Squared Numbers

Overview

Lesson 6 of 10 in Area and Squared Numbers. Students use physical and visual square arrays to connect equal side lengths with squared notation and calculate the area of squares.

Learning intentions

• WALT recognise a square array with equal rows and columns.
• WALT connect square arrays to squared numbers such as 2², 3² and 4².
• WALT explain that a squared number means a number multiplied by itself.
• WALT calculate the area of a square using side × side.

Success criteria

• I can identify a square array.
• I can explain what a squared number represents.
• I can write a square number using multiplication and squared notation.
• I can calculate the area of a square using side × side.

Curriculum links

• Number and algebra: use multiplication facts and recognise patterns in whole numbers.
• Measurement: calculate and compare area using square units.
• Geometry: recognise and describe squares, including equal side lengths.
• Mathematical processes and competencies: communicate mathematical ideas, use representations, and justify thinking.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and prior knowledge Open with the square-array hook. Display a 4 by 4 arrangement of dots or tiles and ask: “How many are there? What makes this arrangement a square?” Students think, pair-share, then explain how they counted. Remind students that area measures the space inside a shape in square units.

2. 5–13 minutes – Explicit teaching Use the teaching slides on square arrays to model 2 × 2, 3 × 3 and 4 × 4 arrays. Build each with tiles or counters, colour-code one side and the matching side, and record:

• 2 × 2 = 4, so 2² = 4
• 3 × 3 = 9, so 3² = 9
• 4 × 4 = 16, so 4² = 16 Read the notation aloud: “three squared means three multiplied by three.” Emphasise that 3² is not 3 × 2 or simply doubling 3.

3. 13–23 minutes – Partner array investigation In pairs, students use counters, square tiles or drawn grids to make 2 × 2, 3 × 3 and 4 × 4 arrays. They complete the matching activity on the squared numbers investigation sheet, linking each array to its multiplication sentence, squared notation and area. Partners take turns explaining: “The side length is __, so the area is __ × __ = __ square units.”

4. 23–31 minutes – Sort and discuss Show examples from the sorting and discussion slides. Pairs decide whether each representation is a square array, a rectangle that is not a square, or neither. Include examples such as 3 × 3, 2 × 5, 4 × 4 and 5 + 5. Ask: “How do you know?” Address the misconception that squared means doubling. Students may respond orally, point to an example, or use tiles rather than writing a long explanation.

5. 31–40 minutes – Independent practice Students complete the remaining questions on the squared numbers practice sheet. Tasks include drawing arrays, writing 5² and 6² as multiplication, calculating areas, and identifying incorrect statements. Support students to use the perimeter and area formula mat as a visual reminder of the square area formula. Circulate and ask students to explain their reasoning, not just provide answers.

6. 40–45 minutes – Plenary and exit check Return to the plenary slides. Ask students to complete these orally or on a small piece of paper:

• What does 4² mean?
• What is the area of a square with side length 5 units?
• Is 3² the same as 3 × 2? Explain. Invite several students to share. Record common errors to revisit in the next lesson.

Resources

• the squared numbers teaching deck
• the squared numbers investigation and practice sheet
• Square tiles, counters or linking cubes
• Large grid paper or mini-whiteboards
• Pencils, coloured pencils and rulers
• Prepared 2 × 2, 3 × 3 and 4 × 4 arrays
• the perimeter and area formula mat
• Small paper slips or mini-whiteboards for the exit check

Assessment

• Observe whether students build arrays with equal side lengths and distinguish squares from non-square rectangles.
• Listen for accurate mathematical language: “side length”, “multiplied by itself”, “squared”, and “square units”.
• Check worksheet responses and the exit check for correct connections between arrays, multiplication, squared notation and area.

Differentiation

• Provide physical square arrays, uncluttered visual models and colour-coded matching sides. Keep the initial number range to 2²–4² for learners needing support, then introduce 5² and 6² when ready.
• Model individually or in a small group using concrete choices: “Is this 3 × 3 or 3 × 2?” Read symbols aloud and repeat sentence frames such as “___ squared means ___ × ___.”
• Use dyslexia-friendly presentation: clear sans-serif print, generous spacing, minimal visual clutter, high-contrast colours and one question at a time. Allow students to point, build, draw or explain orally instead of completing extended writing.
• Support the student with Down syndrome through a peer partner, repeated routines, reduced choices, concrete materials and frequent checking for understanding. Celebrate accurate demonstrations and verbal responses.

Extension

• Students investigate the pattern 1², 2², 3², 4², 5² and 6². They predict the next two square numbers and explain how the increases change.
• Challenge students to find two different ways to represent 25 and explain why only 5 × 5 makes a square array with side length 5.