ReasoningAges 7-9

Balance scale puzzles

Use equal-weight reasoning to work out the mass of a single mystery box on a balanced scale. Review suitability for your learners before teaching.

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Age band:Ages 7-9 Ages 10-12

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Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 4 identical boxes and a 12 kg weight balance 60 kg altogether. What is the mass of 1 box?
4 · 12 kg · 60 kg · 1 · Balance scale puzzles
2. 4 identical boxes and a 12 kg weight balance 72 kg altogether. What is the mass of 1 box?
4 · 12 kg · 72 kg · 1 · Balance scale puzzles
3. 2 identical boxes and a 12 kg weight balance 28 kg altogether. What is the mass of 1 box?
2 · 12 kg · 28 kg · 1 · Balance scale puzzles
4. 4 identical boxes and a 6 kg weight balance 66 kg altogether. What is the mass of 1 box?
4 · 6 kg · 66 kg · 1 · Balance scale puzzles
5. 5 identical boxes and a 8 kg weight balance 43 kg altogether. What is the mass of 1 box?
5 · 8 kg · 43 kg · 1 · Balance scale puzzles
6. 6 identical boxes and a 3 kg weight balance 81 kg altogether. What is the mass of 1 box?
6 · 3 kg · 81 kg · 1 · Balance scale puzzles
7. 3 identical boxes and a 12 kg weight balance 18 kg altogether. What is the mass of 1 box?
3 · 12 kg · 18 kg · 1 · Balance scale puzzles
8. 3 identical boxes and a 12 kg weight balance 24 kg altogether. What is the mass of 1 box?
3 · 12 kg · 24 kg · 1 · Balance scale puzzles
9. 4 identical boxes and a 8 kg weight balance 16 kg altogether. What is the mass of 1 box?
4 · 8 kg · 16 kg · 1 · Balance scale puzzles
10. 5 identical boxes and a 4 kg weight balance 79 kg altogether. What is the mass of 1 box?
5 · 4 kg · 79 kg · 1 · Balance scale puzzles
11. 3 identical boxes and a 2 kg weight balance 20 kg altogether. What is the mass of 1 box?
3 · 2 kg · 20 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 10 kg weight balance 25 kg altogether. What is the mass of 1 box?
3 · 10 kg · 25 kg · 1 · Balance scale puzzles

12 questions · Seed 42 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 4 identical boxes and a 12 kg weight balance 60 kg altogether. What is the mass of 1 box?
12 kg
Subtract 12 kg from 60 kg to get 48 kg for 4 boxes. Divide by 4: 12 kg per box.
2. 4 identical boxes and a 12 kg weight balance 72 kg altogether. What is the mass of 1 box?
15 kg
Subtract 12 kg from 72 kg to get 60 kg for 4 boxes. Divide by 4: 15 kg per box.
3. 2 identical boxes and a 12 kg weight balance 28 kg altogether. What is the mass of 1 box?
8 kg
Subtract 12 kg from 28 kg to get 16 kg for 2 boxes. Divide by 2: 8 kg per box.
4. 4 identical boxes and a 6 kg weight balance 66 kg altogether. What is the mass of 1 box?
15 kg
Subtract 6 kg from 66 kg to get 60 kg for 4 boxes. Divide by 4: 15 kg per box.
5. 5 identical boxes and a 8 kg weight balance 43 kg altogether. What is the mass of 1 box?
7 kg
Subtract 8 kg from 43 kg to get 35 kg for 5 boxes. Divide by 5: 7 kg per box.
6. 6 identical boxes and a 3 kg weight balance 81 kg altogether. What is the mass of 1 box?
13 kg
Subtract 3 kg from 81 kg to get 78 kg for 6 boxes. Divide by 6: 13 kg per box.
7. 3 identical boxes and a 12 kg weight balance 18 kg altogether. What is the mass of 1 box?
2 kg
Subtract 12 kg from 18 kg to get 6 kg for 3 boxes. Divide by 3: 2 kg per box.
8. 3 identical boxes and a 12 kg weight balance 24 kg altogether. What is the mass of 1 box?
4 kg
Subtract 12 kg from 24 kg to get 12 kg for 3 boxes. Divide by 3: 4 kg per box.
9. 4 identical boxes and a 8 kg weight balance 16 kg altogether. What is the mass of 1 box?
2 kg
Subtract 8 kg from 16 kg to get 8 kg for 4 boxes. Divide by 4: 2 kg per box.
10. 5 identical boxes and a 4 kg weight balance 79 kg altogether. What is the mass of 1 box?
15 kg
Subtract 4 kg from 79 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
11. 3 identical boxes and a 2 kg weight balance 20 kg altogether. What is the mass of 1 box?
6 kg
Subtract 2 kg from 20 kg to get 18 kg for 3 boxes. Divide by 3: 6 kg per box.
12. 3 identical boxes and a 10 kg weight balance 25 kg altogether. What is the mass of 1 box?
5 kg
Subtract 10 kg from 25 kg to get 15 kg for 3 boxes. Divide by 3: 5 kg per box.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 4 identical boxes and a 12 kg weight balance 60 kg altogether. What is the mass of 1 box?
4 · 12 kg · 60 kg · 1 · Balance scale puzzles
2. 4 identical boxes and a 12 kg weight balance 72 kg altogether. What is the mass of 1 box?
4 · 12 kg · 72 kg · 1 · Balance scale puzzles
3. 2 identical boxes and a 12 kg weight balance 28 kg altogether. What is the mass of 1 box?
2 · 12 kg · 28 kg · 1 · Balance scale puzzles
4. 4 identical boxes and a 6 kg weight balance 66 kg altogether. What is the mass of 1 box?
4 · 6 kg · 66 kg · 1 · Balance scale puzzles
5. 5 identical boxes and a 8 kg weight balance 43 kg altogether. What is the mass of 1 box?
5 · 8 kg · 43 kg · 1 · Balance scale puzzles
6. 6 identical boxes and a 3 kg weight balance 81 kg altogether. What is the mass of 1 box?
6 · 3 kg · 81 kg · 1 · Balance scale puzzles
7. 3 identical boxes and a 12 kg weight balance 18 kg altogether. What is the mass of 1 box?
3 · 12 kg · 18 kg · 1 · Balance scale puzzles
8. 3 identical boxes and a 12 kg weight balance 24 kg altogether. What is the mass of 1 box?
3 · 12 kg · 24 kg · 1 · Balance scale puzzles
9. 4 identical boxes and a 8 kg weight balance 16 kg altogether. What is the mass of 1 box?
4 · 8 kg · 16 kg · 1 · Balance scale puzzles
10. 5 identical boxes and a 4 kg weight balance 79 kg altogether. What is the mass of 1 box?
5 · 4 kg · 79 kg · 1 · Balance scale puzzles
11. 3 identical boxes and a 2 kg weight balance 20 kg altogether. What is the mass of 1 box?
3 · 2 kg · 20 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 10 kg weight balance 25 kg altogether. What is the mass of 1 box?
3 · 10 kg · 25 kg · 1 · Balance scale puzzles

