Applying Proportions in Context: Grade 8 Unit Mastery Quiz with Full Solutions

Grade 8 scope

This record is a dedicated unit mastery quiz for Applying Proportions in Context within Grade 8 ratios, rates, and proportions. It focuses on contextual proportion problems rather than reteaching the full equivalent-ratio unit.

For broader end-of-unit assessment across equivalent ratios, proportionality, and ratio comparison, see the linked records instead of duplicating them here.

Quiz format

• Questions: 10
• Suggested time: 35-45 minutes
• Total marks: 20
• Calculator: optional unless your course expectations say otherwise

What this quiz is intended to measure

A student is showing mastery if they can:

• decide whether a context is proportional
• identify and use equivalent ratios correctly
• solve for an unknown in a proportion
• interpret proportional relationships in tables and scales
• explain whether an answer makes sense in context

Unit Mastery Quiz

Question 1 (2 marks)

A recipe uses 3 cups of flour for 8 muffins. How many cups of flour are needed for 24 muffins?

Question 2 (2 marks)

A map scale is 1 cm : 5 km. Two towns are 7.6 cm apart on the map. What is the real distance between the towns?

Question 3 (2 marks)

Five notebooks cost $12.50. At the same rate, how much do 8 notebooks cost?

Question 4 (2 marks)

A car travels 180 km using 15 L of fuel. At the same rate, how many litres are needed for 300 km?

Question 5 (2 marks)

A table shows the number of red and blue beads in different bags.

Bag	Red	Blue
A	4	6
B	10	15
C	12	20
Which bags have the same red:blue ratio? Show how you know.

Question 6 (2 marks)

A plant grows 6 cm in 4 weeks. Assuming the relationship is proportional, how much would it grow in 10 weeks? Then state one reason why a real plant might not keep growing proportionally forever.

Question 7 (2 marks)

A store sign says: "3 granola bars for $4.50." Mia says 7 bars will cost $10.50 because she multiplied by 2.5. Is Mia correct? If not, find the correct cost and explain the mistake.

Question 8 (2 marks)

A class is mixing paint in the ratio 2 parts yellow to 3 parts blue. They use 18 cups of blue paint. How many cups of yellow paint are needed to keep the colour the same?

Question 9 (2 marks)

At a fundraiser, 9 volunteers can pack 360 snack bags in one hour. Assuming everyone works at the same constant rate, how many snack bags can 15 volunteers pack in one hour?

Question 10 (2 marks)

A table shows a relationship between distance walked and time.

Time (min)	Distance (m)
5	400
8	640
12	920
Is this relationship proportional? Explain using ratios or unit rates.

Full Marking Key and Solutions

Question 1 solution

We compare muffins to flour:

3 cups / 8 muffins = x cups / 24 muffins

Since 24 is 3 times 8, multiply 3 cups by 3:

x = 9 cups

Answer: 9 cups

Marking (2 marks)

• 1 mark for setting up or recognizing the scale factor
• 1 mark for correct answer 9 cups

Question 2 solution

Scale: 1 cm represents 5 km.

So 7.6 cm represents:

7.6 x 5 = 38

Answer: 38 km

Marking (2 marks)

• 1 mark for multiplying by the scale factor 5 km per cm
• 1 mark for correct answer 38 km

Question 3 solution

First find the cost per notebook:

$12.50 / 5 = $2.50 per notebook

Then for 8 notebooks:

8 x $2.50 = $20.00

Answer: $20.00

Marking (2 marks)

• 1 mark for unit rate or correct proportion setup
• 1 mark for correct answer $20.00

Question 4 solution

Fuel use is proportional to distance.

15 L / 180 km = x L / 300 km

Scale factor from 180 to 300:

300 / 180 = 5 / 3

So:

x = 15 x 5/3 = 25

Answer: 25 L

Marking (2 marks)

• 1 mark for correct proportional setup or equivalent reasoning
• 1 mark for correct answer 25 L

Question 5 solution

Compare the ratios.

