park 3 times. The total distance she walked was less than 1 mile. What must be true about the length of the path in the park?

(A) The length of the path must be shorter than mile.

(B) The length of the path must be between and 1 mile.

(D) The length of the path must be longer than 3 miles.

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Unit 2 LEQ #2: ANSWER KEY:

(A)(B)(C)(D)

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2. The table below lists the number of pints of blueberries that are needed for two different recipes.

Each recipe makes one batch. A cook decides to make a half batch of each recipe. Which pair of statements about the recipes is true?

(A) Both recipe L and recipe M use less than 1 pint each.
The cook needs less than 1 pint of blueberries to make both half batches.

(B) Both recipe L and recipe M use more than 1 pint each.
The cook needs more than 1 pint of blueberries to make both half batches.

(C) Recipe L uses less than 1 pint and recipe M uses more than 1 pint.
The cook needs less than 1 pint of blueberries to make both half batches.

(D) Recipe L uses less than 1 pint and recipe M uses more than 1 pint.
The cook needs more than 1 pint of blueberries to make both half batches.

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3. The product of and any whole number is less than the whole number. Which statement about the fraction is a reason why this is true?

(A) The numerator is greater than 1.

(B) The denominator is greater than 1.

(D) The difference between the denominator and the numerator is greater than the numerator.

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4. Kaitlin walked the length of a path in a park 3 times. The total distance she walked was less than 1 mile. What must be true about the length of the path in the park?

(A) The length of the path must be shorter than mile.

(B) The length of the path must be between and 1 mile.

(D) The length of the path must be longer than 3 miles.

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