Operation: Math -- A Year of Puzzles
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Following are 36 Operation Math puzzles. Each puzzle includes four equations for students to solve. Write on a chalkboard or chart the four equations in the left column below -- the ones with asterisks (*) in place of the math operation signs (+, -, x, or /). Students study the equations and determine which math operations must be performed to arrive at the solution stated for each equation. For example:
(4 * 1) * (6 * 2) = 1
The correct answer is (4 + 1) - (6 - 2) = 1
The equation stated in its simplest terms: 5 - 4 = 1
Adapting "Operation: Math" for Your Grade Level
All the Year of "Operation: Math" Puzzles require students to use the four math operations -- addition, subtraction, multiplication, and division. Because they involve all four operations, they are probably best used with students in grades 4 and above.
Teachers in grades 1 to 3 can easily adapt this activity by using only simple addition and subtraction operations. For example, first and second graders can solve the following simple equations:
| PROBLEMS | SOLUTIONS |
| 6 * 4 = 10 | 6 + 4 = 10 |
| 5 * 2 = 3 | 5 - 2 = 3 |
Second and third graders might solve the following simple equations:
| PROBLEMS | SOLUTIONS |
| (5 * 1) * 6 = 10 | (5 - 1) + 6 = 10 |
| (5 * 2) * (2 * 1) = 4 | (5 - 2) + (2 - 1) = 4 |
Teachers in upper grades can adapt the activity to include negative integers, fractions, decimals or other math concepts they might be teaching.
| PROBLEMS | SOLUTIONS | |
| 1. | (6 * 4) * 12 = 12 | (6 x 4) - 12 = 12 |
| (7 * 3) * (4 * 1) = 26 | (7 x 3) + (4 + 1) = 26 | |
| (4 * 2) * (4 * 3) = 24 | (4 / 2) x (4 x 3) = 24 | |
| (6 * 5) * (9 * 2) = 19 | (6 - 5) + (9 x 2) = 19 | |
| 2. | (5 * 5) * 10 = 15 | (5 x 5) - 10 = 15 |
| (8 * 1) * (6 * 3) = 11 | (8 x 1) + (6 - 3) = 11 | |
| (8 * 2) * (3 * 0) = 1 | (8 / 2) - (3 - 0) = 1 | |
| (9 * 4) * (7 * 0) = 36 | (9 x 4) + (7 x 0) = 36 | |
| 3. | 9 * (4 * 6) = 33 | 9 + (4 x 6) = 33 |
| (8 * 3) * (3 * 3) = 45 | (8 - 3) x (3 x 3) = 45 | |
| (5 * 3) * (3 * 0) = 5 | (5 x 3) / (3 + 0) = 5 | |
| (7 * 4) * (3 * 4) = 10 | (7 - 4) + (3 + 4) = 10 | |
| 4. | (8 * 4) * 2 = 24 | (8 + 4) x 2 = 24 |
| (4 * 7) * (3 * 3) = 20 | (4 + 7) + (3 x 3) = 20 | |
| (8 * 4) * (2 * 1) = 4 | (8 - 4) / (2 - 1) = 4 | |
