Grade 8 Unit Mastery Quiz: Part-to-Part and Part-to-Whole Relationships

Use and links

This quiz is the dedicated end-of-unit assessment for Part-to-Part and Part-to-Whole Relationships in Grade 8. Use it after studying the linked overview and worked examples and after completing the linked practice set.

Linked support records:

• Overview: rea.m08.number.ratios-rates-proportions.ratio-concepts.part-whole.overview
• Worked examples: rea.m08.number.ratios-rates-proportions.ratio-concepts.part-whole.worked-examples
• Practice set: rea.m08.number.ratios-rates-proportions.ratio-concepts.part-whole.practice-set
• Broader end-of-unit quiz: rea.m08.number.ratios-rates-proportions.ratio-concepts.unit-mastery-quiz

Quiz structure

• 10 questions
• 20 marks total
• Recommended time: 25-35 minutes
• No calculator required, though one does not change the mathematics here

Mastery target

• Recommended mastery threshold: 16/20 (80%)
• In addition, a learner should earn at least 6/8 marks on Questions 5-8, because those questions directly test the core distinction between part-to-part and part-to-whole ratios in words and context.

Questions

Question 1 (1 mark)

A basket contains 6 red apples and 10 green apples.

Write the ratio of red apples to green apples in simplest form.

Question 2 (1 mark)

A class has 9 students wearing glasses and 21 students not wearing glasses.

Write the ratio of students wearing glasses to the whole class in simplest form.

Question 3 (2 marks)

There are 8 cats and 12 dogs in a shelter section.

1. Write the part-to-part ratio cats : dogs in simplest form.
2. Write the part-to-whole ratio cats : total animals in simplest form.

Question 4 (2 marks)

A jar contains 15 blue beads, 5 yellow beads, and 10 white beads.

1. Write the ratio yellow : white in simplest form.
2. Write the ratio blue : total beads in simplest form.

Question 5 (2 marks)

A school club has 14 boys and 18 girls.

A student says, "The ratio of boys to girls is 14 : 32."

1. Explain what is wrong.
2. Give the correct ratio of boys to girls.

Question 6 (2 marks)

In a tray of muffins, the ratio of chocolate muffins to all muffins is 3 : 8. There are 24 muffins in total.

How many chocolate muffins are there? Show your reasoning.

Question 7 (3 marks)

A team has 12 defenders and 8 attackers.

1. Write the ratio defenders : attackers.
2. Write the ratio attackers : whole team.
3. Explain in one sentence why your two ratios are different.

Question 8 (3 marks)

At a fundraiser, the ratio of juice boxes to sandwiches is 5 : 7. There are 35 sandwiches.

1. How many juice boxes are there?
2. How many items are there altogether?
3. Write the ratio juice boxes : total items.

Question 9 (2 marks)

A bag contains red, black, and white marbles. The ratio red : black is 4 : 3. There are 12 black marbles.

1. How many red marbles are there?
2. If there are also 5 white marbles, write the ratio red : total marbles.

Question 10 (2 marks)

Create your own example of a set with two categories where:

• the part-to-part ratio is 2 : 5, and
• the part-to-whole ratio for the first category is 2 : 7.

State the quantities clearly and verify both ratios.

Full marking key and solutions

Question 1 solution (1 mark)

Red : green = 6 : 10

Simplify by dividing both terms by 2: 6 : 10 = 3 : 5

Answer: 3 : 5

Marking:

• 1 mark for 3 : 5

Question 2 solution (1 mark)

Whole class = 9 + 21 = 30

Wearing glasses : whole = 9 : 30

Simplify by dividing by 3: 9 : 30 = 3 : 10

Answer: 3 : 10

Marking:

• 1 mark for 3 : 10

Question 3 solution (2 marks)

Cats = 8, dogs = 12, total = 20

1. Cats : dogs = 8 : 12 = 2 : 3
2. Cats : total = 8 : 20 = 2 : 5

Answers:

• Cats : dogs = 2 : 3
• Cats : total = 2 : 5

Marking:

• 1 mark for 2 : 3
• 1 mark for 2 : 5

Question 4 solution (2 marks)

Blue = 15, yellow = 5, white = 10, total = 30

1. Yellow : white = 5 : 10 = 1 : 2
2. Blue : total = 15 : 30 = 1 : 2

These happen to simplify to the same numbers, but they compare different quantities.

