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. 5 identical boxes and a 1 kg weight balance 56 kg altogether. What is the mass of 1 box?
5 · 1 kg · 56 kg · 1 · Balance scale puzzles
2. 5 identical boxes and a 6 kg weight balance 71 kg altogether. What is the mass of 1 box?
5 · 6 kg · 71 kg · 1 · Balance scale puzzles
3. 6 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
6 · 10 kg · 70 kg · 1 · Balance scale puzzles
4. 5 identical boxes and a 10 kg weight balance 60 kg altogether. What is the mass of 1 box?
5 · 10 kg · 60 kg · 1 · Balance scale puzzles
5. 4 identical boxes and a 4 kg weight balance 64 kg altogether. What is the mass of 1 box?
4 · 4 kg · 64 kg · 1 · Balance scale puzzles
6. 5 identical boxes and a 3 kg weight balance 43 kg altogether. What is the mass of 1 box?
5 · 3 kg · 43 kg · 1 · Balance scale puzzles
7. 3 identical boxes and a 11 kg weight balance 29 kg altogether. What is the mass of 1 box?
3 · 11 kg · 29 kg · 1 · Balance scale puzzles
8. 2 identical boxes and a 4 kg weight balance 30 kg altogether. What is the mass of 1 box?
2 · 4 kg · 30 kg · 1 · Balance scale puzzles
9. 2 identical boxes and a 3 kg weight balance 33 kg altogether. What is the mass of 1 box?
2 · 3 kg · 33 kg · 1 · Balance scale puzzles
10. 6 identical boxes and a 12 kg weight balance 66 kg altogether. What is the mass of 1 box?
6 · 12 kg · 66 kg · 1 · Balance scale puzzles
11. 5 identical boxes and a 12 kg weight balance 77 kg altogether. What is the mass of 1 box?
5 · 12 kg · 77 kg · 1 · Balance scale puzzles
12. 2 identical boxes and a 1 kg weight balance 27 kg altogether. What is the mass of 1 box?
2 · 1 kg · 27 kg · 1 · Balance scale puzzles

12 questions · Seed 44 · 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. 5 identical boxes and a 1 kg weight balance 56 kg altogether. What is the mass of 1 box?
11 kg
Subtract 1 kg from 56 kg to get 55 kg for 5 boxes. Divide by 5: 11 kg per box.
2. 5 identical boxes and a 6 kg weight balance 71 kg altogether. What is the mass of 1 box?
13 kg
Subtract 6 kg from 71 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.
3. 6 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
10 kg
Subtract 10 kg from 70 kg to get 60 kg for 6 boxes. Divide by 6: 10 kg per box.
4. 5 identical boxes and a 10 kg weight balance 60 kg altogether. What is the mass of 1 box?
10 kg
Subtract 10 kg from 60 kg to get 50 kg for 5 boxes. Divide by 5: 10 kg per box.
5. 4 identical boxes and a 4 kg weight balance 64 kg altogether. What is the mass of 1 box?
15 kg
Subtract 4 kg from 64 kg to get 60 kg for 4 boxes. Divide by 4: 15 kg per box.
6. 5 identical boxes and a 3 kg weight balance 43 kg altogether. What is the mass of 1 box?
8 kg
Subtract 3 kg from 43 kg to get 40 kg for 5 boxes. Divide by 5: 8 kg per box.
7. 3 identical boxes and a 11 kg weight balance 29 kg altogether. What is the mass of 1 box?
6 kg
Subtract 11 kg from 29 kg to get 18 kg for 3 boxes. Divide by 3: 6 kg per box.
8. 2 identical boxes and a 4 kg weight balance 30 kg altogether. What is the mass of 1 box?
13 kg
Subtract 4 kg from 30 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.
9. 2 identical boxes and a 3 kg weight balance 33 kg altogether. What is the mass of 1 box?
15 kg
Subtract 3 kg from 33 kg to get 30 kg for 2 boxes. Divide by 2: 15 kg per box.
10. 6 identical boxes and a 12 kg weight balance 66 kg altogether. What is the mass of 1 box?
9 kg
Subtract 12 kg from 66 kg to get 54 kg for 6 boxes. Divide by 6: 9 kg per box.
11. 5 identical boxes and a 12 kg weight balance 77 kg altogether. What is the mass of 1 box?
13 kg
Subtract 12 kg from 77 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.
12. 2 identical boxes and a 1 kg weight balance 27 kg altogether. What is the mass of 1 box?
13 kg
Subtract 1 kg from 27 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 5 identical boxes and a 1 kg weight balance 56 kg altogether. What is the mass of 1 box?
5 · 1 kg · 56 kg · 1 · Balance scale puzzles
2. 5 identical boxes and a 6 kg weight balance 71 kg altogether. What is the mass of 1 box?
5 · 6 kg · 71 kg · 1 · Balance scale puzzles
3. 6 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
6 · 10 kg · 70 kg · 1 · Balance scale puzzles
4. 5 identical boxes and a 10 kg weight balance 60 kg altogether. What is the mass of 1 box?
5 · 10 kg · 60 kg · 1 · Balance scale puzzles
5. 4 identical boxes and a 4 kg weight balance 64 kg altogether. What is the mass of 1 box?
4 · 4 kg · 64 kg · 1 · Balance scale puzzles
6. 5 identical boxes and a 3 kg weight balance 43 kg altogether. What is the mass of 1 box?
5 · 3 kg · 43 kg · 1 · Balance scale puzzles
7. 3 identical boxes and a 11 kg weight balance 29 kg altogether. What is the mass of 1 box?
3 · 11 kg · 29 kg · 1 · Balance scale puzzles
8. 2 identical boxes and a 4 kg weight balance 30 kg altogether. What is the mass of 1 box?
2 · 4 kg · 30 kg · 1 · Balance scale puzzles
9. 2 identical boxes and a 3 kg weight balance 33 kg altogether. What is the mass of 1 box?
2 · 3 kg · 33 kg · 1 · Balance scale puzzles
10. 6 identical boxes and a 12 kg weight balance 66 kg altogether. What is the mass of 1 box?
6 · 12 kg · 66 kg · 1 · Balance scale puzzles
11. 5 identical boxes and a 12 kg weight balance 77 kg altogether. What is the mass of 1 box?
5 · 12 kg · 77 kg · 1 · Balance scale puzzles
12. 2 identical boxes and a 1 kg weight balance 27 kg altogether. What is the mass of 1 box?
2 · 1 kg · 27 kg · 1 · Balance scale puzzles

