Subject
Mathematics — Pāngarau
Pāngarau / Mathematics · Fractions · Years 3–6
Hāngī Fractions & Sharing
Te Tohatoha Kai · Fair Sharing Through Fractions — Learning fractions through the manaakitanga of sharing hāngī kai with whānau and community.
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This handout is ready to print and use. For localised contexts, bilingual te reo prompts, or assessment-aligned follow-up tasks, Te Wānanga can generate an adapted sequence instantly.
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Ngā Whāinga Akoranga · Learning Intentions
- We are learning to describe fractions as equal parts of a whole or a set.
- We are learning to find equivalent fractions using fraction walls and patterns.
- We are learning to connect fair sharing with the mathematical concept of fractions.
- We are learning to use fractions to solve real sharing problems.
Paearu Angitu · Success Criteria
- I can share a set of objects equally and write the result as a fraction.
- I can use a fraction wall to find fractions that are equal in size.
- I can solve a hāngī sharing problem and show my working.
- I can explain how fractions connect to manaakitanga (fair, generous sharing).
Hononga Marautanga · Curriculum Alignment
NZC Mathematics strands
- Number — fractions of sets and wholes
- Number — equivalent fractions
- Number — mixed numbers (extension)
Te Ao Māori integration
- Manaakitanga — generous and fair sharing
- Hāngī as a context for proportional thinking
- Kupu Māori for fractions (hautau, tohatoha)
Horopaki · Cultural Context — He aha te hāngī?
A hāngī is a traditional Māori method of cooking kai in an earth oven. Hot stones are placed in a pit, food is wrapped in leaves and baskets, then covered with earth to steam for several hours. Hāngī is central to manaakitanga — the practice of caring for others through generous hospitality.
When food is cooked in a hāngī, it must be shared fairly among all whānau and guests. This is not just a cultural value — it is mathematics in action. Fair sharing is the foundation of fractions.
Rapanga 1 · Problem 1: Sharing Kūmara
Te horopaki · The scenario
Nana has cooked 12 kūmara in the hāngī. She wants to share them equally among 4 whānau (families).
a) How many kūmara does each whānau get? Show your working.
b) Write each whānau's share as a fraction of all 12 kūmara.
Each whānau gets out of 12 kūmara, which we write as .
c) Can you simplify that fraction? What is the simplest form?
d) Draw 12 kūmara below and circle groups to show how they are shared among 4 whānau.
Rapanga 2 · Problem 2: Chicken Portions
Te horopaki · The scenario
The hāngī has 8 pieces of chicken (heihei). There are 16 people to feed.
a) What fraction of one piece of chicken does each person get? Show your reasoning.
b) Four people at the gathering are vegetarian and don't eat chicken. Now how much chicken can each of the remaining people have? Write your answer as a fraction and a decimal.
Rapanga 3 · Problem 3: Hāngī for the Hui
Te horopaki · The scenario
The marae is hosting a large hui with 60 manuhiri (guests). The hāngī team has prepared:
- 30 kūmara
- 45 rīwai (potatoes)
- 20 pieces of chicken
a) What fraction of a kūmara does each guest receive? Simplify your answer.
b) How many potatoes does each guest get? Write this as a fraction and simplify.
c) One-third (⅓) of guests are vegetarian and do not eat chicken. How many guests share the chicken? How much chicken does each of them receive? Show your working.
Pakitara Hautau · Fraction Wall
Each row below shows one whole divided into equal parts. Use this wall to find and compare fractions.
Halves
Hawhe
Hawhe
½
½
Thirds
Hautoru
Hautoru
⅓
⅓
⅓
Quarters
Hauwhā
Hauwhā
¼
¼
¼
¼
Sixths
Haurima
Haurima
⅙
⅙
⅙
⅙
⅙
⅙
Using the fraction wall above, answer these questions:
a) How many sixths equal one half? _______
b) How many sixths equal one third? _______
c) How many thirds equal two quarters? _______
Hautau Ōrite · Equivalent Fractions Activity
Complete the table. The first row is done for you.
| Fraction | Equivalent fraction (×2) | Equivalent fraction (×3) | In simplest form |
|---|---|---|---|
| ½ | 2/4 | 3/6 | ½ |
| ⅓ | ⅓ | ||
| ¼ | ¼ | ||
| 3/12 | |||
| 4/6 |
Challenge: Write two equivalent fractions for the share of kūmara each whānau received in Problem 1.
