Grade 8 Unit Rates and Rate Interpretation: Unit Mastery Quiz with Full Solutions

Purpose and placement

This is a Grade 8 unit mastery quiz for Unit Rates and Rate Interpretation. Use it after the main unit record [rea.m08.number.ratios-rates-proportions] for concept development, vocabulary, and guided learning. This record is an assessment, not the primary lesson.

Coverage

The quiz samples whether a learner can:

• compute a unit rate from whole-number, decimal, and fractional data
• interpret the meaning of a unit rate in words
• compare two rates fairly by converting both to unit rates
• use unit rates to make decisions in real contexts such as shopping, travel, earnings, and recipes
• detect and correct a common rate-comparison error

Quiz directions

• Show all work.
• Write units in every answer.
• When a question asks for an interpretation, answer in a full sentence.
• Round only if the question tells you to round.

Recommended marking

Suggested total: 25 marks.

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Questions

1. Unit price from a simple ratio (2 marks)

A pack of 6 granola bars costs $4.50.

1. Find the cost per granola bar.
2. Interpret your answer in a sentence.

2. Unit speed from a measurement context (2 marks)

A cyclist travels 42 km in 3 hours.

1. Find the cyclist's speed in kilometres per hour.
2. Explain what that unit rate means.

3. Unit rate from decimal quantities (2 marks)

A 1.5 kg bag of rice costs $5.40.

1. Find the cost per kilogram.
2. State whether this is a rate or a ratio, and why.

4. Best buy comparison (3 marks)

Two juice boxes are on sale:

• Brand A: 2.0 L for $3.80
• Brand B: 2.5 L for $4.50

Which brand is the better buy? Justify using unit rates.

5. Earnings rate (2 marks)

Maya earns $52.50 for 3.5 hours of babysitting.

1. Find her pay rate in dollars per hour.
2. If she works 6 hours at the same rate, how much will she earn?

6. Table interpretation (3 marks)

A water fountain fills bottles at a constant rate.

Time (s)	Water (mL)
4	300
8	600
12	900

1. Find the unit rate in mL per second.
2. Predict how much water fills in 15 seconds.
3. Explain how the table shows the relationship is proportional.

7. Recipe scaling with unit rate reasoning (3 marks)

A recipe uses 5 cups of flour for 8 dozen cookies.

1. Find the amount of flour per dozen cookies.
2. How many cups of flour are needed for 20 dozen cookies?
3. Interpret the unit rate in context.

8. Distance per litre (3 marks)

A car travels 468 km using 36 L of gasoline.

1. Find the unit rate in kilometres per litre.
2. At the same rate, how far can the car travel on 50 L?
3. Write one sentence comparing the meanings of "468 km in 36 L" and your unit rate.

9. Error analysis (2 marks)

Noah says: "A 750 g cereal box for $4.20 is a better buy than a 1 kg cereal box for $5.40 because 4.20 is less than 5.40."

Explain Noah's mistake and determine the better buy using unit rates.

10. Mixed-format mastery problem (3 marks)

A runner completes 2.4 km in 12 minutes.

1. Find the unit rate in km per minute.
2. Convert this to km per hour.
3. Explain why both unit rates describe the same runner, even though the numbers are different.

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Full marking solutions

1. Solution (2 marks)

1. Cost per bar:
   • $4.50 / 6 = $0.75
   • Unit rate = $0.75 per granola bar. (1 mark)
2. Interpretation:
   • Each granola bar costs 75 cents. (1 mark)

2. Solution (2 marks)

1. Speed:
   • 42 km / 3 h = 14 km/h
   • Unit rate = 14 km/h. (1 mark)
2. Interpretation:
   • The cyclist travels 14 kilometres in 1 hour at this rate. (1 mark)

3. Solution (2 marks)

1. Cost per kilogram:
   • $5.40 / 1.5 = $3.60
   • Unit rate = $3.60/kg. (1 mark)
2. Classification:
   • It is a rate because it compares two different kinds of quantities: dollars and kilograms. (1 mark)

4. Solution (3 marks)

Find each unit price.