Bag A: 4:6 = 2:3

Bag B: 10:15 = 2:3

Bag C: 12:20 = 3:5

So Bags A and B have the same red:blue ratio.

Answer: Bags A and B

Marking (2 marks)

• 1 mark for simplifying or comparing ratios correctly
• 1 mark for identifying A and B only

Question 6 solution

If growth is proportional:

6 cm / 4 weeks = x cm / 10 weeks

x = 6 x 10/4 = 15

So the model predicts 15 cm growth in 10 weeks.

A real plant might not keep growing proportionally because growth conditions change, such as sunlight, water, temperature, or the plant reaching maturity.

Answer: 15 cm; real growth may stop being proportional because conditions or growth stage change.

Marking (2 marks)

• 1 mark for correct proportional calculation to 15 cm
• 1 mark for a valid contextual limitation

Question 7 solution

The cost per granola bar is:

$4.50 / 3 = $1.50 per bar

For 7 bars:

7 x $1.50 = $10.50

So Mia's answer is correct, but her explanation is weak. Multiplying by 2.5 works from 3 bars to 7.5 bars, not to 7 bars. The safer method is to use the unit rate or a correct proportion.

Answer: The cost is $10.50, but Mia's stated method is not valid for exactly 7 bars.

Marking (2 marks)

• 1 mark for correct cost $10.50
• 1 mark for explaining that the method, not the final number, is the issue

Question 8 solution

Ratio yellow:blue = 2:3

If blue is 18 cups, then the scale factor is:

18 / 3 = 6

So yellow must be:

2 x 6 = 12

Answer: 12 cups of yellow paint

Marking (2 marks)

• 1 mark for identifying the scale factor or setting a correct proportion
• 1 mark for correct answer 12 cups

Question 9 solution

If 9 volunteers pack 360 bags, then each volunteer packs:

360 / 9 = 40 bags per hour

For 15 volunteers:

15 x 40 = 600

Answer: 600 snack bags

Marking (2 marks)

• 1 mark for finding the unit rate 40 bags per volunteer
• 1 mark for correct answer 600

Question 10 solution

Check the unit rates.

At 5 min: 400 / 5 = 80 m/min

At 8 min: 640 / 8 = 80 m/min

At 12 min: 920 / 12 is about 76.7 m/min

The unit rate is not constant, so the relationship is not proportional.

Answer: No, it is not proportional because the unit rate changes.

Marking (2 marks)

• 1 mark for checking ratios or unit rates correctly
• 1 mark for correct conclusion with explanation

Total and Mastery Recommendation

• Total marks: 20
• Suggested mastery threshold: 16/20 or better, with no major breakdown on contextual reasoning questions
• Stronger mastery signal: 16/20 overall and at least 6/8 on Questions 7-10, since those require interpretation rather than routine scaling alone

Interpretation Guide

• 18-20: secure mastery; ready to apply proportions in unfamiliar contexts
• 16-17: meets mastery; minor errors only
• 13-15: developing; revisit proportional reasoning in tables, rates, and justification
• 12 or below: not yet secure; reteach with linked equivalent-ratio and ratio-comparison records before reassessment

Common Error Patterns to Watch For

• Using additive thinking instead of multiplicative thinking
• Matching the wrong quantities in a proportion
• Assuming every table is proportional without checking for a constant ratio or unit rate
• Getting a numerically correct answer with invalid reasoning
• Forgetting to interpret whether a proportional model is realistic in context

Linkage to Existing Records

Use these linked records for broader coverage rather than repeating them here:

• the broader Equivalent Ratios and Proportions unit mastery quiz
• the Equivalent Ratios and Simplification quiz for prerequisite fluency
• the Comparing Ratios quiz for ratio-comparison methods
• the Percent as a Number quiz when a learner needs reinforcement converting multiplicative relationships into familiar benchmark forms