AC9M4N06 • Homework

Efficient Calculation Strategies and Digital Tools worksheet

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

Open practice

Written practice: draw, explain and check

These eight tasks cover the whole topic. Show your working or model before checking the answers. The PDF includes writing space and an answer guide.

  1. Solve 1 997 + 468 in two different ways. Show each method and explain why one is useful for these numbers.

  2. Calculate 6 002 − 2 786. Show a clear strategy and check with addition.

  3. Draw 6 rows with 8 counters in each. Write a multiplication sentence and explain what all three numbers mean.

  4. There are 84 cards. First put 7 cards in each pack; then consider sharing all 84 equally into 12 packs. Draw or label a model for each situation and explain the two division sentences.

  5. Use doubling and halving to solve 25 × 28. Show the changed factors and explain why the product stays the same.

  6. Draw a region for 34 × 6, split into widths 30 and 4. Label both partial products and find the total.

  7. Share 132 equally among 3 groups by splitting it into 120 and 12. Draw or describe the shares and check the result.

  8. Use a spreadsheet or calculator to add 128, 176, 94 and 202. Record the entries and total. In a spreadsheet put the four amounts in B2:B5 and enter =SUM(B2:B5) in B6, outside that range. Change 94 to 104; predict and then check the new total.

Answer guide for parents and teachers
  1. Both methods give 2 465. Compensation: 2 000 + 468 − 3. Partitioning adds 400, then 60, then 8 to the first addend. Compensation uses the nearby thousand; a correct explained written method is also acceptable.
  2. 6 002 − 2 700 = 3 302; 3 302 − 86 = 3 216. A correct regrouping method is also acceptable. Check: 3 216 + 2 786 = 6 002.
  3. 6 × 8 = 48. The model has six equal rows, eight counters in each row and forty-eight counters altogether. Labels must match the drawn groups.
  4. 84 ÷ 7 = 12 packs when 7 cards per pack is known. 84 ÷ 12 = 7 cards per pack when 12 packs is known. Both use all 84 cards; the quotient has a different meaning.
  5. 25 × 28 = 50 × 14 = 700. Doubling the number of groups while halving each group preserves the total. A model may rearrange equal unit squares without adding or removing any.
  6. The common height is 6. The parts give 30 × 6 = 180 and 4 × 6 = 24. Total: 180 + 24 = 204. Both parts must be multiplied by 6.
  7. Each group receives 120 ÷ 3 = 40 and 12 ÷ 3 = 4, giving 44. The three equal groups use all the counters. Check: 44 × 3 = 132.
  8. The original total is 600; B6 contains =SUM(B2:B5), adding the four entries without overwriting an input or including itself. Check (128 + 202) + (176 + 94) = 330 + 270 = 600. Changing 94 to 104 adds 10, so the new total is 610. A calculator record must include each value once.