Equal Parts: Haurua

Overview

In this first lesson of the five-part unit Fair Sharing: Hautau, 25 Year 2–3 students explore halves by sharing model pizza and toast fairly. They fold, cut, match, shade and explain equal parts, using everyday contexts that reflect the varied kai and sharing practices of whānau and cultures.

Learning intentions

• WALT recognise and make equal halves, or haurua.
• WALT explain why two parts must be equal to be fair.
• WALT represent a half using pictures, words and, for Year 3, the symbol 1/2.
• WALT use mathematical language to explain our thinking.

Success criteria

• I can explain that a whole divided into two equal parts makes halves.
• I can make and check two equal parts.
• I can label each half as haurua, one-half or 1/2.
• I can explain why two unequal pieces are not halves.

Curriculum links

• Sharing a whole equally and recognising simple fractions.
• Recognising and using halves in practical situations.
• Using mathematical language, representations and reasoning to explain ideas.
• Solving fair-sharing problems through collaborative investigation.

Lesson structure (50 minutes)

1. 0–7 min – Connect to fair sharing Gather students in a circle. Discuss how kai may be shared fairly at home, at school or during a class gathering. Invite students to notice that foods and sharing practices differ across whānau and cultures; the common idea is that everyone is treated fairly. Open with the sharing-kai hook slides and introduce hautau (fraction), katoa (whole), haurua (half), ōrite (equal) and wāhanga (part).

2. 7–15 min – Model a whole and halves Show one whole paper pizza and one whole paper toast shape under the document camera. Ask, “If two people share this fairly, what could we do?” Fold or cut each model into two equal parts. Match the pieces by placing one on top of the other. Emphasise that two pieces are not automatically halves: each part must be the same size and shape in relation to the whole. Use the modelling and vocabulary slides and ask, “How do you know these parts are equal?” and “Would two unequal pieces be fair?”

3. 15–20 min – Read and represent 1/2 Display two equal pieces and name each one haurua or one-half. For Year 3, write 1/2 and explain that the 1 tells us we are thinking about one part, while the 2 tells us the whole has been divided into two equal parts. Year 2 students may use the words and picture representation. Ask, “What does the 1 tell us? What does the 2 tell us?” Students show whole, half or not-half using the whole-half-not-half response sheet or hand signals.

4. 20–35 min – Pair investigation Place students in mixed-ability pairs. Give each pair paper toast and pizza templates, crayons, scissors, fraction cards and paper counters or toppings. Students fold first where possible, draw or cut a dividing line, check the parts by matching them, and shade or place toppings on one half. Partners take turns explaining how they know the parts are equal. Use the pair-investigation instruction slides to show the steps. Adults circulate, asking, “How do you know these parts are equal?” and “Would two unequal pieces be fair?” Follow school safety procedures; use only paper, cardboard or clean unopened packaging models unless real food is permitted.

5. 35–44 min – Apply and compare Year 2 students identify halves in picture cards and make halves by folding or drawing a line. Year 3 students label their models 1/2 and one-half, explain why an unequal example is not a half, and find one-half of collections of 6 or 10 toppings by sharing them between two groups. Invite selected pairs to compare examples using equal, whole, part and haurua. Use the reasoning and sharing prompts to support discussion.

6. 44–50 min – Share and assess Revisit the learning intention. Invite two or three pairs to show a model and explain their check. Give each student a quick whole/half/not-half show-me card or use the final section of the reflection and assessment section. Students draw or circle a half and, if ready, write 1/2. Record students who need further support in the next lesson.

Resources

• the complete fair-sharing slide deck
• the whole-half-not-half response sheet
• Paper or cardboard pizza and toast templates
• Folded paper for modelling
• Crayons or coloured pencils
• Child-safe scissors
• Fraction cards showing whole, half and not-half examples
• Paper counters or topping shapes
• Document camera
• Show-me cards or mini whiteboards

Assessment

• Observe whether students fold, cut or draw two equal parts and whether they check by matching.
• Listen for explanations using whole, part, equal, fair and haurua; note the misconception that any two pieces are halves.
• Collect or photograph the response sheets and record students who need support with equal parts, vocabulary or the 1/2 representation.

Differentiation

• Support: use larger shapes, pre-fold some templates, provide only clear visual examples first, and pair students with a supportive partner. Accept pointing, matching or oral explanations before written labels.
• Support for English language learners and students with additional learning needs: use gestures and repeated visuals for each key word, provide sentence frames such as “These are halves because ___,” and rehearse explanations with a partner.
• Year 2: focus on making, matching and identifying two equal parts using pictures, folding and simple language.
• Year 3 extension within the activity: represent halves as 1/2 and one-half, justify why unequal parts are not halves, and find one-half of 6 or 10 counters.