Grade 8 Choosing the Best Option: Unit Mastery Quiz with Full Solutions

Position in the unit

Use this quiz after studying the main proportional-modeling unit and after practicing unit-rate comparison. For broader end-of-unit assessment across all proportional-modeling skills, see [rea.m08.number.ratios-rates-proportions.proportional-modeling.unit-mastery-quiz]. For extra review on calculating and interpreting unit rates, see [rea.m08.number.ratios-rates-proportions.unit-rates.find-unit-rates.unit-mastery-quiz].

Grade 8 unit mastery quiz

Focus: choosing the better option in proportional situations by comparing unit rates, equivalent costs, scaled quantities, and practical conditions.

Suggested timing: 30-40 minutes
Materials: calculator optional unless your teacher specifies mental or paper methods only
Total: 20 marks

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Question 1 (2 marks)

A store sells apples in two bags:

• Bag A: 6 apples for $4.50
• Bag B: 10 apples for $7.00

Which bag is the better buy? Show your comparison.

Solution 1

Find the cost per apple.

• Bag A: $4.50 / 6 = $0.75 per apple
• Bag B: $7.00 / 10 = $0.70 per apple

Since $0.70 per apple is less than $0.75 per apple, Bag B is the better buy.

Marks:

• 1 mark for correct unit-rate work
• 1 mark for correct conclusion

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Question 2 (2 marks)

Two phone plans charge by data used:

• Plan X: 3 GB for $12
• Plan Y: 5 GB for $18

Which plan gives more data per dollar? Show your reasoning.

Solution 2

Find GB per dollar.

• Plan X: 3 / 12 = 0.25 GB per dollar
• Plan Y: 5 / 18 = 0.277... GB per dollar

Since 0.277... > 0.25, Plan Y gives more data per dollar.

Marks:

• 1 mark for correct comparison values
• 1 mark for correct conclusion

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Question 3 (2 marks)

A student can buy granola bars in either package:

• Pack 1: 8 bars for $5.60
• Pack 2: 15 bars for $10.20

Without rounding too early, determine which pack is cheaper per bar.

Solution 3

Compute cost per bar.

• Pack 1: $5.60 / 8 = $0.70 per bar
• Pack 2: $10.20 / 15 = $0.68 per bar

Since $0.68 per bar is cheaper than $0.70 per bar, Pack 2 is the better option.

Marks:

• 1 mark for correct unit rates
• 1 mark for correct decision

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Question 4 (2 marks)

Two taxi companies charge proportionally:

• Company A: $9 for 6 km
• Company B: $13.50 for 9 km

Which company is cheaper per kilometre, or are they the same?

Solution 4

Find cost per kilometre.

• Company A: 9 / 6 = $1.50 per km
• Company B: 13.50 / 9 = $1.50 per km

Both companies charge the same rate: $1.50 per km.

Marks:

• 1 mark for correct rates
• 1 mark for correct conclusion that they are equal

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Question 5 (2 marks)

Juice is sold in two bottles:

• Bottle A: 1.5 L for $3.90
• Bottle B: 2 L for $5.40

Which bottle is the better buy? Explain using cost per litre.

Solution 5

Find cost per litre.

• Bottle A: 3.90 / 1.5 = $2.60 per L
• Bottle B: 5.40 / 2 = $2.70 per L

Since $2.60 per L is less than $2.70 per L, Bottle A is the better buy.

Marks:

• 1 mark for correct unit-rate calculations
• 1 mark for correct conclusion

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Question 6 (2 marks)

A school is ordering notebooks.

• Supplier A sells 12 notebooks for $18
• Supplier B sells 20 notebooks for $31

The school needs 60 notebooks. Which supplier should it choose if it must buy whole packs only?

Solution 6

Compare based on the actual order of 60 notebooks.

Supplier A:

• 12 notebooks per pack
• 60 / 12 = 5 packs
• Cost = 5 x 18 = $90

Supplier B:

• 20 notebooks per pack
• 60 / 20 = 3 packs
• Cost = 3 x 31 = $93

So Supplier A is the better option for 60 notebooks.

Check with unit rates:

• A: 18 / 12 = $1.50 per notebook
• B: 31 / 20 = $1.55 per notebook

This agrees with the pack comparison.

