Equivalent Ratios in Tables and Structured Representations: Grade 8 Unit Mastery Quiz with Full Solutions

Position in the unit

This record is the dedicated assessment for Grade 8 equivalent ratios in tables and structured representations. Use the linked overview for teaching the ideas, and use the broader equivalent-ratios quizzes for adjacent coverage beyond structured forms.

Linked records:

• Overview: rea.m08.number.ratios-rates-proportions.equivalent-ratios.ratio-tables.overview
• Broader unit quiz: rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz
• Adjacent prerequisite/related quiz: rea.m08.number.ratios-rates-proportions.ratio-concepts.equivalent-ratios.unit-mastery-quiz

Quiz directions

• Grade level: Grade 8
• Suggested time: 30-40 minutes
• Total: 20 marks
• Show multiplicative reasoning. Answers without method earn at most partial credit where explanation is requested.
• Calculators are not necessary.

Coverage

This quiz samples the unit outcomes:

• complete ratio tables using multiplicative scale factors
• interpret equivalent ratios in tables and double number lines
• detect when a table is not proportional
• solve missing-value problems from structured representations
• explain why additive reasoning does not work for equivalent ratios

Questions

1. Complete a ratio table (2 marks)

A ratio table begins with the ratio 3 : 5.

A	3	6	9	?
B	5	?	15	25

Fill in the missing entries.

2. Find a missing value using a scale factor (2 marks)

A table shows equivalent ratios.

Red beads	4	10	?
Blue beads	7	?	35

Find the two missing values.

3. Decide whether a table is proportional (2 marks)

Decide whether the table represents equivalent ratios. If yes, state the constant multiplier from the first column to each other column. If no, explain briefly.

Flour (cups)	2	4	6	8
Water (cups)	3	6	10	12

4. Read a double number line (2 marks)

A double number line compares kilometres and metres.

• 1.5 km lines up with 1500 m
• 3 km lines up with 3000 m
• 4.5 km lines up with ? m
• ? km lines up with 6000 m

Fill in the two missing values.

5. Compare two structured representations (2 marks)

Table A:

Juice concentrate	2	4	6
Water	7	14	21

Table B:

Juice concentrate	3	6	9
Water	10	20	31

Which table shows equivalent ratios throughout? Explain.

6. Build a table from context (2 marks)

A recipe uses 5 cups of oats for every 2 bananas.

Create a ratio table showing four equivalent ratios, including the original ratio and one ratio with 20 cups of oats.

7. Solve from an incomplete table (2 marks)

A school club prints posters in a constant ratio of posters to markers used.

Posters	8	24	?	56
Markers	2	?	10	?

Find all missing values.

8. Error analysis: additive vs multiplicative reasoning (2 marks)

A student says:

"Since 4 : 6 becomes 8 : 10 by adding 4 to the first number and 4 to the second number, the ratios are equivalent."

Is the student correct? Explain why or why not using structured-ratio reasoning.

9. Multi-step table question (2 marks)

A table starts with the ratio 7 : 9.

Left	7	14	21	?	56
Right	9	?	27	45	?

Fill in the missing values.

10. Short response: explain the structure (2 marks)

In one or two sentences, explain how a ratio table helps you decide whether two ratios are equivalent.

Full marking solutions

1. Solution

The starting ratio is 3 : 5.

• From 3 to 6, multiply by 2, so 5 x 2 = 10.
• From 3 to 9, multiply by 3, and 5 x 3 = 15, which matches.
• From 5 to 25, multiply by 5, so 3 x 5 = 15.

Completed table:

A	3	6	9	15
B	5	10	15	25

Marking:

• 1 mark for 10
• 1 mark for 15

2. Solution

Use the base ratio 4 : 7.

• To get from 4 to 10, multiply by 2.5, so 7 x 2.5 = 17.5.
• To get from 7 to 35, multiply by 5, so 4 x 5 = 20.

Missing values:

• Blue beads under 10 red beads: 17.5
• Red beads over 35 blue beads: 20

Marking:

• 1 mark for 17.5
• 1 mark for 20

3. Solution

Check whether each column keeps the same ratio as 2 : 3.

• 4 : 6 is equivalent because both numbers are multiplied by 2.
• 6 : 10 is not equivalent because 2 x 3 = 6, but 3 x 3 = 9, not 10.
• 8 : 12 is equivalent because both numbers are multiplied by 4.

Because one column breaks the multiplicative pattern, the table does not represent equivalent ratios throughout.