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 4 identical boxes and a 12 kg weight balance 60 kg altogether. What is the mass of 1 box?
12 kg
Subtract 12 kg from 60 kg to get 48 kg for 4 boxes. Divide by 4: 12 kg per box.
2. 4 identical boxes and a 12 kg weight balance 72 kg altogether. What is the mass of 1 box?
15 kg
Subtract 12 kg from 72 kg to get 60 kg for 4 boxes. Divide by 4: 15 kg per box.
3. 2 identical boxes and a 12 kg weight balance 28 kg altogether. What is the mass of 1 box?
8 kg
Subtract 12 kg from 28 kg to get 16 kg for 2 boxes. Divide by 2: 8 kg per box.
4. 4 identical boxes and a 6 kg weight balance 66 kg altogether. What is the mass of 1 box?
15 kg
Subtract 6 kg from 66 kg to get 60 kg for 4 boxes. Divide by 4: 15 kg per box.
5. 5 identical boxes and a 8 kg weight balance 43 kg altogether. What is the mass of 1 box?
7 kg
Subtract 8 kg from 43 kg to get 35 kg for 5 boxes. Divide by 5: 7 kg per box.
6. 6 identical boxes and a 3 kg weight balance 81 kg altogether. What is the mass of 1 box?
13 kg
Subtract 3 kg from 81 kg to get 78 kg for 6 boxes. Divide by 6: 13 kg per box.
7. 3 identical boxes and a 12 kg weight balance 18 kg altogether. What is the mass of 1 box?
2 kg
Subtract 12 kg from 18 kg to get 6 kg for 3 boxes. Divide by 3: 2 kg per box.
8. 3 identical boxes and a 12 kg weight balance 24 kg altogether. What is the mass of 1 box?
4 kg
Subtract 12 kg from 24 kg to get 12 kg for 3 boxes. Divide by 3: 4 kg per box.
9. 4 identical boxes and a 8 kg weight balance 16 kg altogether. What is the mass of 1 box?
2 kg
Subtract 8 kg from 16 kg to get 8 kg for 4 boxes. Divide by 4: 2 kg per box.
10. 5 identical boxes and a 4 kg weight balance 79 kg altogether. What is the mass of 1 box?
15 kg
Subtract 4 kg from 79 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
11. 3 identical boxes and a 2 kg weight balance 20 kg altogether. What is the mass of 1 box?
6 kg
Subtract 2 kg from 20 kg to get 18 kg for 3 boxes. Divide by 3: 6 kg per box.
12. 3 identical boxes and a 10 kg weight balance 25 kg altogether. What is the mass of 1 box?
5 kg
Subtract 10 kg from 25 kg to get 15 kg for 3 boxes. Divide by 3: 5 kg per box.

12 questions · Seed 42 · Age guidance, not curriculum certification