Strategy Swap Shop

Overview

In this hands-on mathematics session, students solve practical number problems using an efficient strategy, explain their thinking and compare methods. The same activity supports Years 3, 5, 7, 9 and 10 through differentiated number sets and challenge cards, building from place-value strategies and basic facts towards proportional reasoning and checking with digital tools.

Learning intentions

• WALT choose an efficient strategy for solving a number problem.
• WALT represent a problem with a number sentence, diagram or table.
• WALT explain why a strategy works.
• WALT check whether an answer makes sense in the situation.

Success criteria

• I can identify the operation or operations needed.
• I can solve using a strategy that suits the numbers.
• I can show my thinking clearly using words, symbols, a diagram or a table.
• I can check and explain my answer.

Curriculum links

• Number — efficient strategies for addition, subtraction, multiplication and division in practical problems.
• Number — place-value partitioning, regrouping, inverse operations and appropriate digital tools.
• Algebra — multiplication and related division facts, extended to larger numbers.
• Mathematical modelling — formulate number sentences, interpret solutions and communicate reasoning.

Lesson structure (30 minutes)

1. 0–4 min · Hook: Which way is clever? Teacher opens the strategy swap shop introduction and displays: “A stall has 48 packs with 6 pencils in each. How many pencils?” Students estimate, discuss whether they would add, multiply, draw groups or use another method, then share quick ideas.

2. 4–9 min · Model and connect. Teacher uses counters, a number line and a simple area model to demonstrate one problem, thinking aloud about choosing an efficient strategy; display the examples on the worked strategy examples. Students help identify the known numbers, operation and meaning of the answer.

Use the following age-appropriate model:

• Years 3–5: (6 \times 48 = 6 \times 40 + 6 \times 8 = 288).
• Years 7–10: (6(40+8)=288), then estimate (6 \times 50 \approx 300) to check reasonableness.

3. 9–20 min · Strategy Swap Shop. Teacher gives each student an appropriate task from the differentiated strategy worksheet and places counters, paper strips and pencils on the table. Students solve three practical problems, choosing from partitioning, compensation, repeated groups, an array or the inverse operation. After each problem, students explain their method to a partner, who asks, “Why did that strategy help?”

Suggested differentiation:

• Year 3: “There are 4 bags with 6 apples in each. How many apples?” and “Mia has 75 stickers and gives away 28. How many remain?”
• Year 5: “A class buys 7 packs of 24 markers. How many markers?” and “A book costs $38. How much do 6 books cost?”
• Year 7: “Five teams share 1,260 points equally. How many points per team?” Include a percentage or decimal comparison.
• Year 9: “A sports club buys 18 boxes of 24 drinks at $2.40 each. Find the total cost and explain an efficient method.”
• Year 10: “A fundraiser earns (3x+20) dollars from each of 8 groups. Form an expression, substitute (x=15), and check the result using estimation.”

4. 20–25 min · Strategy swap and check. Teacher asks students to place one solved example beside another student’s work and use the compare-and-check prompts. Students identify one similarity, one difference and one checking method, such as inverse operation, estimation, a calculator or a second representation.

5. 25–30 min · Plenary and exit check. Teacher displays the final prompt on the reflection and exit prompt: “Which strategy was most efficient for your hardest problem, and why?” Students complete the final worksheet box with an answer, working and one sentence of explanation, then share one useful strategy with the group.

Resources

• the strategy swap shop slide deck
• the differentiated strategy worksheet
• Linking cubes, counters or small household objects
• Place-value materials or grid paper
• Paper strips and pencils
• Mini whiteboards or scrap paper
• Calculators or a simple spreadsheet for checking Years 7–10 work
• Coloured pens or highlighters

Assessment

• Observe whether students select a suitable operation and can connect each number to the situation.
• Question individuals: “What does this number represent?”, “Could you solve it another way?” and “How do you know your answer is reasonable?”
• Collect the final worksheet response as an exit check, looking for a correct answer, visible reasoning and a clear explanation.

Differentiation

• Support: Read each problem aloud, reduce the number size, provide counters and a number sentence frame: “I know ___ groups of ___, so I calculate ___.” Allow students to draw before writing.
• Years 3–5: Use concrete materials, arrays, part-part-whole diagrams and multiplication facts for 3, 4, 5 and 10. Offer a word bank with groups, total, share, altogether.
• Years 7–10: Include decimals, percentages, algebraic expressions and multi-step financial contexts. Encourage estimation, inverse operations and calculator or spreadsheet checking rather than replacing reasoning.
• Dyslexia-friendly options: Use a clear sans-serif font, large print, generous spacing, short instructions, one problem per section and coloured operation symbols. Read text aloud, allow oral explanations or scribing, and do not penalise spelling.
• Advanced learners: Require two different strategies, compare their efficiency and create a new practical problem for another student to solve. Challenge students to explain when a calculator is useful and when mental or written calculation is more efficient.