Design a Fair Share

Overview

In this final lesson of Fair Sharing: Hautau, students design and justify a fair pizza or toast-sharing plan. They use halves, quarters and equal partitioning, then communicate their mathematical thinking through drawings, symbols, words and oral explanation.

Learning intentions

• WALT design a fair sharing plan using halves and quarters.
• WALT partition a whole into equal parts and label the fractions.
• WALT explain why a sharing plan is fair using mathematical vocabulary.
• WALT compare different ways of representing the same share.

Success criteria

• I can divide a whole into equal parts.
• I can label shares as halves, quarters, 2/4 or 4/4.
• I can show who receives each share.
• I can explain, “My plan is fair because…” and describe how I know.

Curriculum links

• Applying simple fractions to equal sharing.
• Recognising and using halves and quarters in meaningful problems.
• Using mathematical language, representations and reasoning to solve problems.
• Communicating, justifying and evaluating mathematical ideas in a group.

Lesson structure (50 minutes)

1. 0–5 minutes – Connect and revisit

Open with the introduction and hook slides. Show one pizza divided into equal halves and another divided into unequal pieces. Ask: “Which plan is fair? How do you know?” Revisit hautau (fraction), haurua (half), hauwhā (quarter), ōrite (equal), tika (fair) and katoa (whole).

2. 5–12 minutes – Model fair sharing

Use the worked-example slides and a large paper pizza or toast template. Model sharing one whole between two people, then between four people. Think aloud as you partition, label and allocate each share. Demonstrate that 1/2 is the same amount as 2/4, and that 4/4 represents one whole.

Ask:

• “How have we proved every share is equal?”
• “What fraction does each person receive?”
• “Can you show the same share another way?”

3. 12–17 minutes – Explain the performance task

Display the task-instructions and vocabulary slides. Students work independently or with a partner. Each chooses or receives a scenario: one pizza shared between two or four people, two pizzas shared fairly, or a mixed-topping pizza where everyone receives an equal-sized share.

Explain that the plan must show the whole, equal parts, fraction labels, recipients and a short explanation. Year 2 students use two- or four-person scenarios and may use supported labels. Year 3 students should show equivalence or solve a more complex scenario where appropriate.

4. 17–34 minutes – Design a fair share

Distribute the fair-share design worksheet and provide paper or cardboard pizza and toast templates, rulers, paper toppings, glue and colouring tools. Students partition, colour, label and annotate their design.

Circulate and ask:

• “What fraction does each person receive?”
• “How do you know the parts are equal?”
• “Can you show the same share another way?”
• “What would change if one more person joined?”

Encourage students to use drawings, fraction symbols and words such as wāhanga (part), ōrite (equal) and tohatoha (share).

5. 34–43 minutes – Explain and give feedback

Students present their plan to a partner or small group, using the partner-explanation and discussion-prompt slides. The listener gives “two stars and a wish”, focusing on equal parts and a clear explanation.

Suggested sentence starters:

• “My plan is fair because…”
• “Each person receives…”
• “I know the parts are equal because…”
• “One way to show the same share is…”

6. 43–48 minutes – Reflect and share

Invite several students to show contrasting plans. Compare one-half, two-quarters and four-quarters. Discuss whether different-looking designs can still be fair. Students complete the reflection on the reflection section: “My plan is fair because…” and “Next time I would…”.

7. 48–50 minutes – Gather evidence and close

Use the plenary and exit-question slide. Ask students to hold up or point to the fraction each person receives in a displayed example. Collect designs and worksheets, noting students who can partition, label, allocate and justify independently.

Resources

• the fair-sharing lesson deck
• the fair-share design worksheet
• Paper or cardboard pizza and toast templates
• Rulers, pencils, colouring tools, glue and scissors
• Paper toppings, laminated food images or clean packaging
• Fraction labels: 1/2, 1/4, 2/4 and 4/4
• Large demonstration template
• Fair-sharing vocabulary cards or word wall
• Teacher assessment rubric and success-criteria checklist

Use paper or cardboard models rather than shared food. Do not require tasting or handling food.

Assessment

• Observe and record whether students partition the whole into equal parts and accurately identify halves, quarters and related representations.
• Assess the final plan for equal partitioning, accurate fraction representation, fair allocation, comparison or equivalence where relevant, and clear oral or written explanation.
• Use the presentation, peer feedback and reflection to report progress against the equal-sharing and meaningful-fractions objectives, then plan next steps. Note whether support is still needed with measuring equal parts, fraction notation or mathematical vocabulary.

Differentiation

• Year 2: provide a two- or four-person scenario, pre-drawn templates, fraction labels and oral rehearsal. Accept drawings and spoken explanations in place of extended writing.
• Year 3: offer two-pizza or mixed-topping scenarios; require students to show equivalence such as 1/2 = 2/4 and justify comparisons.
• Support learners with clear visual models, pre-folded or lightly marked templates, bilingual vocabulary, sentence frames and a partner who can rehearse the explanation. Allow pointing, drawing or using an adult scribe.
• Extend students by asking them to investigate what changes when another person joins, or to create and solve a different fair-sharing scenario. Explore thirds or tenths only when this is appropriate to the learner’s understanding.