| (16 * 4) * (3 * 4) = 28 | (16 / 4) x (3 + 4) = 28 | |
| 5. | 16 * (2 * 8) = 32 | 16 + (2 x 8) = 32 |
| (14 * 7) * (7 * 1) = 49 | (14 - 7) x (7 x 1) = 49 | |
| (6 * 0) * (6 * 1) = 36 | (6 - 0) x (6 x 1) = 36 | |
| (2 * 1) * (1 * 1) = 0 | (2 - 1) - (1 x 1) = 0 | |
| 6. | (9 * 0) * 6 = 3 | (9 + 0) - 6 = 3 |
| (5 * 7) * (4 * 4) = 35 | (5 x 7) - (4 - 4) = 35 | |
| (8 * 8) * (4 * 4) = 48 | (8 x 8) - (4 x 4) = 48 | |
| (36 * 6) * (4 * 2) = 14 | (36 / 6) + (4 x 2) = 14 | |
| 7. | 18 * (9 * 1) = 9 | 18 - (9 x 1) = 9 |
| (1 * 6) * (15 * 3) = 1 | (1 x 6) - (15 / 3) = 1 | |
| (8 * 3) * (6 * 2) = 44 | (8 + 3) x (6 - 2) = 44 | |
| (7 * 3) * (18 * 2) = 12 | (7 x 3) - (18 / 2) = 12 | |
| 8. | (4 * 9) * 16 = 20 | (4 x 9) - 16 = 20 |
| (2 * 1) * (2 * 0) = 0 | (2 / 1) - (2 + 0) = 0 | |
| (3 * 8) * (2 * 2) = 28 | (3 x 8) + (2 x 2) = 28 | |
| (9 * 5) * (9 * 3) = 15 | (9 x 5) / (9 / 3) = 15 | |
| 9. | (6 * 4) 2 = 20 | (6 + 4) x 2 = 20 |
| (18 * 9) * (6 * 0) = 8 | (18 / 9) + (6 + 0) = 8 | |
| (4 * 4) * (6 * 3) = 3 | (4 - 4) + (6 - 3) = 3 | |
| (7 * 4) * (6 * 4) = 30 | (7 x 4) + (6 - 4) = 30 | |
| 10. | (6 * 3) * 8 = 24 | (6 - 3) x 8 = 24 |
| (6 * 0) * (3 * 7) = 27 | (6 + 0) + (3 x 7) = 27 | |
| (5 * 4) * (9 * 3) = 3 | (5 + 4) / (9 / 3) = 3 | |
| (27 * 9) * (3 * 3) = 12 | (27 / 9) + (3 x 3) = 12 | |
| 11. | (5 * 3) * 10 = 20 | (5 - 3) x 10 = 20 |
| (28 * 2) * (6 * 6) = 14 | (28 / 2) + (6 - 6) = 14 | |
| (12 * 2) * (4 * 2) = 28 | (12 + 2) x (4 - 2) = 28 | |
| (4 * 6) * (10 * 2) = 2 | (4 + 6) / (10 / 2) = 2 | |
| 12. | (7 * 7) * 7 = 42 | (7 x 7) - 7 = 42 |
| (7 * 2) * (4 * 3) = 35 | (7 - 2) x (4 + 3) = 35 | |
| (15 * 5) * (9 * 3) = 9 | (15 / 5) x (9 / 3) = 9 | |
| (4 * 7) * (5 * 2) = 18 | (4 x 7) - (5 x 2) = 18 | |
| 13. | (7 * 2) * 4 = 10 | (7 x 2) - 4 = 10 |
| (9 * 3) * (9 * 3) = 54 | (9 x 3) + (9 x 3) = 54 | |
| (16 * 8) * (2 * 2) = 32 | (16 - 8) x (2 x 2) = 32 | |
| (5 * 4) * (7 * 0) = 7 | (5 - 4) x (7 + 0) = 7 | |
| 14. | (8 * 8) * 8 = 56 | (8 x 8) - 8 = 56 |
| (7 * 2) * (3 * 1) = 1 | (7 - 2) - (3 + 1) = 1 | |
| (5 * 3) * (9 * 4) = 40 | (5 + 3) x (9 - 4) = 40 | |
| (15 * 2) * (3 * 4) = 5 | (15 + 2) - (3 x 4) = 5 | |
| 15. | (5 * 6) * 6 = 5 | (5 x 6) / 6 = 5 |
| (6 * 4) * (5 * 4) = 9 | (6 + 4) - (5 - 4) = 9 | |
| (11 * 6) * (4 * 3) = 17 | (11 - 6) + (4 x 3) = 17 | |
| (6 * 8) * (5 * 4) = 14 | (6 + 8) x (5 - 4) = 14 | |
