Design Your Whare

Overview

Students design a simple floor plan for a whare using rectangles and labelled measurements. They calculate the horahanga (area) and paenga (perimeter) of their design, then explain how their calculations show the size and boundary of the whare. This beginner-friendly challenge builds from prior learning about measuring length and multiplying whole numbers.

Teacher note: “Paenga” is used here as the requested term for perimeter. In many mathematics resources, the Māori term is paenga. Use the terminology familiar to your school and explain both terms if needed.

Learning intentions

• WALT use a scale and measurements to create a floor plan.
• WALT calculate horahanga by finding the area of rectangles.
• WALT calculate Paenga by adding the lengths around a shape.
• WALT explain how our measurements help us describe a whare.

Success criteria

• I can draw a clear floor plan using rectangles and a simple scale.
• I can label the length and width of each part of my whare.
• I can correctly calculate the horahanga and Paenga.
• I can show my working and explain how I checked my answers.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: applying familiar mathematical ideas in a relevant, connected context.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: creating, testing and explaining a mathematical design.
• Mathematical practices: communicating mathematical thinking, using representations, and reasoning about measurement.

Lesson structure (50 minutes)

1. 0–5 min · Hook and connect. Teacher opens the hook and learning intention slides and shows a simple floor plan with one missing measurement, asking, “How could we work out how much floor space this whare has?” Students make a quick estimate and share what they already know about area, perimeter and scale.

2. 5–13 min · Teach the key ideas. Teacher uses the area and perimeter teaching slides to model a rectangle measuring 6 m by 4 m: horahanga is (6 \times 4 = 24\text{ m}^2), while painga is (6+4+6+4=20\text{ m}). Emphasise that area describes the space inside and perimeter describes the distance around the outside. Students use finger-tracing or a ruler to identify “inside” and “around”.

3. 13–18 min · Model the design task. Teacher displays the design instructions and worked example and sketches a basic floor plan made from two or three rectangles. Model choosing a scale, such as 1 square = 1 metre, labelling every outside length, and checking that connected lengths make sense. Students suggest one feature they might include, such as a sleeping area, entrance, kitchen or meeting space.

4. 18–33 min · Create a floor plan. Teacher distributes the whare floor-plan design worksheet and supports students to draft an individual design. Students draw a simple top-down plan using rectangles, include at least two connected spaces, choose a scale, label measurements and name each area. Encourage practical discussion: “Would people be able to move through this space?” and “Which lengths do we need to know?”

5. 33–43 min · Calculate and check. Teacher returns to the calculation and checking slides and conferences with each student, prompting them to split a compound design into rectangles if necessary. Students calculate the horahanga of each rectangle, combine areas where appropriate, and find the painga by adding the complete outside boundary. They record units, compare answers with a partner and check using a different strategy or by measuring the drawing.

6. 43–48 min · Share mathematical thinking. Teacher invites students to use the discussion prompt slides to present their design to a partner or the group. Students explain one design choice, state the total horahanga and painga, and identify one calculation they checked. Peers ask, “How do you know?” rather than simply judging whether an answer is correct.

7. 48–50 min · Exit reflection. Teacher displays the plenary and exit-question slide. Students complete the final boxes on the worksheet: “My whare has a horahanga of…” and “My painga is…” followed by one sentence explaining the difference between the two measurements.

Resources

• the complete teaching slide deck
• the whare floor-plan design worksheet
• Centimetre rulers
• Pencils, erasers and coloured pencils
• Squared paper or exercise books
• Whiteboard and pens
• Optional metre-square visual or grid displayed on the board
• Calculators for checking, if appropriate

Assessment

• During the hook and modelling, listen for whether students distinguish space inside from distance around.
• Check each plan for a usable scale, labelled lengths, correct units and a complete outside boundary.
• Review the worksheet and exit reflection for accurate calculations and an explanation of the difference between horahanga and Paenga/paenga. Ask students to correct one error they find.

Differentiation

• Support students with a pre-drawn rectangular outline, a scale of 1 square = 1 metre, and a formula reminder: area = length × width; perimeter = add all outside sides.
• Work with one student at a time using concrete language and physically trace the inside or outside of a shape. Provide a word bank including whare, horahanga, Paenga/paenga, length, width, metres and square metres.
• Pair students strategically so they can explain calculations aloud before recording them. Accept labelled sketches and oral explanations while developing written language.
• Extend confident students by asking them to create a compound shape with the same horahanga but a different Paenga, or to redesign the whare to increase floor space without increasing the boundary.