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 5 identical boxes and a 1 kg weight balance 56 kg altogether. What is the mass of 1 box?
11 kg
Subtract 1 kg from 56 kg to get 55 kg for 5 boxes. Divide by 5: 11 kg per box.
2. 5 identical boxes and a 6 kg weight balance 71 kg altogether. What is the mass of 1 box?
13 kg
Subtract 6 kg from 71 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.
3. 6 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
10 kg
Subtract 10 kg from 70 kg to get 60 kg for 6 boxes. Divide by 6: 10 kg per box.
4. 5 identical boxes and a 10 kg weight balance 60 kg altogether. What is the mass of 1 box?
10 kg
Subtract 10 kg from 60 kg to get 50 kg for 5 boxes. Divide by 5: 10 kg per box.
5. 4 identical boxes and a 4 kg weight balance 64 kg altogether. What is the mass of 1 box?
15 kg
Subtract 4 kg from 64 kg to get 60 kg for 4 boxes. Divide by 4: 15 kg per box.
6. 5 identical boxes and a 3 kg weight balance 43 kg altogether. What is the mass of 1 box?
8 kg
Subtract 3 kg from 43 kg to get 40 kg for 5 boxes. Divide by 5: 8 kg per box.
7. 3 identical boxes and a 11 kg weight balance 29 kg altogether. What is the mass of 1 box?
6 kg
Subtract 11 kg from 29 kg to get 18 kg for 3 boxes. Divide by 3: 6 kg per box.
8. 2 identical boxes and a 4 kg weight balance 30 kg altogether. What is the mass of 1 box?
13 kg
Subtract 4 kg from 30 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.
9. 2 identical boxes and a 3 kg weight balance 33 kg altogether. What is the mass of 1 box?
15 kg
Subtract 3 kg from 33 kg to get 30 kg for 2 boxes. Divide by 2: 15 kg per box.
10. 6 identical boxes and a 12 kg weight balance 66 kg altogether. What is the mass of 1 box?
9 kg
Subtract 12 kg from 66 kg to get 54 kg for 6 boxes. Divide by 6: 9 kg per box.
11. 5 identical boxes and a 12 kg weight balance 77 kg altogether. What is the mass of 1 box?
13 kg
Subtract 12 kg from 77 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.
12. 2 identical boxes and a 1 kg weight balance 27 kg altogether. What is the mass of 1 box?
13 kg
Subtract 1 kg from 27 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.

12 questions · Seed 44 · Age guidance, not curriculum certification