Grade 8 Unit Mastery Quiz: Ratio Concepts and Comparison

Position in the unit

This record is a mastery quiz for Grade 8 learners studying Ratio Concepts and Comparison. It should be used after the linked unit pathway, worked examples, and practice set:

• See rea.m08.number.ratios-rates-proportions for the broader unit sequence.
• See rea.m08.number.ratios-rates-proportions.ratio-concepts.worked-examples for fully developed model solutions before attempting this quiz.
• See rea.m08.number.ratios-rates-proportions.ratio-concepts.practice-set for additional rehearsal problems.
• See rea.m08.number.ratios-rates-proportions.proportional-modeling.overview for where these ideas lead next in proportional decision-making.

This quiz does not reteach the full topic; it checks whether the learner can now perform and justify the main comparison skills independently.

Quiz structure

• Total: 20 marks
• Questions: 10
• Suggested time: 30-40 minutes
• Calculator: not necessary

Mastery target

Recommended mastery threshold: 16/20 (80%), with the additional condition that the learner earns at least:

• 4/6 marks across Questions 7-9 (core comparison reasoning), and
• 1/2 marks on Question 10 (written justification).

Reason: a learner should not be considered secure on this unit through routine simplification alone; they must also compare ratios fairly and explain why a comparison method is valid.

Marking principles

Award marks for:

• correct ratio writing and simplification,
• use of equivalent ratios, common scaling, tables, or cross-products where appropriate,
• fair comparison of quantities in the same form,
• clear statements in context,
• justified reasoning, not answer-only guessing.

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Questions

1. Write and simplify a ratio. (2 marks)

A class has 12 girls and 18 boys.

1. Write the ratio of girls to boys.
2. Write it in simplest form.

2. Part-to-whole ratio. (2 marks)

A basket contains 9 red apples and 6 green apples.

1. Write the ratio of red apples to total apples.
2. Write the ratio in simplest form.

3. Find a missing value in an equivalent ratio. (2 marks)

Complete the ratio table:

3 : 5 = 12 : __

Show how you know.

4. Generate an equivalent ratio. (2 marks)

A fruit punch recipe uses juice and water in the ratio 2 : 7.

Write one equivalent ratio that could be used to make a larger batch.

5. Decide whether two ratios are equivalent. (2 marks)

Are 4 : 10 and 6 : 15 equivalent? Show your reasoning.

6. Compare using simplification. (2 marks)

Which class has the greater ratio of pencils to students?

• Class A: 15 pencils for 20 students
• Class B: 18 pencils for 24 students

7. Compare using common scaling. (2 marks)

Which sports drink is more concentrated with syrup?

• Mix A: 3 cups syrup to 8 cups water
• Mix B: 5 cups syrup to 12 cups water

Compare fairly and state which has more syrup relative to water.

8. Compare ratios in context. (2 marks)

Two shelters report cat-to-dog ratios:

• Shelter P: 14 cats to 21 dogs
• Shelter Q: 18 cats to 24 dogs

Which shelter has the greater proportion of cats relative to dogs?

9. Choose the better value by ratio comparison. (2 marks)

A snack mix has:

• Brand X: 16 peanuts for every 20 raisins
• Brand Y: 18 peanuts for every 30 raisins

Which brand has more peanuts relative to raisins?

10. Explain a valid comparison method. (2 marks)

A student says, "To compare 7 : 12 and 8 : 15, I can just compare 7 to 8 and decide 8 : 15 is larger."

Explain why this method is not reliable, and describe one correct way to compare the ratios.

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Full marking key and solutions

1. Write and simplify a ratio. (2 marks)

Answer:

1. Girls to boys = 12 : 18
2. Simplest form = 2 : 3

Solution: The ratio of girls to boys compares 12 with 18, so it is 12 : 18. To simplify, divide both parts by their greatest common factor, 6:

• 12 ÷ 6 = 2
• 18 ÷ 6 = 3 So the simplified ratio is 2 : 3.

Marking:

• 1 mark for 12 : 18
• 1 mark for 2 : 3

2. Part-to-whole ratio. (2 marks)

Answer: 9 : 15 = 3 : 5

Solution: Total apples = 9 + 6 = 15. So the ratio of red apples to total apples is 9 : 15. Simplify by dividing both terms by 3:

• 9 ÷ 3 = 3
• 15 ÷ 3 = 5 So the simplified ratio is 3 : 5.

Marking:

• 1 mark for finding total and writing 9 : 15
• 1 mark for simplifying to 3 : 5

3. Find a missing value in an equivalent ratio. (2 marks)

Answer: 20

Solution: To go from 3 to 12, multiply by 4. Equivalent ratios must scale both parts by the same factor. So multiply 5 by 4:

• 5 × 4 = 20 Therefore, 3 : 5 = 12 : 20.

Marking:

• 1 mark for identifying scale factor 4 or equivalent reasoning
• 1 mark for correct missing value 20

4. Generate an equivalent ratio. (2 marks)

Sample answer: 4 : 14

Solution: An equivalent ratio is made by multiplying both terms by the same number. Starting with 2 : 7:

• multiply both terms by 2 to get 4 : 14 Other correct answers include 6 : 21, 8 : 28, 10 : 35, and so on.