• Brand A:
  • $3.80 / 2.0 = $1.90 per litre
• Brand B:
  • $4.50 / 2.5 = $1.80 per litre

Since $1.80/L < $1.90/L, Brand B is the better buy. (2 marks)

Justification sentence:

• Brand B costs less for each litre, so it gives more juice for each dollar spent. (1 mark)

5. Solution (2 marks)

1. Hourly pay:
   • $52.50 / 3.5 = $15.00
   • Pay rate = $15 per hour. (1 mark)
2. Earnings for 6 hours:
   • 6 x $15 = $90
   • She will earn $90. (1 mark)

6. Solution (3 marks)

1. Unit rate:
   • 300 mL / 4 s = 75 mL/s
   • Check with other rows: 600 / 8 = 75 and 900 / 12 = 75
   • Unit rate = 75 mL/s. (1 mark)
2. Water in 15 s:
   • 15 x 75 = 1125
   • 1125 mL. (1 mark)
3. Why proportional:
   • The ratio of water to time stays constant at 75 mL for each second, so the table shows a constant rate. (1 mark)

7. Solution (3 marks)

1. Flour per dozen:
   • 5 cups / 8 dozen = 0.625 cups per dozen
   • Unit rate = 0.625 cups per dozen cookies. (1 mark)
2. Flour for 20 dozen:
   • 20 x 0.625 = 12.5
   • 12.5 cups of flour. (1 mark)
3. Interpretation:
   • For every 1 dozen cookies, the recipe needs 0.625 cup of flour. (1 mark)

8. Solution (3 marks)

1. Kilometres per litre:
   • 468 / 36 = 13
   • Unit rate = 13 km/L. (1 mark)
2. Distance on 50 L:
   • 50 x 13 = 650
   • 650 km. (1 mark)
3. Comparison sentence:
   • "468 km in 36 L" describes the trip as a whole, while "13 km/L" tells the distance for 1 litre and makes comparison easier. (1 mark)

9. Solution (2 marks)

Noah compared the total prices only, but the package sizes are different. To compare fairly, he must compare the price per same amount, such as per kilogram. (1 mark)

Unit prices:

• 750 g = 0.75 kg
• First box: $4.20 / 0.75 = $5.60/kg
• Second box: $5.40 / 1 = $5.40/kg

Since $5.40/kg < $5.60/kg, the 1 kg box is the better buy. (1 mark)

10. Solution (3 marks)

1. km per minute:
   • 2.4 / 12 = 0.2
   • Unit rate = 0.2 km/min. (1 mark)
2. km per hour:
   • 0.2 km/min x 60 min/h = 12 km/h
   • Unit rate = 12 km/h. (1 mark)
3. Explanation:
   • Both rates describe the same speed, but they use different time units. The number changes because 1 hour is much longer than 1 minute. (1 mark)

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Answer key summary

1. $0.75 per bar
2. 14 km/h
3. $3.60/kg
4. Brand B at $1.80/L
5. $15/h; $90
6. 75 mL/s; 1125 mL
7. 0.625 cups/dozen; 12.5 cups
8. 13 km/L; 650 km
9. 1 kg box is better
10. 0.2 km/min; 12 km/h

Mastery threshold recommendation

Recommend 20/25 or higher (80%) for unit mastery, with these conditions:

• the learner must correctly solve at least 7 of 10 questions, and
• the learner must show success on both of the comparison/decision items (Questions 4 and 9), because fair comparison is a core application of unit-rate thinking.

Interpretation of results

• 22-25 marks: strong mastery; ready to apply unit rates in unfamiliar contexts
• 20-21 marks: secure mastery; continue with proportional reasoning and more complex applications
• 16-19 marks: developing; review interpretation sentences, unit labels, and best-buy comparisons
• 15 marks or below: not yet secure; revisit the main unit materials before advancing

Common error patterns to look for while marking

• dividing in the wrong order and writing units backwards
• giving a numerical answer without interpreting what it means in context
• comparing total prices instead of unit prices
• dropping units such as km/h, $/kg, or mL/s
• assuming a larger package is always the better buy

Links to related records

• Use [rea.m08.number.ratios-rates-proportions] for the parent unit sequence and concept instruction.
• For another example of a full mastery-check format, compare the structure of [rea.m08.algebra.solving-linear-equations.linear-modeling.unit-mastery-quiz].