Best for
Halves, quarters, equal parts, fractions of sets, and early comparison language grounded in real sharing situations.
Pāngarau / Mathematics • Years 3-6 • Equal parts and sharing
Fractions Basics
Use this handout to help ākonga understand that fractions describe equal parts of a whole or equal shares of a set. Fraction teaching becomes clearer when students cut, sort, share, and explain instead of only memorising the top and bottom numbers.
Free fractions foundation, premium adaptation path
This page already gives equal-part prompts, set-sharing tasks, and write-on explanation space. Te Wānanga becomes useful when you want the same scaffold rebuilt for junior learners, bilingual maths routines, or more visual support.
- Generate support versions with simpler shapes, fewer items, or more oral-response prompts.
- Swap in local contexts such as fruit sharing, sports equipment, or classroom collections.
- Save adapted copies in My Kete and refine them later in Creation Studio.
Kaiako planning snapshot
- Use length: 35-45 minutes.
- Grouping: Whole-class modelling, then pairs or independent follow-through.
- Prep: Paper strips, counters, paper circles, or quick sketched food and set models.
- Teaching move: Ask "Are the parts equal?" before asking "What fraction is it?"
Resources already provided
- Equal-part check task
- Halves and quarters language prompts
- Fractions-of-sets practice
- Write-on explanation space
- Teacher-only curriculum companion
If the lesson mentions shapes, fair shares, fractions of sets, or simple explanation writing, that scaffold already exists on this page.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning how fractions describe equal parts of a whole or a set.
- We are learning how to identify halves and quarters in different models.
- We are learning how to explain whether sharing is fair and equal.
Paearu Angitu / Success Criteria
- I can tell whether parts are equal.
- I can label one half and one quarter correctly.
- I can explain a fraction of a set using words, numbers, or a drawing.
Curriculum integration / Te Mātaiaho alignment
The companion page links this handout to halves, quarters, fractions of sets, equal sharing, and using a known fraction to reason about the whole. The same page also helps kaiako keep the maths language precise without overcomplicating the notation too early.
Why fraction basics matter in Aotearoa classrooms
Early fraction ideas grow out of fair sharing: splitting fruit, cutting baking, sharing equipment, or dividing a collection so everyone gets the same amount. Students need to see that equal shares matter more than the shape or arrangement alone.
This also creates a natural bridge to classroom language such as hautau, and to values of manaakitanga and fairness when students talk through how a whole or set has been shared.
What makes a fraction model fair?
Equal parts
The whole must be cut or grouped into parts of the same size.
Same whole
We can only compare fractions fairly if the whole is the same size.
One half
One of two equal parts, or one of two equal groups in a set.
One quarter
One of four equal parts, or one of four equal groups in a set.
Check the model
| Situation | Is it a fair fraction model? | Why or why not? |
|---|---|---|
| A sandwich is cut into two same-size pieces. | ||
| A pizza is cut into four pieces, but one piece is much bigger. | ||
| Eight counters are shared equally between two people. |
Show the fraction in three ways
Fraction
1/4
Draw or shade it
Use a set example
Support, core, stretch
Support
Stay with halves and quarters using concrete materials and teacher-guided sharing.
Core
Identify halves and quarters in shapes and sets, then explain how you know the parts are equal.
Stretch
If one quarter of a set is 3, work out how many objects are in the whole set.
Students may respond with counters, drawings, oral explanation, or full written sentences. The goal is still precise fraction reasoning.
Fractions of sets
| Prompt | My answer | How I know |
|---|---|---|
| One half of 10 counters is... | ||
| One quarter of 12 shells is... | ||
| If one quarter of a set is 4, the whole set is... |
My fraction explanation
Explain why a fraction is not fair if the parts are different sizes.
Hononga Marautanga · Curriculum Alignment
Curriculum alignment for this handout has not yet been verified against the live curriculum statements. A generated placeholder that stood here was removed on 2026-08-29 because it matched no real statement.
Aronga Mātauranga Māori
Mathematics has always been part of mātauranga Māori — in the navigation of Te Moana-nui-a-Kiwa, in the architectural precision of wharenui, in the sophisticated storage and accounting systems of rua kūmara, and in the patterns of kōwhaiwhai and tukutuku that encode mathematical relationships in visual form. When Māori students engage with mathematics, they are not encountering something foreign: they are meeting a domain of knowledge that their tīpuna practised with extraordinary sophistication. Framing mathematical learning through whakapapa — connecting concepts to real Māori contexts — is not "cultural add-on" but recognition of where much mathematical knowledge lives in this land.
Ngā Rauemi Tautoko · Support Materials
This handout is designed to be used alongside the broader unit resources available at Te Kete Ako handouts library. Related resources from the same unit are linked in the unit planner. All resources are provided — no additional preparation is required to use this handout in your classroom.