Marks:

• 1 mark for correct scaling to 60 notebooks
• 1 mark for correct conclusion

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Question 7 (2 marks)

A recipe uses flour in proportional amounts.

• Brand A: 2.5 kg for $6.25
• Brand B: 4 kg for $9.80

Which brand gives more flour for each dollar spent?

Solution 7

Find kilograms per dollar.

• Brand A: 2.5 / 6.25 = 0.4 kg per dollar
• Brand B: 4 / 9.80 ≈ 0.40816 kg per dollar

Since 0.40816... > 0.4, Brand B gives more flour per dollar.

Equivalent check using cost per kg:

• A: 6.25 / 2.5 = $2.50 per kg
• B: 9.80 / 4 = $2.45 per kg

Again, Brand B is better.

Marks:

• 1 mark for correct rate comparison
• 1 mark for correct conclusion

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Question 8 (2 marks)

A student says, "Option C is better because it has the lower total price."

Compare these two options and decide whether the student's statement is correct:

• Option C: 7 markers for $6.30
• Option D: 10 markers for $8.50

Solution 8

A lower total price does not automatically mean a better buy. Compare unit prices.

• Option C: 6.30 / 7 = $0.90 per marker
• Option D: 8.50 / 10 = $0.85 per marker

Even though Option C costs less in total, Option D is cheaper per marker.

So the student's statement is not correct. Option D is the better buy.

Marks:

• 1 mark for correct unit-rate comparison
• 1 mark for correctly rejecting the faulty reasoning and choosing D

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Question 9 (2 marks)

A family is choosing between two rice bags:

• Bag P: 3 kg for $7.20
• Bag Q: 5 kg for $11.75

They have a coupon for $1 off Bag Q only. Which bag becomes the better buy after the coupon is used?

Solution 9

First adjust the price of Bag Q.

• New price of Bag Q = 11.75 - 1.00 = $10.75

Now compare cost per kilogram.

• Bag P: 7.20 / 3 = $2.40 per kg
• Bag Q: 10.75 / 5 = $2.15 per kg

Since $2.15 per kg is less than $2.40 per kg, Bag Q is the better buy after the coupon.

Marks:

• 1 mark for correctly applying the coupon
• 1 mark for correct comparison and conclusion

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Question 10 (2 marks)

Two gyms advertise proportional pricing for entry passes:

• Gym M: 8 visits for $52
• Gym N: 12 visits for $75

A student writes: "Gym M is better because 52 is less than 75."

1. Explain the mistake.
2. Decide which gym is the better buy.

Solution 10

The mistake is comparing only the total prices instead of the price per visit.

Find the unit rate.

• Gym M: 52 / 8 = $6.50 per visit
• Gym N: 75 / 12 = $6.25 per visit

Since $6.25 per visit is less than $6.50 per visit, Gym N is the better buy.

Marks:

• 1 mark for explaining the mistake
• 1 mark for correct unit-rate conclusion

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Marking key summary

1. B
2. Y
3. Pack 2
4. Same rate
5. Bottle A
6. Supplier A
7. Brand B
8. Option D
9. Bag Q after coupon
10. Gym N

Mastery recommendation

Recommended mastery threshold: 16/20 (80%)

Interpretation:

• 18-20: strong mastery; the learner consistently compares proportional options accurately and explains decisions clearly.
• 16-17: secure mastery; ready to move on, but should still review any errors involving setup or interpretation.
• 12-15: partial mastery; revisit unit rates, equivalent comparisons, and the difference between lower total cost and lower unit cost.
• 0-11: not yet secure; return to worked examples and guided practice before reassessment.

Common error checks

Use errors on this quiz to diagnose next steps:

• If the learner compares only total prices, review unit-price reasoning.
• If the learner calculates the rate backwards, review what the unit should be: "cost per item" versus "items per dollar."
• If the learner ignores pack sizes or coupons, review how context can change the best option.
• If the learner gets correct arithmetic but wrong conclusions, require sentence answers that name both the rate and the better choice.

Record links

• Broader end-of-unit assessment: [rea.m08.number.ratios-rates-proportions.proportional-modeling.unit-mastery-quiz]
• Focused unit-rate reinforcement: [rea.m08.number.ratios-rates-proportions.unit-rates.find-unit-rates.unit-mastery-quiz]