Rational Number Showcase

Overview

In this final lesson of the unit, teams will demonstrate and communicate rational-number knowledge through an authentic Aotearoa New Zealand context. They will design a plan for 25 people, explain their mathematical decisions, and individually reflect on their learning and next steps.

Learning intentions

• WALT demonstrate and communicate rational-number knowledge in an authentic design.
• WALT integrate representation, equivalence, ordering, proportional reasoning, missing values and relative measures.
• WALT justify mathematical decisions using evidence, estimates and clear language.
• WALT reflect on our mathematical practice and respond to questions.

Success criteria

• I can produce accurate calculations and check whether answers are reasonable.
• I can use at least three representations, such as fractions, decimals, percentages, tables, diagrams or number lines.
• I can justify decisions about scale, order, proportion, measurement and relative quantity.
• I can communicate clearly, respond to questions and identify a strength, misconception corrected and next step.

Curriculum links

• Use fractions, decimals and percentages to represent, compare, order and find equivalent rational numbers.
• Apply proportional reasoning, scale factors and missing-value strategies in practical situations.
• Convert and use metric measurements, estimate and judge the reasonableness of results.
• Communicate mathematical thinking, use representations, justify conclusions and reflect on strategies.

Lesson structure (60 minutes)

1. 0–5 minutes – Reconnect and introduce the task Open with the opening challenge slide: “How can mathematics help us plan fairly for 25 people?” Revisit the WALT, vocabulary and the unit evidence portfolio. Explain that teams of five will complete one shared design, while each student submits an individual reflection.

2. 5–12 minutes – Unpack the brief and rubric Display the task requirements and rubric slides and distribute the performance-task planning and reflection booklet. Teams choose a respectful context: a kai plan, school māra, community event, sport activity, sustainability project or appropriately researched local context. Remind students not to present cultural knowledge they do not own; they may use local seasonal produce, family examples or a context approved by the teacher.

The final design must:

• scale quantities for 25 people;
• show one fraction-decimal-percentage equivalence;
• order or compare at least two options;
• solve a missing value;
• include a measurement conversion;
• explain a relative-quantity claim;
• use at least three representations and clear mathematical language.

3. 12–18 minutes – Model assumptions and checking Model a short example, such as scaling a recipe from 4 to 25 people. Annotate assumptions, identify the scale factor, show a calculation, represent part of the answer as a fraction, decimal and percentage, and estimate to check it. Use the slides’ misconception prompts: larger denominators do not always mean larger fractions; percentages are not simply whole numbers; quantities should be scaled rather than added; unit conversions must move in the correct direction.

4. 18–40 minutes – Team design workshop Teams assign purposeful roles such as facilitator, calculator/checker, recorder/designer, resource manager and presenter. They plan on the planning template, using measuring equipment and data sets as needed. The teacher conferences with each team, checking calculations, representations and explanations. Ask: “What is your scale factor?”, “How do you know these values are equivalent?”, “Are you comparing amounts or proportions?”, and “What evidence makes your claim reasonable?” Teams may create a poster, written report or digital presentation. Encourage them to show working rather than only final answers.

5. 40–48 minutes – Peer review and revision Teams exchange plans with a nearby team or conduct a structured gallery review. Reviewers use the checklist in the peer-feedback checklist to identify one accurate feature, one question and one suggested improvement. Teams revise at least one calculation or explanation and rehearse a concise response to a likely question.

6. 48–56 minutes – Presentations and questioning Each team gives a brief presentation, focusing on its context, key calculations, representations and most important justification. If time is limited, teams present simultaneously to another team, followed by two questions. Assess using the agreed weighting: accuracy 30%, strategy and proportional reasoning 25%, representations and mathematical language 20%, contextual justification 15%, collaboration and reflection 10%.

7. 56–60 minutes – Individual reflection and exit ticket Students complete the reflection section of the individual reflection and exit ticket independently. They record one strength, one misconception they corrected and one next step. Collect team products, individual reflections and peer feedback for the class evidence portfolio across all ten lessons.

Resources

• the Rational Number Showcase slide deck
• the performance-task planning and reflection booklet
• Team data sets: recipes, prices, event quantities, distances or water-use information
• Measuring equipment, rulers, measuring cups, scales and calculators
• Paper, coloured pens, graph paper and presentation materials
• Devices and presentation tools, where available
• the Units Conversion Ladder for student reference
• Class evidence portfolio and summative rubric

Assessment

• Use conference notes, questioning, whiteboards, peer feedback and the checklist to assess accuracy, reasoning, representations and communication during the workshop.
• Assess the final team design with the performance rubric, while also assessing each student’s individual reflection and contribution.
• Compare today’s evidence with diagnostic evidence from Lesson 1 and the midpoint check after Lesson 5 to identify growth and future teaching needs.

Differentiation

• Offer choice of context, presentation format and data set. Provide a partially completed planning template, worked example, vocabulary bank and the conversion ladder for students needing support.
• Use mixed-ability teams with purposeful roles. Allow calculators, speech-to-text, enlarged print, oral recording or a teacher/scribe for students with processing, language or fine-motor needs.
• For EAL learners, pre-teach rational number, equivalent, proportion, scale, relative and justify; encourage bilingual glossaries, labelled diagrams and rehearsed sentence stems such as “Our evidence shows…”.
• Extend confident learners by asking them to optimise cost, waste or fairness, compare two possible scale factors, or analyse uncertainty in estimates and data.