Sharing Kai Fairly

Overview

Students explore fractions through a shared kai scenario, using paper models to divide kūmara and fruit into equal parts. They connect fraction symbols with English and te reo Māori labels, explain their decisions, and build on prior understanding of equal parts and unit fractions.

Learning intentions

• We are learning to represent halves, thirds and quarters as equal parts of a whole.
• We are learning to match fraction symbols with English and te reo Māori names.
• We are learning to explain how we know a sharing arrangement is fair.
• We are learning to use simple te reo Māori phrases when discussing fractions.

Success criteria

• I can divide a whole into equal parts and show the fraction represented.
• I can match ½, ⅓ and ¼ with half/third/quarter, haurua/hautoru/hauwhā.
• I can explain why the parts are equal.
• I can say or write “Ko te haurua tēnei”, “Ko te hautoru tēnei” or “Ko te hauwhā tēnei” accurately.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge tasks with classroom mathematics content.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Te Mātaiaho capabilities: communicating mathematical thinking, reasoning, representing ideas, and using language purposefully in a familiar cultural context.

Lesson structure (45 minutes)

1. 0–5 min · Shared kai hook. Teacher opens the kūmara sharing hook and presents: “Three people share one kūmara fairly. How could we cut it?” Students quietly sketch or gesture a possible solution, then share with a partner. Emphasise that fair sharing means equal-sized parts.

2. 5–12 min · Teach and model. Teacher uses the fraction language slides to model one whole divided into two, three and four equal parts. Introduce and rehearse: haurua (half), hautoru (third) and hauwhā (quarter), alongside ½, ⅓ and ¼. Model the phrase “Ko te haurua tēnei” and explain that “This is the half” identifies the fraction being shown. Students echo the words, trace the equal parts in the air, and identify the numerator and denominator in each symbol.

3. 12–25 min · Paper kai models. Teacher distributes the shared kai fraction model sheet and provides paper circles or rectangles representing kūmara and fruit. Demonstrate folding or partitioning one model into equal halves, thirds and quarters without naming the answer first. Students work in pairs, with one triad, to create and shade models for ½, ⅓ and ¼. They label each model in English and te reo Māori and practise saying the matching phrase to their partner.

4. 25–34 min · Sharing decisions. Teacher displays the fair-sharing challenge slides with scenarios such as one kūmara shared between two people, three people or four people. Ask: “How many equal pieces are needed?” and “How can your model prove it is fair?” Students choose the appropriate model, record the fraction on the worksheet, and explain their decision using a sentence such as “Ko te hautoru tēnei. E toru ngā wāhanga ōrite” (“This is a third. There are three equal parts”). Accept English explanations while encouraging the te reo phrase.

5. 34–41 min · Reasoning discussion. Teacher shows two contrasting models on the compare-and-explain slides—one divided equally and one divided into unequal pieces. Students use a think-pair-share routine to decide which represents a fair fraction and justify their choice. Invite pairs to present one model, saying its te reo Māori and English labels. Clarify that the denominator tells how many equal parts the whole has, while the numerator tells how many parts are selected.

6. 41–45 min · Exit check and wrap-up. Teacher returns to the plenary and exit prompt. Students complete the final worksheet prompt: draw and label one fraction model, write its English and te reo Māori names, and finish the sentence “I know it is fair because…”. Collect responses and invite the class to repeat the three key phrases together.

Resources

• the shared kai fraction slide deck
• the shared kai fraction model sheet
• Paper circles or rectangles for fraction models
• Coloured pencils or felt-tip pens
• Scissors and glue sticks, if students cut and assemble models
• Board or display screen
• Optional real or pictured kūmara and fruit for the opening scenario

Assessment

• Listen for students identifying equal parts and using the correct connection between ½, ⅓ and ¼.
• Observe pair models and explanations: check that the whole is partitioned equally and that labels match the representation.
• Use the exit response to identify students who can represent, label and justify a fraction independently.

Differentiation

• Support students with pre-folded or lightly marked paper models, a visible word bank, gestures, repeated pronunciation and sentence frames: “Ko te ___ tēnei. There are ___ equal parts.”
• Pair students strategically and allow students to explain first in English, then substitute the relevant te reo Māori fraction word.
• For students needing further challenge, ask them to show that the same whole can be partitioned in different orientations while remaining fair, or to compare the size of ½, ⅓ and ¼ and justify the order.
• Provide larger models, reduced writing demands, oral recording, or a peer scribe for students with fine-motor, literacy or processing needs. Check pronunciation respectfully and value students’ existing knowledge of te reo Māori.