Comparing Rates with Unit Rates: Grade 8 Unit Mastery Quiz with Full Solutions

Position in the unit

This quiz is for the Grade 8 topic Comparing Rates with Unit Rates. It should be used after students have already studied the broader records on unit rates, ratio comparison, and equivalent ratios. For prior teaching, review, or wider unit coverage, use the linked records rather than treating this quiz as the first exposure to the topic.

What this quiz assesses

Students should be able to:

• convert rates to comparable unit rates;
• compare rates with different totals fairly;
• state which option is greater or more efficient and explain why;
• track units correctly (for example, dollars per item, kilometres per hour, words per minute);
• interpret whether a larger or smaller unit rate is better in context.

Recommended use

• Grade level: Grade 8
• Timing: 20-30 minutes
• Materials: calculator optional unless a teacher wants mental or written computation only
• Scoring: 10 questions, 20 marks total

Mastery threshold

Recommended mastery threshold: 16/20 (80%), with at least:

• 1 correct response from Questions 1-3;
• 2 correct responses from Questions 4-7;
• 2 correct responses from Questions 8-10.

This prevents a student from reaching mastery through routine computation alone while still missing contextual comparison and interpretation.

Quiz questions

Question 1 (2 marks)

A 12-pack of juice boxes costs $9.00. A 20-pack costs $14.00. Which is the better buy?

Question 2 (2 marks)

Lina bikes 18 km in 1.5 hours. Omar bikes 24 km in 2 hours. Who is biking faster?

Question 3 (2 marks)

Store A sells 5 notebooks for $8.25. Store B sells 8 notebooks for $12.80. Which store has the lower price per notebook?

Question 4 (2 marks)

A recipe uses 3 cups of flour for 24 cookies. Another recipe uses 5 cups of flour for 35 cookies. Which recipe uses less flour per cookie?

Question 5 (2 marks)

A printer prints 45 pages in 3 minutes. Another printer prints 68 pages in 4 minutes. Which printer is faster?

Question 6 (2 marks)

A car travels 156 km on 12 L of gas. Another car travels 210 km on 15 L of gas. Which car is more fuel-efficient if efficiency is measured in km/L?

Question 7 (2 marks)

Team Red scores 42 points in 6 games. Team Blue scores 55 points in 8 games. Which team has the higher average points per game?

Question 8 (2 marks)

A 750 g box of cereal costs $5.25. A 1.2 kg box costs $8.04. Which cereal is cheaper per 100 g?

Question 9 (2 marks)

Mia earns $36 for 4.5 hours of work. Jay earns $52 for 6 hours of work. Who earns the higher hourly wage?

Question 10 (2 marks)

Internet Plan A gives 15 GB for $30. Plan B gives 24 GB for $44. Which plan gives more data per dollar? Explain your choice using unit rates.

Full marking key and worked solutions

Question 1 solution

12-pack: $9.00 / 12 = $0.75 per juice box.

20-pack: $14.00 / 20 = $0.70 per juice box.

Since $0.70 < $0.75, the 20-pack is the better buy.

Marking:

• 1 mark for finding at least one correct unit rate
• 1 mark for correct comparison and conclusion

Question 2 solution

Lina: 18 / 1.5 = 12 km/h.

Omar: 24 / 2 = 12 km/h.

They have the same speed: 12 km/h.

Marking:

• 1 mark for correct unit-rate calculation
• 1 mark for correct comparison

Question 3 solution

Store A: $8.25 / 5 = $1.65 per notebook.

Store B: $12.80 / 8 = $1.60 per notebook.

Since $1.60 < $1.65, Store B has the lower price per notebook.

Marking:

• 1 mark for correct unit rates
• 1 mark for correct conclusion

Question 4 solution

Recipe 1: 3 / 24 = 0.125 cups per cookie.

Recipe 2: 5 / 35 = 1 / 7 about 0.143 cups per cookie.

Since 0.125 < 0.143, the first recipe uses less flour per cookie.

Marking:

• 1 mark for correct unit-rate setup
• 1 mark for correct interpretation

Question 5 solution

Printer 1: 45 / 3 = 15 pages per minute.

Printer 2: 68 / 4 = 17 pages per minute.

Since 17 > 15, the second printer is faster.

Marking:

• 1 mark for correct unit rates
• 1 mark for correct comparison

Question 6 solution

Car 1: 156 / 12 = 13 km/L.

Car 2: 210 / 15 = 14 km/L.

Since 14 > 13, the second car is more fuel-efficient.

Marking:

• 1 mark for correct unit rates in km/L
• 1 mark for correct conclusion

Question 7 solution

Team Red: 42 / 6 = 7 points per game.

Team Blue: 55 / 8 = 6.875 points per game.

Since 7 > 6.875, Team Red has the higher average points per game.

Marking:

• 1 mark for correct average rate calculation
• 1 mark for correct comparison

Question 8 solution

Convert to price per 100 g.

First box: 750 g costs $5.25. Price per 100 g = 5.25 / 7.5 = $0.70.

Second box: 1.2 kg = 1200 g. Price per 100 g = 8.04 / 12 = $0.67.

Since $0.67 < $0.70, the 1.2 kg box is cheaper per 100 g.

Marking:

• 1 mark for handling units correctly, including 1.2 kg = 1200 g
• 1 mark for correct unit-rate comparison

Question 9 solution

Mia: 36 / 4.5 = 8 dollars per hour.

Jay: 52 / 6 about 8.67 dollars per hour.

Since 8.67 > 8, Jay earns the higher hourly wage.

Marking:

• 1 mark for correct hourly rates
• 1 mark for correct comparison

Question 10 solution

Compare data per dollar.

Plan A: 15 / 30 = 0.5 GB per dollar.

Plan B: 24 / 44 = 6 / 11 about 0.545 GB per dollar.

Since 0.545 > 0.5, Plan B gives more data per dollar.

A complete explanation should say that both plans were converted to the same unit, GB per $1, so the comparison is fair.

Marking:

• 1 mark for correct unit-rate calculation
• 1 mark for conclusion with explanation of fair comparison

Total score guide

• 18-20: Strong mastery. The student compares rates accurately and interprets unit rates reliably in context.
• 16-17: Meets mastery. The student is generally secure, with only minor computational or interpretation slips.
• 12-15: Developing. The student can often compute unit rates but may misread units or misinterpret which rate is better.
• 0-11: Not yet secure. The student needs reteaching on building comparable unit rates and interpreting them in context.

Common misconceptions to check when marking

• Comparing raw totals instead of unit rates: for example, choosing the larger package just because it has more items.
• Using the wrong unit direction: for example, dollars per notebook versus notebooks per dollar, then comparing inconsistently.
• Assuming bigger is always better: in price questions, a smaller cost per unit is better.
• Ignoring unit conversion: especially grams versus kilograms, or minutes versus hours.
• Rounding too early: early rounding can change a close comparison.

Repair moves after the quiz

If a student struggles, have them use this routine every time:

1. Write the two rates with units.
2. Decide on one common unit rate for both options.
3. Divide to find each unit rate.
4. Compare the numbers.
5. Ask: in this context, is a larger unit rate better, or is a smaller one better?

Linkage within Rea

Use this record as a focused assessment of comparing rates with unit rates. For broader unit-rate assessment, use the general unit-rate mastery quiz. For earlier comparison structures and proportional reasoning support, use the linked ratio-comparison and equivalent-ratio quiz records.