Best for
Equivalent-ratio work, recipe scaling, map and model contexts, and early percentage and rate connections.
Pāngarau / Mathematics • Years 7-10 • Multiplicative thinking
Ratios and Proportions
Use this handout to help ākonga see ratios as relationships, not just pairs of numbers. Students need to compare, scale, simplify, and explain why proportional thinking fits the situation.
Free multiplicative-thinking base, premium adaptation path
This page already includes equivalent-ratio prompts, scale contexts, and write-on reasoning space. Te Wānanga becomes useful when you want the same scaffold rebuilt around a class enterprise, food technology context, or a more advanced proportion pathway.
- Generate support versions with visual ratio tables and smaller whole-number steps.
- Swap in local contexts such as recipe scaling, kapa haka costume design, or school maps.
- Save the adapted version in My Kete and keep refining it in Creation Studio.
Kaiako planning snapshot
- Use length: 40-50 minutes.
- Grouping: Whole-class worked example, then pairs for ratio tables, then independent application.
- Prep: Visual ratio models or counters can help if learners need concrete support.
- Teaching move: Ask “What multiplicative relationship stays the same?”
Resources already provided
- Ratio-type quick guide
- Equivalent-ratio table
- Scale and recipe problem set
- Support, core, and stretch pathways
- Teacher-only curriculum companion
If the lesson mentions a ratio table, scale challenge, or write-on explanation space, that scaffold is already on the page.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning how ratios compare quantities in a multiplicative way.
- We are learning how to find equivalent ratios and solve proportion problems.
- We are learning how to explain why a proportional strategy is appropriate.
Paearu Angitu / Success Criteria
- I can write and simplify a ratio correctly.
- I can find an equivalent ratio or missing value by scaling.
- I can explain what stays the same in a proportional situation.
Curriculum integration / Te Mātaiaho alignment
The companion page links this handout to Phase 4 expectations around whole-number ratios, rates, and proportional scaling, while giving a bridge for emerging learners who still need visual ratio reasoning.
Why this matters in Aotearoa classrooms
Ratios show up in recipes, maps, sports stats, budget comparisons, scale drawings, and scientific mixtures. Students need to recognise when a situation is additive and when it is multiplicative.
There is also a natural Aotearoa design lens here: scaling a recipe for a whānau event, enlarging a pattern, or planning a map route all depend on the relationship staying consistent.
A small manaakitanga lens is genuine here too: when kai, resources, or shared materials are being scaled fairly for others, proportional thinking helps students act carefully rather than approximately.
Quick ratio guide
Part to part
Example: 3 red counters to 2 blue counters is 3:2.
Part to whole
Example: 3 red out of 5 total counters is 3:5.
Equivalent ratios
3:2, 6:4, and 9:6 describe the same relationship because each part is scaled equally.
Rates
A rate compares quantities with different units, such as 60 km per hour or $4 per item.
Equivalent-ratio table
| Original ratio | Scale factor | Equivalent ratio | How I know it matches |
|---|---|---|---|
| 2 : 3 | × 2 | ________ | ________________________________ |
| 5 : 8 | × 3 | ________ | ________________________________ |
| 12 : 18 | ÷ 6 | ________ | ________________________________ |
Scale contexts
Recipe scale-up
A recipe serves 4 people and uses 2 cups of rice. How much rice is needed for 10 people if the proportion stays the same?
Map scale
On a school map, 1 cm represents 5 m. If the distance on the map is 7.5 cm, what is the real distance?
Support, core, and stretch pathways
Support
Use visual ratio tables, double-number lines, and simple whole-number scale factors.
Core
Simplify ratios, find missing values, and explain proportional reasoning using scale factors.
Stretch
Create a real-world rate or ratio problem and include a second method for checking the answer.
My explanation
How can you tell when a situation is proportional and when it is not?
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.
Tuhia ōu whakaaro · Write Your Thoughts
Reflect on what you have learned today. What was the most important idea? What question do you still have?
Ngā Rauemi Tautoko · Support Materials
This handout is designed to be used alongside the broader unit resources available at Te Kete Ako handouts library. This handout stands on its own; it is not part of a linked unit planner. All resources are provided — no additional preparation is required to use this handout in your classroom.