Best for
Grid-based geometry, measurement lessons, design briefs, and tasks where students need to explain which measure fits the context.
Pāngarau / Mathematics • Years 5-8 • Measurement and geometry
Area and Perimeter
Use this handout to help ākonga separate two ideas that are often mixed together: perimeter measures the distance around a shape, while area measures the space inside it. Students need both pictures and calculations to make the difference stick.
Free measurement base, premium adaptation path
This page already contains models, formulas, comparison tasks, and a design brief. Te Wānanga becomes useful when you want the same structure rebuilt around a school garden, classroom redesign, or a more supported or extended geometry pathway.
- Generate simpler square-grid versions for support learners.
- Swap in local spaces such as a māra kai bed, sports court, or community plan.
- Save an adapted version in My Kete and keep refining it in Creation Studio.
Kaiako planning snapshot
- Use length: 40-50 minutes.
- Grouping: Whole-class model, then partner practice, then design challenge.
- Prep: Rulers and coloured pencils if students will shade area and trace perimeter.
- Teaching move: Keep asking “Do we care about the inside space or the outside distance?”
Resources already provided
- Area vs perimeter comparison cards
- Calculation table
- Design brief with grid space
- Support, core, and stretch pathways
- Teacher-only curriculum companion
If the lesson mentions a design task, comparison prompts, or write-on calculation space, those materials are already on this page.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning how area and perimeter measure different things.
- We are learning how to calculate perimeter and area using units and multiplication.
- We are learning how to choose the right measure for a real design problem.
Paearu Angitu / Success Criteria
- I can explain the difference between area and perimeter.
- I can calculate the perimeter and area of rectangles correctly.
- I can justify which measurement matters most in a given context.
Curriculum integration / Te Mātaiaho alignment
The companion page links this handout to Phase 2 measurement expectations around perimeter, area of rectangles, and irregular-shape reasoning on grids.
Why this matters in Aotearoa classrooms
Students meet area and perimeter in garden planning, fabric design, floor plans, sports spaces, and environmental projects. It matters that they can name the measurement they actually need.
A natural mātauranga Māori connection here is design with purpose: whether a space is being planned for movement, planting, gathering, or display, measurement serves a real decision. The mathematics is useful because it helps us care for space accurately.
Area or perimeter?
Perimeter
The distance around the outside edge of a shape. Use units such as cm or m.
Area
The amount of space inside a shape. Use square units such as cm² or m².
When perimeter matters
Fencing a garden, edging a court, or measuring ribbon around a border.
When area matters
Planning carpet, paint coverage, planting space, or the size of a display board.
Calculate and compare
| Shape | Measurements | Perimeter | Area | What do you notice? |
|---|---|---|---|---|
| Rectangle A | 8 cm by 3 cm | ________ | ________ | ________________________________ |
| Rectangle B | 6 cm by 4 cm | ________ | ________ | ________________________________ |
| Rectangle C | 10 cm by 2 cm | ________ | ________ | ________________________________ |
Challenge: Which two shapes have the same perimeter but different areas, or the same area but different perimeters?
Design brief: plan a small māra kai bed
You have 20 m of edging for a rectangular garden bed. Sketch one possible design, label the side lengths, then calculate the area inside the bed.
My side lengths
Length: __________
Width: __________
My calculations
Perimeter: __________
Area: __________
Support, core, and stretch pathways
Support
Shade area and trace perimeter on square grids before moving to calculations.
Core
Calculate the perimeter and area of rectangles, then compare shapes that share one measure but not the other.
Stretch
Design two different rectangles with the same perimeter but different areas and explain why that happens.
My explanation
When would a builder, gardener, or event planner care more about perimeter than area? When would area matter more?
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
This resource sits within a kaupapa that recognises mātauranga Māori as a living knowledge system with its own frameworks, values, and ways of understanding the world. The New Zealand Curriculum calls for learning that reflects the bicultural partnership of Te Tiriti o Waitangi, which means every subject area has an obligation to engage authentically with Māori perspectives — not as cultural decoration but as substantive contributions to how we understand our topics. The concepts of manaakitanga (care for others), kaitiakitanga (guardianship), whanaungatanga (relationship and belonging), and tino rangatiratanga (self-determination) provide a values framework applicable across all learning areas, and all are relevant to the work in this handout.
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.