AC9M4A01 • Homework

Unknown Values in Addition and Subtraction Equations worksheet

Use this printable homework sheet for written working, application and reflection alongside the online learning activities.

Open practice

Written working

Complete these eight tasks. Show a model or calculation and explain how it preserves equality. For drawing tasks, use the writing space or extra paper. The PDF contains these tasks and a separate answer guide.

  1. Draw matching number lines to show 8 + 5 and 5 + 8. Label the jumps and endpoints. Explain why the totals are equal.

  2. Use a diagram of equal counters to complete 9 + 6 = □ + 11. Then remove 2 counters from each side and write a new true equation.

  3. Draw a bar for 46 + □ = 112. Label the whole and both parts, find the missing number, and write a related subtraction check.

  4. Solve both equations and explain why the missing values have different roles: □ − 37 = 85 and 122 − □ = 85.

  5. Draw number lines using the same scale to explain why 39 − 16 = 44 − 21. Label both gaps and describe how the endpoints change.

  6. Find the box in 47 + □ + 53 = 168. Show a useful grouping and explain why rearranging is allowed.

  7. A class collects 87 cans in the morning and some more later. Another class collects 96 cans and then 34 more. The two classes finish with equal totals. Write and solve an equation for the first class’s later collection.

  8. A student writes 71 + 28 = 72 + 29 and says increasing both numbers preserves a sum. Correct the right-hand side by changing only its second addend, and explain the mistake.

Answer guide — open after completing the work

  1. Both journeys start at 0 and finish at 13. One journey has jumps of 8 then 5; the other has 5 then 8. The same two addends are reordered, so their sum is unchanged.

  2. The box is 4. One possible new equation is 9 + 4 = 4 + 9. Both original totals are 15. Removing 2 from the group of 6 and 2 from the group of 11 leaves equal totals of 13. Other equations are valid if exactly 2 counters are removed from each side.

  3. The missing part is 66. Whole 112; parts 46 and 66. A related check is 112 − 46 = 66. Whole minus known part finds the other part. Addition also checks the relationship: 46 + 66 = 112.

  4. First box: 122. Second box: 37. The first unknown is the starting whole, so add 37 + 85. The second unknown is the removed part, so subtract 85 from 122. Both checks give 122 − 37 = 85.

  5. Both differences are 23. Each endpoint increases by 5. The intervals 16 to 39 and 21 to 44 have equal length. Shifting both endpoints by 5 preserves the gap.

  6. The missing addend is 68. Reorder and group 47 + 53 = 100. Then 100 + 68 = 168. Reordering the same addends preserves their sum.

  7. 87 + □ = 96 + 34; the missing collection is 43 cans. The second class collects 130 cans. The first class needs 130 − 87 = 43 more. Check: 87 + 43 = 96 + 34 = 130.

  8. 71 + 28 = 72 + 27. The left sum is 99. Increasing both addends would increase the sum by 2 to 101. If the first addend increases by 1, the second must decrease by 1 to preserve the total.