Marking:

• 1 mark for correctly deciding "not proportional / not equivalent throughout"
• 1 mark for identifying 6 : 10 as the breaking column with multiplicative explanation

4. Solution

Since 1 km = 1000 m, the given pairs are equivalent.

• 4.5 km = 4500 m
• 6000 m = 6 km

Marking:

• 1 mark for 4500 m
• 1 mark for 6 km

5. Solution

Check each table for a constant multiplicative relationship.

Table A:

• 2 : 7
• 4 : 14 is multiply by 2
• 6 : 21 is multiply by 3 So Table A is consistent.

Table B:

• 3 : 10
• 6 : 20 is multiply by 2
• 9 : 31 is not multiply by 3, because 10 x 3 = 30, not 31 So Table B is not consistent.

Therefore, Table A shows equivalent ratios throughout.

Marking:

• 1 mark for choosing Table A
• 1 mark for valid explanation that Table B breaks the multiplicative pattern

6. Solution

The base ratio is 5 : 2 (oats : bananas). Possible table:

Oats	5	10	15	20
Bananas	2	4	6	8

Any four correct equivalent ratios earn full marks if they include the original ratio and a ratio with 20 cups of oats.

Marking:

• 1 mark for maintaining the ratio 5 : 2
• 1 mark for including four equivalent ratios, including 20 : 8

7. Solution

Base ratio: 8 : 2, which simplifies to 4 : 1.

• From 8 posters to 24 posters is multiply by 3, so markers are 2 x 3 = 6.
• If markers are 10, that is 5 times as many as 2, so posters are 8 x 5 = 40.
• From 8 posters to 56 posters is multiply by 7, so markers are 2 x 7 = 14.

Completed table:

Posters	8	24	40	56
Markers	2	6	10	14

Marking:

• 1 mark for 6
• 1 mark for both 40 and 14

8. Solution

The student is not correct. Equivalent ratios must be made by multiplying or dividing both terms by the same number, not by adding the same number.

• 4 : 6 simplifies to 2 : 3
• 8 : 10 simplifies to 4 : 5 Since 2 : 3 and 4 : 5 are different, the ratios are not equivalent.

In a ratio table, equivalent columns must keep the same multiplicative scale factor. Here, the scale factor from 4 to 8 is 2, but from 6 to 10 it is 10/6, so the structure is inconsistent.

Marking:

• 1 mark for saying the student is incorrect
• 1 mark for explaining multiplicative inconsistency or correct simplification comparison

9. Solution

Base ratio is 7 : 9.

• 14 is 2 x 7, so matching value is 18
• 21 is 3 x 7, and matching value 27 confirms the pattern
• 45 is 5 x 9, so matching left value is 5 x 7 = 35
• 56 is 8 x 7, so matching right value is 8 x 9 = 72

Completed table:

Left	7	14	21	35	56
Right	9	18	27	45	72

Marking:

• 1 mark for 18
• 1 mark for both 35 and 72

10. Solution

Sample strong response:

"A ratio table helps because each column should be made from the same original ratio by multiplying or dividing both parts by the same factor. If one column does not follow that multiplicative pattern, then the ratios are not equivalent."

Marking:

• 1 mark for mentioning same multiplicative factor / multiplying or dividing both terms equally
• 1 mark for connecting that idea to testing equivalence in a table

Answer key only

1. 10, 15
2. 17.5, 20
3. Not equivalent throughout; 6 : 10 breaks the pattern
4. 4500 m, 6 km
5. Table A
6. Example: 5:2, 10:4, 15:6, 20:8
7. 6, 40, 14
8. No; additive change does not preserve equivalence
9. 18, 35, 72
10. Any correct explanation of constant multiplicative scaling

Recommended mastery threshold

Recommended threshold for unit mastery:

• 16/20 or higher, and
• no more than one error on questions 3, 8, 10 combined, because those questions check the central idea that equivalent ratios are multiplicative and structurally consistent.

Interpretation:

• 18-20: strong mastery
• 16-17: secure mastery
• 13-15: developing; revisit the overview and reattempt structured-representation items
• 0-12: not yet secure; reteach ratio tables and multiplicative scaling before moving on

Common error patterns to watch for in marking

• Using addition instead of multiplication to extend a ratio
• Treating one correct column as proof that the entire table is proportional
• Filling tables by matching only one entry instead of checking both terms
• Ignoring non-integer scale factors such as 2.5

Follow-up guidance

If a learner misses mostly explanation items, return to the overview record and require them to verbalize the scale factor in each column. If a learner misses mostly computation items, assign targeted practice on building and extending ratio tables before moving to broader proportion problems.