Marking:

• 2 marks for any correct equivalent ratio
• 1 mark only if the idea is right but one term is scaled incorrectly

5. Decide whether two ratios are equivalent. (2 marks)

Answer: Yes, they are equivalent.

Solution: Simplify both ratios.

For 4 : 10:

• divide both terms by 2
• 4 : 10 = 2 : 5

For 6 : 15:

• divide both terms by 3
• 6 : 15 = 2 : 5

Since both simplify to 2 : 5, the ratios are equivalent.

A cross-product check also works:

• 4 × 15 = 60
• 10 × 6 = 60 Same result, so the ratios are equivalent.

Marking:

• 1 mark for a valid method
• 1 mark for correct conclusion

6. Compare using simplification. (2 marks)

Answer: They are equal.

Solution: Class A: 15 : 20 Simplify by dividing by 5:

• 15 : 20 = 3 : 4

Class B: 18 : 24 Simplify by dividing by 6:

• 18 : 24 = 3 : 4

Both classes have the same ratio of pencils to students, so neither class has a greater ratio.

Marking:

• 1 mark for correct simplification of at least one class or equivalent comparison setup
• 1 mark for correct conclusion that the ratios are equal

7. Compare using common scaling. (2 marks)

Answer: Mix B is more concentrated.

Solution: We compare syrup to water.

Mix A is 3 : 8. Mix B is 5 : 12.

Use a common number of water parts. The least common multiple of 8 and 12 is 24.

Scale Mix A:

• 3 : 8 = 9 : 24

Scale Mix B:

• 5 : 12 = 10 : 24

Now compare:

• Mix A has 9 parts syrup for 24 parts water
• Mix B has 10 parts syrup for 24 parts water

So Mix B has more syrup relative to water and is more concentrated.

Marking:

• 1 mark for fair comparison setup
• 1 mark for correct conclusion

8. Compare ratios in context. (2 marks)

Answer: Shelter Q has the greater cat-to-dog ratio.

Solution: Shelter P: 14 : 21 Simplify by dividing by 7:

• 14 : 21 = 2 : 3

Shelter Q: 18 : 24 Simplify by dividing by 6:

• 18 : 24 = 3 : 4

Now compare 2 : 3 and 3 : 4. Use a common number of dogs: 12.

• 2 : 3 = 8 : 12
• 3 : 4 = 9 : 12

Since 9 : 12 has more cats for the same 12 dogs, Shelter Q has the greater cat-to-dog ratio.

Marking:

• 1 mark for simplifying or setting up a valid comparison
• 1 mark for correct contextual conclusion

9. Choose the better value by ratio comparison. (2 marks)

Answer: Brand X has more peanuts relative to raisins.

Solution: Brand X: 16 : 20 Simplify by dividing by 4:

• 16 : 20 = 4 : 5

Brand Y: 18 : 30 Simplify by dividing by 6:

• 18 : 30 = 3 : 5

Now the second term matches: both are "for 5 raisins."

• Brand X gives 4 peanuts for 5 raisins.
• Brand Y gives 3 peanuts for 5 raisins.

So Brand X has the greater peanut-to-raisin ratio.

Marking:

• 1 mark for valid comparison work
• 1 mark for correct conclusion

10. Explain a valid comparison method. (2 marks)

Sample answer: Comparing only the first numbers is not reliable because the second numbers are different. A ratio compares two quantities together, not just one part. For example, 7 : 12 and 8 : 15 cannot be compared fairly by looking only at 7 and 8.

One correct method is cross-products:

• 7 × 15 = 105
• 8 × 12 = 96

Since 105 > 96, 7 : 12 is greater than 8 : 15.

Another correct method is to scale to a common second term.

Marking:

• 1 mark for explaining why the student's method is invalid
• 1 mark for describing and correctly using a valid comparison method

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Score interpretation

• 18-20 marks: Secure mastery. The learner is ready to move into equivalent ratios, proportions, and richer rate contexts.
• 16-17 marks: Meets mastery threshold. Minor review may help, but the learner is generally ready for the next topic.
• 13-15 marks: Partial mastery. Review comparison methods, especially fair scaling and justification.
• 0-12 marks: Not yet secure. Revisit the linked worked examples and practice set before advancing.

Diagnostic reading of errors

Common error patterns and likely meaning:

• Confuses part-to-part with part-to-whole: Review what each ratio is comparing before computing.
• Simplifies only one term: Rebuild the idea that equivalent ratios must multiply or divide both terms by the same number.
• Compares first terms only: Emphasize fair comparison using common scaling, simplification, or cross-products.
• Gives answer without context statement: Practice ending with a sentence such as "Shelter Q has the greater cat-to-dog ratio."
• Treats larger numbers as automatically larger ratios: Revisit the idea that ratio size depends on the relationship between both terms, not raw size.

Suggested follow-up after the quiz

• If Questions 1-4 are weak: return to rea.m08.number.ratios-rates-proportions.ratio-concepts.worked-examples for foundational setup and simplification.
• If Questions 7-10 are weak: revisit both rea.m08.number.ratios-rates-proportions.ratio-concepts.worked-examples and rea.m08.number.ratios-rates-proportions.ratio-concepts.practice-set with emphasis on fair comparison methods.
• If the learner meets mastery: continue toward rea.m08.number.ratios-rates-proportions.proportional-modeling.overview and the next records on equivalent ratios and proportions.