AC9M4N08 • Homework

Mathematical Modelling in Multi-step Problems worksheet

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

Open practice

Write, model and explain

Complete the eight tasks below on paper or download the matching PDF homework. Use the stated digital tool for digital tasks and show your work to a parent or teacher.

  1. A collection has 154 stamps, including 89 animal stamps. Draw a labelled bar or part-part-whole model. Write and solve a sentence for the other stamps. Use a separate sheet for the model and working.

  2. Forty-two seedlings are shared equally among 7 trays. Model the sharing and explain what 42, 7 and the answer measure. Use a separate sheet for the model and working.

  3. Forty-two seedlings are instead packed with 6 in each tray. Model this arrangement and explain what the answer counts. Use a separate sheet for the model and working.

  4. A club has $200. It buys 5 balls at $27 each and pays $18 delivery once. Make a cost table, write connected number sentences and use an efficient strategy. Check the result and give a budget conclusion.

  5. Eight seats cost $49 each. Show a compensation strategy from $50, calculate the exact cost and explain the adjustment.

  6. Mila reads 19 pages. Kai reads 4 times as many. Draw a comparison bar or array, then calculate with partitioning and state Kai’s pages. Use a separate sheet for the model and working.

  7. A group has 44 students and 3 adults. Plan A has 45 places for $300; Plan B has 50 places for $360. The budget is $380. Compare both plans in a table and justify the choice.

  8. Use a spreadsheet or calculator to compare three kit offers: 12 kits at $6.50 each; 18 at $6.20; 24 at $6.00. At least 18 kits are needed and the budget is $120. State your calculation model, record all totals, check one total another way and justify a choice.

Answer and work checks

  1. 154 − 89 = 65 other stamps. Inspect a whole of 154 and parts of 89 and 65, or an equivalent correctly labelled model. Require a number sentence, working and the answer unit.

  2. 42 ÷ 7 = 6 seedlings per tray. Require 7 equal groups containing 6 each. The 42 counts all seedlings and the 7 counts trays. Inspect the actual model and explanation.

  3. 42 ÷ 6 = 7 trays. Require 7 groups of 6. The 6 means seedlings per tray; the answer 7 counts trays. Contrast this with sharing among 7 trays.

  4. 5 × $27 = 5 × $20 + 5 × $7 = $135; $135 + $18 = $153. The budget is enough and $47 remains. Check $153 + $47 = $200. Inspect the actual table, connected sentences, explained strategy, check and contextual conclusion. Accept another correct efficient strategy.

  5. 8 × $50 − 8 × $1 = $400 − $8 = $392. Every price was increased by $1, so all 8 increases must be removed. Require written working and that explanation.

  6. 4 × 19 = 4 × 10 + 4 × 9 = 40 + 36 = 76 pages. Inspect four equal 19-page units, the number sentence and the requested partitioning working. Four more pages would mean 23 pages, a different comparison.

  7. 44 + 3 = 47 people need places. A is too small; B fits all 47 and leaves $380 − $360 = $20. Require the actual comparison table and both capacity and budget checks.

  8. Quantity × price gives $78, $111.60 and $144. Choose 18 kits for $111.60: enough kits and within budget, leaving $8.40. Require actual digital results, a stated model and an independent check of one total. Twelve kits are too few; 24 kits exceed the budget.

Inspect the actual models, working and explanations. A correct final number or completion tick alone does not show the required reasoning.