Problem-Solving Workshop

Overview

In this ninth lesson of the Rational Number Knowledge Practices unit, students apply fractions, percentages, scaling and measurement to authentic multi-step planning problems. Contexts may include a school māra, marae or community event; use a familiar local setting and ensure cultural details are accurate and respectful.

Learning intentions

• WALT apply rational-number knowledge to authentic multi-step problems.
• WALT select efficient representations and strategies.
• WALT communicate reasoning and evaluate solutions.
• WALT check whether answers are reasonable and meet the constraints.

Success criteria

• I can identify the relevant information, the whole and any constraints.
• I can choose and use an efficient strategy or representation.
• I can show connected steps and explain my reasoning.
• I can check and justify whether my answer is reasonable.

Curriculum links

• Number: use fractions, decimals and percentages to represent, compare and calculate with quantities.
• Measurement: select appropriate units and apply scaling in practical situations.
• Mathematical and statistical inquiry: interpret information, plan a solution, investigate and revise.
• Mathematical communication and reasoning: represent ideas, justify strategies and critique solutions.

Lesson structure (60 minutes)

1. 0–5 minutes – Connect and introduce Open with the hook and learning intentions. Present a quick scenario: “We need to plan kai for 25 people, but the recipe serves 10. What information would we need before calculating?” Students turn and talk, then share assumptions they would need to check.

2. 5–15 minutes – Teacher modelling Display the worked planning example and think aloud through a recipe or māra-planning problem. Model understand–plan–solve–check: identify the whole, distinguish relative values, choose a representation such as a table, bar model or number line, scale quantities, and check units, totals and reasonableness. Deliberately state an assumption, such as serving size, and show how it affects the solution.

3. 15–23 minutes – Guided unpacking Give each pair the problem-solving planning sheet. Work through one shared problem, pausing to ask: “What is the whole?”, “Which values are relative?”, “What operation or representation could help?”, and “Can another representation verify this?” Students complete the understand and plan sections before comparing strategies with a partner.

4. 23–43 minutes – Collaborative problem-solving Place students in mixed-ability teams of four and distribute different tiered task cards from the collaborative task set. Tasks could involve scaling kai for a community event, calculating the percentage of a māra planted with different crops, or sharing materials and measuring spaces. Assign roles: reader, information finder, recorder and checker. Students may use manipulatives or calculators, but must explain why their strategy is efficient and record connected steps.

5. 43–53 minutes – Peer review and revision Teams swap their planning sheets with another team. Using the peer-review prompts, reviewers identify one clear representation, check at least one calculation, and ask one question about an assumption or constraint. The original team discusses the feedback and revises or annotates its solution. Invite two teams to briefly compare different valid strategies.

6. 53–60 minutes – Plenary and exit ticket Revisit the reflection and exit-ticket slide. Students complete: “The strategy that was most useful today was ___ because ___.” Add one sentence explaining how they checked their answer. Collect planning sheets and exit tickets as students leave.

Resources

• the 8-slide lesson deck: hook, WALT, worked example, prompts, task instructions, peer review and reflection.
• the problem-solving planning sheet: understand–plan–solve–check organiser and tiered team tasks.
• Fraction strips, counters, measuring tools and place-value materials.
• Calculators for checking, not replacing, reasoning.
• Whiteboard and markers.
• Prepared team role cards.
• Local context information or photographs, if appropriate and approved.

Assessment

• Listen for students identifying the whole, relative values, assumptions and constraints during modelling and group work.
• Check planning sheets for a suitable representation, connected calculations, correct units and an explicit reasonableness check.
• Use the exit ticket to identify students who can select and justify a strategy, then address misconceptions in the final unit lesson.

Differentiation

• Support learners with tiered tasks, chunked instructions, worked-example prompts, vocabulary banks for strategy, representation, justify, efficient, constraint, solution, reason and reasonableness, and concrete fraction or measurement materials.
• Confer with selected groups, reread problems aloud and highlight the whole, known values and required answer. Accept diagrams, oral explanations, labelled tables or written reasoning.
• Provide calculators and enlarged task text for learners with processing, literacy or fine-motor needs; pair strategically and assign meaningful roles rather than removing the mathematical challenge.
• Extend advanced learners by adding constraints, comparing two solutions, finding the most efficient option or proving that a solution is optimal.