| 16. | (16 * 4) * 5 = 20 | (16 / 4) x 5 = 20 |
| (9 * 6) * (7 * 1) = 18 | (9 - 6) x (7 - 1) = 18 -2 | |
| (4 * 4) * (4 * 2) = 32 | (4 + 4) x (4 ) = 32 | |
| (11 * 7) * (10 * 5) = 2 | (11 - 7) / (10 / 5) = 2 | |
| 17. | (10 * 3) * 3 = 21 | (10 - 3) x 3 = 21 |
| ( 4 * 5) * (5 * 3) = 10 | (4 x 5) / (5 - 3) = 10 | |
| (11 * 2) * (6 * 2) = 34 | (11 x 2) + (6 x 2) = 34 | |
| (5 * 9) * (8 * 4) = 13 | (5 x 9) - (8 x 4) = 13 | |
| 18. | (16 * 4) * 9 = 36 | (16 / 4) x 9 = 36 |
| (5 * 4) * (1 * 1) = 2 | (5 - 4) x (1 + 1) = 2 | |
| (5 * 1) * (2 * 7) = 84 | (5 + 1) x (2 x 7) = 84 | |
| (18 * 2) * (4 * 2) = 1 | (18 / 2) - (4 x 2) = 1 | |
| 19. | (6 * 4) * 4 = 8 | (6 - 4) x 4 = 8 |
| (9 * 3) * (6 * 3) = 27 | (9 / 3) x (6 + 3) = 27 | |
| (4 * 4) * (4 * 2) = 8 | (4 + 4) / (4 / 2) = 8 | |
| (7 * 1) * (4 * 3) = 42 | (7 - 1) x (4 + 3) = 42 | |
| 20. | (7 * 2) * 5 = 25 | (7 - 2) x 5 = 25 |
| (24 * 8) * (6 * 3) = 27 | (24 / 8) x (6 + 3) = 27 | |
| (8 * 4) * (4 * 4) = 16 | (8 x 4) - (4 x 4) = 16 | |
| (6 * 0) * (8 * 1) = 56 | (6 + 0) x (8 - 1) = 56 | |
| 21. | (9 * 6) * 1 = 3 | (9 - 6) / 1 = 3 |
| (6 * 6) * (9 * 3) = 6 | (6 x 6) / (9 - 3) = 6 | |
| (15 * 7) * (8 * 1) = 64 | (15 - 7) x (8 x 1) = 64 | |
| (12 * 6) * (5 * 2) = 20 | (12 / 6) x (5 x 2) = 20 | |
| 22. | (16 * 1) * 4 = 4 | (16 x 1) / 4 = 4 |
| (21 * 7) * (3 * 3) = 27 | (21 / 7) x (3 x 3) = 27 | |
| (6 * 4) * (5 * 2) = 6 | (6 - 4) x (5 - 2) = 6 | |
| (5 * 6) * (10 * 7) = 33 | (5 + 6) x (10 - 7) = 33 | |
| 23. | (8 * 7) * 2 = 30 | (8 + 7) x 2 = 30 |
| (5 * 5) * (8 * 4) = 32 | (5 - 5) + (8 x 4) = 32 | |
| (5 * 3) * (8 * 1) = 7 | (5 x 3) - (8 x 1) = 7 | |
| (14 * 1) * (9 * 3) = 45 | (14 + 1) x (9 / 3) = 45 | |
| 24. | (12 * 2) * 2 = 48 | (12 x 2) x 2 = 48 |
| (64 * 8) * (3 * 3) = 72 | (64 / 8) x (3 x 3) = 72 | |
| (9 * 2) * (3 * 3) = 2 | (9 + 2) - (3 x 3) = 2 | |
| (4 * 4) * (8 * 2) = 0 | (4 x 4) - (8 x 2) = 0 | |
| 25. | (14 * 2) * 3 = 21 | (14 / 2) x 3 = 21 |
| (10 * 4) * (9 * 4) = 4 | (10 x 4) - (9 x 4) = 4 | |
| (5 * 1) * (2 * 5) = 40 | (5 - 1) x (2 x 5) = 40 | |
| (11 * 4) * (5 * 1) = 3 | (11 + 4) / (5 / 1) = 3 | |
| 26. | (6 * 1) * 6 = 36 | (6 x 1) x 6 = 36 |
| (11 * 4) * (4 * 1) = 28 | (11 - 4) x (4 x 1) = 28 | |
| (10 * 2) * (6 * 2) = 2 | (10 / 2) - (6 / 2) = 2 | |
| (15 * 15) * (5 * 2) = 3 | (15 + 15) / (5 x 2) = 3 | |
