5th Grade Multiplication as Scaling Test Solutions and Scoring (PDF)

5th Grade math test solutions: Multiplication as Scaling – Maths PDF

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This scaling test answers for 5th Grade covers multiplication as scaling (Common Core 5.NF.B.5a, 5.NF.B.5b), with a free PDF to print.

This answer key gives worked solutions and a scoring guide for each of the 9 test questions, worth 20 points in all. Use the scoring notes to award points for correct reasoning about the scale factor, even when the calculation has a slip.

Grade 5 · Common Core State Standards: 5.NF.B.5a, 5.NF.B.5b

Scaling test answers: worked solutions

Question 1 – Predict without calculating [2 pts]

(a) \(\frac{5}{6} < 1\), so \(7 \times \frac{5}{6} < 7\).

(b) \(\frac{11}{8} > 1\), so \(7 \times \frac{11}{8} > 7\).

Scoring: 1 point for each correct symbol.

Question 2 – Order the products [2 pts]

\(20 \times \frac{1}{4} = 5\), \(20 \times 1 = 20\), \(20 \times \frac{5}{4} = 25\), \(20 \times \frac{3}{2} = 30\).

Least to greatest: \(20 \times \frac{1}{4}\), \(20 \times 1\), \(20 \times \frac{5}{4}\), \(20 \times \frac{3}{2}\).

Scoring: 2 points for the correct order. Give 1 point if only one expression is out of place.

Question 3 – Find the scale factor [2 pts]

Twelve is 3 of the 4 equal parts of 16.

(a) Each part is 4. The bottom bar is 3 parts out of 4: \(\frac{3}{4}\). Check: \(16 \times \frac{3}{4} = 12\).

(b) Less than 1, because the bottom bar is shorter than the top bar (12 is less than 16).

Scoring: 1 point for 3/4; 1 point for a correct explanation.

Question 4 – Calculate and compare [3 pts]

(a) \(\frac{5}{6} \times 18 = \frac{90}{6} = 15\): 15.

(b) \(\frac{7}{2} \times \frac{10}{7} = \frac{70}{14} = 5\): 5.

Scoring: 1 point for each part (part c needs both comparisons).

Question 5 – Find the mistake [2 pts]

(a) The scale factor \(\frac{2}{3}\) is less than 1, so the product is less than 9. Multiplying by a number less than 1 makes a number smaller.

(b) \(9 \times \frac{2}{3} = \frac{18}{3} = 6\): 6.

Scoring: 1 point for a correct explanation; 1 point for 6.

Question 6 – Photo sizes [3 pts]

Enlarged photo: 9 in by 6 in.

(a) Width: \(6 \times \frac{3}{2} = 9\) inches. Height: \(4 \times \frac{3}{2} = 6\) inches: 9 inches by 6 inches.

(b) \(6 \times \frac{2}{3} = 4\): 4 inches.

Scoring: (a) 1 point for each dimension. (b) 1 point.

Question 7 – Smoothie recipe [2 pts]

(a) \(\frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = 1\frac{1}{2}\): \(1\frac{1}{2}\) cups.

(b) \(\frac{9}{4} \times \frac{4}{3} = \frac{36}{12} = 3\): 3 cups.

Scoring: 1 point for each correct amount with units.

Question 8 – Fraction on a number line [2 pts]

The product 1/2 is to the left of 3/4.

(a) Left. The factor \(\frac{2}{3}\) is less than 1, so the product is less than \(\frac{3}{4}\).

(b) \(\frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}\): \(\frac{1}{2}\).

Scoring: 1 point for left with a correct reason; 1 point for 1/2.

Question 9 – Slide lengths [2 pts]

(a) \(\frac{3}{5} \times 20 = 12\): 12 feet.

(b) \(\frac{9}{4} \times 20 = 45\): 45 feet.

Scoring: 1 point for each correct length with units.

Total score

Total

20 points

Key facts behind this scaling test answers

Key facts

A scale factor greater than 1 makes the product larger.
A scale factor equal to 1 leaves the product the same.
A scale factor less than 1 makes the product smaller.
A fraction times a fraction less than 1 is smaller than both factors.
Compare the factor to 1 to predict the size before you calculate.

How to use this scaling test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

Download the scaling test answers as a PDF with the button below and keep it with your notes.

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