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

Position in the unit

This quiz is a focused mastery check for Finding Unit Rates in Grade 8 Ratios, Rates and Proportions. It assesses whether a learner can compute a rate "per 1" accurately, express the result with correct units, and use unit rates to compare options.

For broader assessment across the whole subunit, including interpretation and decision-making beyond computation, use [rea.m08.number.ratios-rates-proportions.unit-rates.unit-mastery-quiz]. For parallel structure in related proportional reasoning topics, see [rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz] and [rea.m08.number.ratios-rates-proportions.proportional-modeling.unit-mastery-quiz].

Quiz overview

• Level: Grade 8
• Focus: Finding unit rates
• Questions: 10
• Suggested time: 25-35 minutes
• Total marks: 20
• Calculator: Optional unless a teacher specifies otherwise

Success criteria

A student is successful if they can:

• divide correctly to rewrite a rate as "per 1"
• keep track of the unit attached to the answer
• find unit rates from whole numbers, decimals, fractions, tables, and graphs of data presented numerically
• compare two situations fairly using unit rates
• explain what the unit rate means in context

Common error patterns this quiz is designed to detect

• dividing in the wrong direction
• giving a number without units
• simplifying a ratio but not expressing it as a rate per 1 unit
• confusing "dollars per item" with "items per dollar"
• rounding too early and changing the comparison result

Questions

1. Basic whole-number rate

Six notebooks cost $9. What is the cost of 1 notebook?

Marks: 2

2. Unit rate with distance and time

A cyclist travels 45 km in 3 hours. Find the cyclist's speed in kilometres per hour.

Marks: 2

3. Decimal rate

3.5 kg of apples cost $8.75. Find the cost per kilogram.

Marks: 2

4. Fractional quantity

A recipe uses 3/4 cup of yogurt for 6 muffins. How much yogurt is used per muffin?

Marks: 2

5. Table to unit rate

Complete the reasoning and state the unit rate.

Minutes	Pages read
5	12
10	24
15	36

How many pages are read per minute?

Marks: 2

6. Compare two prices fairly

Store A sells 8 granola bars for $6.40. Store B sells 5 granola bars for $3.75. Which store has the better price? Show unit rates.

Marks: 2

7. Which rate is requested?

A car uses 18 L of gas to travel 240 km.

1. Find litres per kilometre.
2. Find kilometres per litre.

Marks: 2

8. Multi-step context

A machine fills 84 bottles in 7 minutes. At the same rate, how many bottles does it fill in 1 minute? How many in 12 minutes?

Marks: 2

9. Non-integer unit rate comparison

Runner A runs 2.4 km in 12 minutes. Runner B runs 3.25 km in 15 minutes. Who runs faster? Compare using kilometres per minute.

Marks: 2

10. Written interpretation

A student finds that 15 oranges cost $10.50, so the unit rate is $0.70 per orange. Explain what $0.70 per orange means in a full sentence, and name one mistake someone might make when finding this unit rate.

Marks: 2

Full solutions and marking key

1. Basic whole-number rate

6 notebooks cost $9.

Unit rate means cost for 1 notebook.

$9 ÷ 6 = $1.50

Answer: $1.50 per notebook

Marking:

• 1 mark for dividing correctly
• 1 mark for correct unit statement

2. Unit rate with distance and time

45 km in 3 hours means:

45 ÷ 3 = 15

Answer: 15 km/h

This means the cyclist travels 15 kilometres in 1 hour.

Marking:

• 1 mark for correct computation
• 1 mark for correct rate and units

3. Decimal rate

3.5 kg cost $8.75.

Cost per kilogram:

8.75 ÷ 3.5 = 2.5

Answer: $2.50 per kg

Marking:

• 1 mark for correct division
• 1 mark for correctly expressed money/unit form

4. Fractional quantity

3/4 cup for 6 muffins means yogurt per muffin is:

(3/4) ÷ 6 = 3/24 = 1/8

Answer: 1/8 cup per muffin

Marking:

• 1 mark for setting up and dividing correctly
• 1 mark for simplified answer with units

5. Table to unit rate

From the table, 12 pages are read in 5 minutes.

Pages per minute:

12 ÷ 5 = 2.4

Check with another row: 24 ÷ 10 = 2.4

So the rate is consistent.

Answer: 2.4 pages per minute

Marking:

• 1 mark for correct unit-rate calculation
• 1 mark for correct statement with units

6. Compare two prices fairly

Store A:

$6.40 ÷ 8 = $0.80 per bar

Store B:

$3.75 ÷ 5 = $0.75 per bar

Since $0.75 < $0.80, Store B is cheaper.

Answer: Store B has the better price.

Marking:

• 1 mark for one correct unit rate
• 1 mark for second unit rate and correct comparison decision

7. Which rate is requested?

18 L for 240 km.

1. Litres per kilometre:

18 ÷ 240 = 0.075

So the car uses 0.075 L/km.

2. Kilometres per litre:

240 ÷ 18 = 13.333...

So the car travels about 13.3 km/L.

Answer: 0.075 L/km and approximately 13.3 km/L

Marking:

• 1 mark for litres per kilometre
• 1 mark for kilometres per litre

8. Multi-step context

84 bottles in 7 minutes.

Bottles per minute:

84 ÷ 7 = 12

So in 1 minute, the machine fills 12 bottles.

In 12 minutes:

12 × 12 = 144

Answer: 12 bottles per minute and 144 bottles in 12 minutes

Marking:

• 1 mark for finding the unit rate
• 1 mark for extending the rate correctly to 12 minutes

9. Non-integer unit rate comparison

Runner A:

2.4 ÷ 12 = 0.2 km/min

Runner B:

3.25 ÷ 15 ≈ 0.2167 km/min

Since 0.2167 > 0.2, Runner B is faster.

Answer: Runner B is faster.

Marking:

• 1 mark for correct unit-rate calculations
• 1 mark for valid comparison and conclusion

10. Written interpretation

$0.70 per orange means each single orange costs 70 cents.

One possible mistake is dividing the wrong way, such as 15 ÷ 10.50, which gives oranges per dollar instead of dollars per orange.

Sample answer: The unit rate $0.70 per orange means one orange costs 70 cents. A common mistake is to divide 15 by 10.50, which gives oranges per dollar instead of the cost of one orange.

Marking:

• 1 mark for correct contextual interpretation
• 1 mark for naming a valid mistake

Score interpretation

• 18-20 marks: Mastery. The learner consistently finds and interprets unit rates accurately across representations.
• 15-17 marks: Near mastery. The learner is mostly secure but should review errors in units, direction of division, or comparison language.
• 11-14 marks: Developing. The learner can find some unit rates but is not yet reliable across contexts.
• 0-10 marks: Not yet secure. The learner needs reteaching on what "per 1" means and how to divide with the correct units.

Recommended mastery threshold

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

• correct solutions on both comparison questions (Questions 6 and 9), and
• no more than one units error across the quiz.

This threshold is appropriate because the skill is procedural but also depends on interpretation: a learner who can compute answers without tracking the meaning of the units is not yet fully secure.

Brief remediation guidance

If a learner falls below mastery:

• reteach unit-rate language using "for 1" and "per 1"
• practice deciding which quantity should be divided by which before calculating
• require every answer to include units in words or symbols
• revisit comparison tasks where both options must be rewritten to the same per-1 basis

Relationship to other records

This record is a focused assessment on one skill inside the larger unit-rates topic. It should be paired with the broader [rea.m08.number.ratios-rates-proportions.unit-rates.unit-mastery-quiz] for full end-of-unit evidence, rather than used as the only assessment for the entire subunit.