| 27. | (1 * 9) * 3 = 3 | (1 x 9) / 3 = 3 |
| (6 * 6) * (6 * 1) = 30 | (6 x 6) - (6 x 1) = 30 | |
| (12 * 4) * (5 * 2) = 30 | (12 / 4) x (5 x 2) = 30 | |
| (7 * 0) * (4 * 3) = 49 | (7 - 0) x (4 + 3) = 49 | |
| 28. | (11 * 6) * 5 = 25 | (11 - 6) x 5 = 25 |
| (2 * 9) * (3 * 3) = 9 | (2 x 9) - (3 x 3) = 9 | |
| (2 * 3) * (5 * 2) = 60 | (2 x 3) x (5 x 2) = 60 | |
| (15 * 8) * (3 * 1) = 21 | (15 - 8) x (3 x 1) = 21 | |
| 29. | (16 * 4) * 8 = 32 | (16 / 4) x 8 = 32 |
| (12 * 3) * (16 * 4) = 36 | (12 - 3) x (16 / 4) = 36 | |
| (11 * 6) * (3 * 2) = 11 | (11 - 6) + (3 x 2) = 11 | |
| (17 * 9) * (1 * 5) = 40 | (17 - 9) x (1 x 5) = 40 | |
| 30. | (9 * 3) * 9 = 27 | (9 / 3) x 9 = 27 |
| (6 * 2) * (4 * 3) = 0 | (6 x 2) - (4 x 3) = 0 | |
| (4 * 4) * (4 * 2) = 32 | (4 + 4) x (4 - 2) = 32 | |
| (9 * 1) * (6 * 1) = 48 | (9 - 1) x (6 / 1) = 48 | |
| 31. | (4 * 6) * 5 = 2 | (4 + 6) / 5 = 2 |
| (5 * 5) * (5 * 5) = 15 | (5 x 5) - (5 + 5) = 15 | |
| (11 * 4) * (7 * 1) = 56 | (11 - 4) x (7 + 1) = 56 | |
| (5 * 1) * (7 * 4) = 44 | (5 -1) x (7 + 4) = 44 | |
| 32. | (5 * 2) * 7 = 1 | (5 + 2) / 7 = 1 |
| (11 * 2) * (3 * 2) = 54 | (11 - 2) x (3 x 2) = 54 | |
| (9 * 4) * (6 * 2) = 1 | (9 + 4) - (6 x 2) = 1 | |
| (4 * 3) * (5 * 4) = 20 | (4 - 3) x (5 x 4) = 20 | |
| 33. | (40 * 10) * 3 = 12 | (40 / 10) x 3 = 12 |
| (54 * 9) * (3 * 2) = 36 | (54 / 9) x (3 x 2) = 36 | |
| (3 * 4) * (5 * 1) = 2 | (3 + 4) - (5 x 1) = 2 | |
| (12 * 2) * (10 * 6) = 6 | (12 x 2) / (10 - 6) = 6 | |
| 34. | (12 * 4) * 9 = 27 | (12 / 4) x 9 = 27 |
| (7 * 3) * (7 * 3) = 17 | (7 x 3) - (7 - 3) = 17 | |
| (5 * 5) * (12 * 3) = 0 | (5 - 5) x (12 / 3) = 0 | |
| (5 * 3) * (5 * 6) = 60 | (5 - 3) x (5 x 6) = 60 | |
| 35. | (10 * 2) * 5 = 40 | (10 - 2) x 5 = 40 |
| (9 * 4) * (2 * 8) = 20 | (9 x 4) - (2 x 8) = 20 | |
| (11 * 2) * (9 * 7) = 26 | (11 + 2) x (9 - 7) = 26 | |
| (7 * 4) * (6 * 2) = 32 | (7 x 4) + (6 - 2) = 32 | |
| 36. | (7 * 5) * 9 = 18 | (7 - 5) x 9 = 18 |
| (8 * 4) * (6 * 2) = 20 | (8 x 4) - (6 x 2) = 20 | |
| (14 * 2) * (7 * 1) = 0 | (14 / 2) - (7 x 1) = 0 | |
| (6 * 3) * (9 * 4) = 54 | (6 x 3) + (9 x 4) = 54 | |
| 37. | (8 * 3) * 9 = 45 | (8 - 3) x 9 = 45 |
| (12 * 4) * (6 * 2) = 4 | (12 + 4) - (6 x 2) = 4 | |
| (18 * 2) * (6 * 2) = 36 | (18 / 2) x (6 - 2) = 36 | |
| (5 * 4) * (9 * 2) = 27 | (5 + 4) + (9 x 2) = 27 |