Generating Equivalent Ratios by Scaling: Grade 8 Unit Mastery Quiz with Full Solutions

Scope and links

This record is a dedicated Grade 8 mastery quiz for the skill "generating equivalent ratios by scaling." It is narrower than the broader quizzes at rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz, rea.m08.number.ratios-rates-proportions.ratio-concepts.equivalent-ratios.unit-mastery-quiz, and rea.m08.number.ratios-rates-proportions.ratio-concepts.unit-mastery-quiz.

Use this quiz when the learner has already studied the core idea that equivalent ratios are formed by scaling both terms by the same non-zero factor. Use the broader linked records when you want mixed assessment across simplification, comparison, proportional relationships, and multi-step proportion solving.

Mastery quiz

Recommended format: 10 questions, 20 marks total, about 25-35 minutes.

Success criterion: A learner should show that they can:

• scale a ratio up correctly;
• scale a ratio down correctly when possible;
• identify the scale factor used;
• fill missing entries in equivalent-ratio tables;
• reject non-equivalent ratios when only one term was scaled or different factors were used.

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Question 1 (2 marks)

Write three ratios equivalent to 3:5 by scaling.

Solution 1

Scale both parts by the same factor.

• Multiply by 2: 3:5 = 6:10
• Multiply by 3: 3:5 = 9:15
• Multiply by 4: 3:5 = 12:20

Answer: 6:10, 9:15, 12:20

Marking:

• 1 mark for two correct equivalent ratios
• 1 mark for a third correct equivalent ratio

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Question 2 (2 marks)

Is 14:21 equivalent to 2:3? Show how you know using scaling.

Solution 2

Starting from 2:3, multiply both parts by 7:

• 2 x 7 = 14
• 3 x 7 = 21

So 2:3 = 14:21.

Answer: Yes, they are equivalent. The scale factor is 7.

Marking:

• 1 mark for identifying that the ratios are equivalent
• 1 mark for correct scaling justification

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Question 3 (2 marks)

Fill in the missing number: 4:7 = 20:__

Solution 3

To get from 4 to 20, multiply by 5. So multiply 7 by 5 as well:

• 7 x 5 = 35

Answer: 35

Marking:

• 1 mark for identifying scale factor 5
• 1 mark for correct missing value 35

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Question 4 (2 marks)

Fill in the missing number: __ : 18 = 5:9

Solution 4

To get from 9 to 18, multiply by 2. So multiply 5 by 2:

• 5 x 2 = 10

Answer: 10

Marking:

• 1 mark for identifying scale factor 2
• 1 mark for correct missing value 10

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Question 5 (2 marks)

A recipe uses flour and sugar in the ratio 2:3. Complete the equivalent ratio table.

Flour	Sugar
2	3
4	?
?	12

Solution 5

From 2:3 to 4:?, the flour doubled, so sugar must also double:

• 3 x 2 = 6

From 2:3 to ?:12, sugar was multiplied by 4, so flour must also be multiplied by 4:

• 2 x 4 = 8

Answer:

Flour	Sugar
2	3
4	6
8	12

Marking:

• 1 mark for 6
• 1 mark for 8

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Question 6 (2 marks)

A student says 6:10 and 12:25 are equivalent because both numbers got bigger. Is the student correct? Explain.

Solution 6

Check whether both parts were scaled by the same factor.

• 6 to 12 is multiply by 2
• 10 to 25 is multiply by 2.5

The scale factors are different, so the ratios are not equivalent.

Answer: No. Equivalent ratios must scale both terms by the same factor, and here the factors are different.

Marking:

• 1 mark for saying they are not equivalent
• 1 mark for correct explanation using unequal scale factors

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Question 7 (2 marks)

Scale 15:24 down to an equivalent ratio with first term 5.

Solution 7

To get from 15 to 5, divide by 3. So divide 24 by 3 too:

• 24 ÷ 3 = 8

So:

• 15:24 = 5:8

Answer: 5:8

Marking:

• 1 mark for identifying division by 3
• 1 mark for correct equivalent ratio 5:8

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Question 8 (2 marks)

Complete the chain of equivalent ratios: 7:11 = 14:__ = __:44

Solution 8

First blank:

• 7 to 14 is multiply by 2
• 11 x 2 = 22

Second blank:

• 11 to 44 is multiply by 4
• 7 x 4 = 28

Answer: 7:11 = 14:22 = 28:44

Marking:

• 1 mark for 22
• 1 mark for 28

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Question 9 (2 marks)

A red-blue bead pattern has ratio 3:4. Maya makes a larger pattern with 21 red beads. How many blue beads should she use to keep the ratio equivalent?

Solution 9

To get from 3 red beads to 21 red beads, multiply by 7. So multiply the blue beads by 7 too:

• 4 x 7 = 28

Answer: 28 blue beads

Marking:

• 1 mark for identifying scale factor 7
• 1 mark for correct answer 28

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Question 10 (2 marks)

Which of the following ratios are equivalent to 4:6?

• 8:12
• 12:18
• 16:20
• 2:3

Explain each choice briefly.

Solution 10

Check by scaling both terms of 4:6 by the same factor, or scaling down.

• 8:12: yes, multiply 4:6 by 2
• 12:18: yes, multiply 4:6 by 3
• 16:20: no, 4 to 16 is multiply by 4, but 6 to 20 is not multiply by 4
• 2:3: yes, divide 4:6 by 2

Answer: Equivalent ratios are 8:12, 12:18, and 2:3. 16:20 is not equivalent.

Marking:

• 1 mark for identifying all correct equivalent ratios
• 1 mark for correct justification, including rejecting 16:20

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Total and mastery recommendation

Total: 20 marks

Recommended mastery threshold: 16/20 (80%)

This threshold is appropriate for a narrow procedural skill because learners should be consistently accurate with scale factors in both directions.

Interpreting results

• 18-20: Strong mastery. Learner can reliably scale ratios up and down and explain equivalence.
• 16-17: Secure mastery. Minor slips only.
• 13-15: Partial mastery. Review reverse-scaling and checking whether both terms used the same factor.
• 0-12: Not yet secure. Re-teach the core rule: equivalent ratios come from multiplying or dividing both terms by the same non-zero number.

Common error patterns to check while marking

• Scaling only one term of the ratio
• Using different scale factors for the two terms
• Adding the same number to both terms instead of multiplying or dividing
• Failing to scale down when the question requires reverse work

For misconception repair and broader end-of-unit assessment, link onward to the existing related quiz records rather than extending this record into a full reteaching sequence.