Squares and Rectangles

Overview

Lesson 7 of 10 in the unit “Area and Squared Numbers”. In a class of 29, students identify squares and rectangles, compare their areas, choose an efficient strategy, and explain their reasoning using dimensions and square units.

Learning intentions

• WALT compare the area of squares and rectangles.
• WALT calculate area by counting square units, multiplying dimensions, or using squared numbers.
• WALT choose and explain an efficient strategy.
• WALT communicate mathematical thinking clearly using diagrams, words and numbers.

Success criteria

• I can identify whether a shape is a square or rectangle.
• I can choose a suitable strategy for finding its area.
• I can calculate and compare areas accurately.
• I can justify my answer using dimensions and square units.

Curriculum links

• Measurement: calculating, comparing and communicating area using square units and standard measurement ideas.
• Number and algebra: using multiplication facts, factors and squared numbers to solve problems.
• Mathematical communication: explaining strategies, checking solutions and comparing the efficiency of methods.
• Key competencies: thinking; using language, symbols and texts; managing self; relating to others.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and connect

Open with the hook and learning intention slides. Display two rectangles that look different but have the same area, such as 3 × 8 and 4 × 6. Ask: “Which shape has the greater area? How could we prove it?” Students make a quick prediction, then share with a partner.

2. 5–12 minutes – Teach and model

Use the comparison and modelling slides to review that area is the amount of surface covered by equal-sized square units. Model a 4 × 6 rectangle by counting rows and columns, then multiplying 4 × 6 = 24 square units. Model a 5 × 5 square and connect 5 × 5 to 5², explaining that a square has equal side lengths. Emphasise that area is written in square units, such as cm².

3. 12–17 minutes – Strategy sort

In groups of four or five, students sort prepared shape cards into “square”, “rectangle but not square”, and “not enough information”. Provide groups with varied-level cards and a strategy-choice scaffold. Students may use counters or square tiles to check shapes. Guide discussion with: “What do you notice about the side lengths?” and “Would counting or multiplication be more efficient here?”

4. 17–30 minutes – Collaborative investigation

Distribute the squares and rectangles investigation worksheet. Students work in pairs, with one partner measuring or identifying dimensions and the other recording. They calculate areas using counting, multiplication, or squared numbers, then compare selected pairs. Encourage students to circle their chosen strategy and complete the sentence: “My strategy was efficient because…”

Use the Perimeter and Area Formula Mat as a reference for students who need a visual reminder of area representations. Move between pairs, checking that students distinguish area from perimeter and include square units.

5. 30–38 minutes – Equal-area challenge

Ask pairs to find two different rectangles with equal area, for example 2 × 12 and 3 × 8. Students draw both on bold-lined graph paper and explain how the dimensions produce the same number of square units. Invite selected pairs to share different strategies and discuss which was most efficient and why.

6. 38–43 minutes – Share and assess

Return to the discussion and explanation slides. Display a shape such as a 6 × 6 square and ask students to give a counting, multiplication and squared-number explanation. Discuss when each method is useful. Address common errors, including confusing side length with area and writing units without “squared”.

7. 43–45 minutes – Exit check

Students complete the final question on the squares and rectangles investigation worksheet independently: “A square has side length 7 cm. Find its area and explain the most efficient strategy.” Collect responses to inform the next lesson.

Resources

• the complete squares and rectangles slide deck
• the squares and rectangles investigation worksheet
• the Perimeter and Area Formula Mat
• Prepared shape cards at varied levels
• Square tiles, counters or centimetre grid paper
• Bold-lined graph paper
• Rulers and pencils
• Whiteboards or scrap paper
• Highlighters and coloured pencils

Assessment

• Observe group sorting and questioning: can students identify squares and rectangles and explain their decisions?
• Check worksheet calculations for correct dimensions, strategies and square units.
• Use the independent exit response to assess whether students can select and justify an efficient strategy.

Differentiation

• Support: provide smaller shapes, pre-labelled dimensions, manipulatives, a visual strategy-choice scaffold and sentence stems such as “I used ___ because ___.”
• Dyslexia-friendly options: use symbol-supported shape cards, clear sans-serif print, minimal copying, short instructions, repeated examples, oral questioning and bold-lined graph paper.
• Down syndrome support: use one-step directions, consistent visual cues, repeated modelling, concrete materials, partner support and guided discussion with extra processing time.
• Extension: find three or more pairs of different shapes with equal area, record their dimensions, and explain the relationship between factors and area. Ask students to decide which method is most efficient for each pair and defend their choice.