Answers:

• Yellow : white = 1 : 2
• Blue : total = 1 : 2

Marking:

• 1 mark for 1 : 2 for yellow : white
• 1 mark for 1 : 2 for blue : total

Question 5 solution (2 marks)

Boys = 14, girls = 18, whole = 32

The student wrote 14 : 32. That compares boys to the whole club, not boys to girls.

Correct boys : girls ratio = 14 : 18 = 7 : 9

Answer:

1. 14 : 32 is wrong because 32 is the whole group, not the number of girls.
2. The correct ratio is 7 : 9.

Marking:

• 1 mark for explaining that 32 is the whole, so the student used part-to-whole instead of part-to-part
• 1 mark for 7 : 9

Question 6 solution (2 marks)

Chocolate : total = 3 : 8

Total muffins = 24

If 8 equal parts make 24 muffins, then 1 part = 24 / 8 = 3 muffins.

Chocolate muffins = 3 parts = 3 x 3 = 9 muffins.

Answer: 9 chocolate muffins

Marking:

• 1 mark for finding 1 part = 3
• 1 mark for finding 9 chocolate muffins

Question 7 solution (3 marks)

Defenders = 12, attackers = 8, whole team = 20

1. Defenders : attackers = 12 : 8 = 3 : 2
2. Attackers : whole = 8 : 20 = 2 : 5
3. The first ratio compares one part to another part, while the second compares one part to the total team.

Answers:

• Defenders : attackers = 3 : 2
• Attackers : whole = 2 : 5
• Explanation: One ratio compares two parts, and the other compares a part to the whole.

Marking:

• 1 mark for 3 : 2
• 1 mark for 2 : 5
• 1 mark for a correct explanation of why the quantities being compared are different

Question 8 solution (3 marks)

Juice boxes : sandwiches = 5 : 7

There are 35 sandwiches, so 7 parts = 35.

1 part = 35 / 7 = 5

1. Juice boxes = 5 parts = 5 x 5 = 25
2. Total items = 25 + 35 = 60
3. Juice boxes : total = 25 : 60 = 5 : 12

Answers:

• Juice boxes = 25
• Total items = 60
• Juice boxes : total = 5 : 12

Marking:

• 1 mark for 25
• 1 mark for 60
• 1 mark for 5 : 12

Question 9 solution (2 marks)

Red : black = 4 : 3

There are 12 black marbles, so 3 parts = 12.

1 part = 12 / 3 = 4

1. Red marbles = 4 parts = 4 x 4 = 16
2. Total marbles = 16 + 12 + 5 = 33

Red : total = 16 : 33

This ratio is already in simplest form because 16 and 33 have no common factor greater than 1.

Answers:

• Red marbles = 16
• Red : total = 16 : 33

Marking:

• 1 mark for 16
• 1 mark for 16 : 33

Question 10 solution (2 marks)

One valid example:

• First category = 2 students
• Second category = 5 students

Then part-to-part ratio = 2 : 5.

Whole = 2 + 5 = 7, so first category : whole = 2 : 7.

Sample answer: In a small group, 2 students play chess and 5 students play badminton. Then chess : badminton = 2 : 5, and chess : total students = 2 : 7.

Any equivalent example earns full marks.

Marking:

• 1 mark for giving quantities that match part-to-part 2 : 5
• 1 mark for correctly verifying the part-to-whole ratio 2 : 7

Total marks

• Q1: 1
• Q2: 1
• Q3: 2
• Q4: 2
• Q5: 2
• Q6: 2
• Q7: 3
• Q8: 3
• Q9: 2
• Q10: 2
• Total: 20 marks

Interpreting results

• 18-20 marks: Strong mastery. The learner can reliably distinguish part-to-part from part-to-whole and use either form in context.
• 16-17 marks: Secure mastery. Minor slips may remain, but the core idea is in place.
• 12-15 marks: Developing. Revisit language cues such as "to," "out of," and "altogether," then return to the worked examples and targeted practice.
• 0-11 marks: Not yet secure. Study the overview and worked examples again before attempting new assessment.

Error diagnosis and repair

• If a learner writes part : whole when asked for part : part, the repair is to name each quantity in words before writing numbers.
• If a learner forgets to add all categories for the whole, the repair is to make a short table of all parts first.
• If a learner gives an unsimplified ratio, the repair is to divide both terms by their greatest common factor and then re-read what the simplified ratio still means.
• If a learner solves scale questions incorrectly, the repair is to find the value of 1 ratio part first, then scale up.