Whakaaro Hōhonu · Reflection — Manaakitanga and Fractions
Manaakitanga means showing respect, generosity, and care for others — especially through the sharing of kai.
In your own words: how does understanding fractions help us practise manaakitanga? What would happen if the sharing was not equal?
Aronga Mātauranga Māori
Fractions in te ao Māori are not an abstract concept — they are embedded in the practice of manaakitanga. The act of tohatoha (sharing) ensures that every person receives their fair portion, reflecting the values of equality and community. The hāngī is a communal technology that feeds entire hapū and iwi, requiring careful proportional thinking to ensure no one goes hungry. Exploring fractions through this lens honours Indigenous mathematical knowledge and connects numeracy to cultural identity and obligation.
Ngā Rauemi Tautoko · Support Materials
Resources already provided:
- Three worked fraction problems with hāngī sharing scenarios
- Fraction wall: halves, thirds, quarters, sixths
- Equivalent fractions table with student completion spaces
- Manaakitanga reflection question
- Bilingual headings (te reo Māori / English)
Aronga Rerekē · Differentiated Pathways
Entry-level support
Provide physical kūmara models or counters to represent the sharing in Problem 1. Use the fraction wall as a visual anchor before attempting the table. Focus on halves and quarters only. Use the stem: "I shared ___ into ___ equal groups, so each group is ___."
On-level
Complete all three problems independently. Use the fraction wall to verify equivalent fractions. Write explanations using both English and kupu Māori. Tackle all rows of the equivalent fractions table.
Extension / Whakaaro Hohonu
Plan your own hāngī for 24 people: decide how much of each kai is needed so every person receives 1 kūmara, 1½ potatoes, and ⅓ of a chicken. Express all quantities as mixed numbers. Calculate total cost if kūmara cost $2.50 each, potatoes $3/kg, and chickens $15 each.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to build pāngarau (mathematical) understanding — developing number sense, pattern recognition, and mathematical reasoning through hands-on, culturally grounded activities that connect to tamariki's world.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can explain their mathematical thinking using words, objects, drawings, or symbols.
- ✅ Students can apply the number or pattern concept in this resource to a real or everyday context.
Differentiation & Inclusion
Scaffold support: Use concrete materials (blocks, counters, fingers) for entry-level engagement before progressing to abstract representations. Offer extension challenges asking students to generalise a pattern, write their own word problem, or explain their strategy to a partner.
ELL / ESOL: Mathematical language is a discipline-specific barrier — pre-teach key terms (e.g., equals, more than, fewer, pattern, factor) using visual representations. Allow students to demonstrate mathematical understanding non-verbally or through drawing. Pair with a bilingual buddy where possible.
Inclusion: Embed choice in how students engage — oral, written, or diagrammatic responses are all valid. Neurodiverse learners benefit from short, chunked task sequences with immediate feedback loops. Avoid timed drills in favour of exploratory tasks that reward curiosity. Make the maths classroom a safe place to be wrong and try again.
Mātauranga Māori lens: Pāngarau is a living tradition in Te Ao Māori — from the geometric precision of tukutuku and kōwhaiwhai patterns to the navigational mathematics of waka hourua, and the seasonal calculations embedded in maramataka. Framing early number sense within these contexts shows tamariki that mathematics is a human, culturally rich endeavour — not a foreign import. Encourage students to see counting, measuring, and patterning as acts of knowing their world.
Prior knowledge: Designed for early learners. No prior formal mathematics knowledge required. Teachers should assess current number knowledge before selecting appropriate entry points.
Curriculum alignment
- Number and Algebra — Number Strategies: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
- Number and Algebra — Patterns and Relationships: Generalise that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many.