Design Your Own Shapes

Overview

Lesson 8 of 10 in Area and Squared Numbers. In groups and independently, students design squares and rectangles that meet given conditions, label dimensions, calculate area, and explain their mathematical thinking.

Learning intentions

• WALT create squares and rectangles with given dimensions or area.
• WALT label side lengths and calculate area using square units.
• WALT explain how our design meets the conditions.
• WALT use mathematical language to communicate our thinking.

Success criteria

• I can create a shape that meets the conditions.
• I can label the dimensions correctly.
• I can calculate and record the area in square units.
• I can clearly explain how I know my answer is correct.

Curriculum links

• Measurement: estimating, measuring and calculating area using square units.
• Number and algebra: using multiplication facts and squared numbers to calculate area.
• Geometry: recognising and describing properties of squares and rectangles.
• Mathematical communication and problem-solving: explaining strategies, checking results and working collaboratively.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and connection Display an image of a tiled courtyard and ask: “How could we prove how much space this design covers?” Open with the hook and learning intention slides. Revisit the area rule: area of a rectangle = length × width; area of a square = side × side.

2. 5–12 minutes – Model a design Demonstrate a condition such as: “Create a rectangle with an area of 24 square units.” Build it with square tiles or draw it on a grid. Label 6 units by 4 units, calculate 6 × 4 = 24, and explain how the dimensions and area can be checked. Complete the first example together using the guided design worksheet.

3. 12–15 minutes – Explain the challenge Place students in mixed-ability groups of three or four, with clear roles such as designer, tile builder or drawer, calculator, and explainer. Show the task instructions in the design challenge and success criteria slides. Each student chooses a tile, grid-paper or digital drawing option.

4. 15–30 minutes – Design and calculate Students complete two or more designs from the target cards on the guided design worksheet. Suggested conditions include:

• Create a square with a side length of 5 units.
• Create a rectangle measuring 3 units by 8 units.
• Create a shape with an area of 36 square units.
• Create two different rectangles with the same area. Students draw or build each shape, label all required dimensions, write the multiplication equation and record the area in square units. Circulate, asking: “What does each number represent?” and “How can you check your area?”

5. 30–39 minutes – Share and compare Pairs select one design to explain to another pair. Use the discussion prompt slides to support mathematical talk: “Our dimensions are…”, “The area is… because…”, and “We checked this by…”. Invite two or three groups to share different designs with the same area and discuss why their dimensions can differ.

6. 39–45 minutes – Reflect and assess Students complete the final reflection on the guided design worksheet: draw one successful design, label it, calculate its area, and finish the sentence, “I know my answer is correct because…”. Use the plenary and reflection slide to revisit the learning intentions and collect work for assessment.

Resources

• the area design lesson deck
• the guided design worksheet
• Square tiles or other square units
• Grid paper and pencils
• Rulers and coloured pencils
• Optional digital drawing tool or interactive whiteboard
• Prepared target cards with dimensions and areas
• Large-print, labelled shape templates
• Mini whiteboards for checking calculations

Assessment

• Observe whether students create shapes that meet the conditions and correctly label length and width.
• Check equations and area calculations, including the use of square units and multiplication or repeated addition.
• Assess the explanation for accurate mathematical vocabulary, logical reasoning and a valid method of checking.
• Use the final reflection to identify students needing further practice with dimensions, multiplication facts or the distinction between perimeter and area.

Differentiation

• Support: provide partially completed templates, smaller target numbers, pre-drawn grids and a worked example. Allow students to build with tiles before recording, and pair them with a supportive peer.
• Dyslexia-friendly options: use large grids, uncluttered sans-serif text, high contrast and short numbered instructions. Present design instructions separately from recording instructions; read instructions aloud and allow an oral explanation instead of written presentation.
• Down syndrome support: use one-step visual prompts, concrete tiles, repeated modelling and a reduced choice of targets. Provide extra processing time, check understanding privately, and accept pointing, drawing, oral explanation or supported writing.
• Extension: design several different shapes with the same area, then investigate the largest possible area within a fixed perimeter. Ask students to justify their conclusion with examples or a table.