Arrays Build Area

Overview

Lesson 3 of 10 in Area and Squared Numbers. Students use square tiles to build rectangular arrays, describe rows and columns, and connect the total number of squares with multiplication to find area.

Learning intentions

• WALT connect rectangular arrays to area.
• WALT describe the rows and columns in an array.
• WALT calculate the area of a rectangle by counting or multiplying.
• WALT explain how two different rectangles can have the same area.

Success criteria

• I can describe the rows and columns in an array.
• I can make a rectangular array using square tiles.
• I can calculate its area by counting squares or multiplying rows by squares in each row.
• I can find different rectangles with the same area.

Curriculum links

• Use multiplication and equal groups to solve problems involving whole numbers.
• Identify and describe features of two-dimensional shapes, including rectangles and squares.
• Measure and calculate area using square units and relate area to arrays.
• Mathematical and Statistical Inquiry: represent, explain and justify mathematical thinking; participate and contribute collaboratively.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and prior knowledge Open with the array hook slide. Display a rectangle made from 3 rows of 4 squares and ask: “How many squares are there? How could we work it out without counting every square?” Invite students to turn and talk. Listen for “3 groups of 4”, “4 + 4 + 4” and “3 × 4”. Clarify that area is the amount of surface covered, measured in square units.

2. 5–12 minutes – Explicit teaching: rows and columns Use the rows, columns and area slides to model a 3-by-4 array. Trace across one row in one colour and down one column in another. Say consistently: “Rows go across. Columns go down.” Record: area = number of rows × number in each row. Model both counting (12 squares) and multiplication (3 × 4 = 12 square units). Check understanding with quick questions: “How many rows? How many in each row? What is the area?”

3. 12–25 minutes – Build and describe arrays Place students in 7 mixed-ability groups of four or pairs within groups. Give each pair square tiles or linking cubes and ask them to build teacher-called arrays, such as 2 × 6, 3 × 5 and 4 × 4. Students colour-code or point to the rows and columns, then rehearse orally: “My array has __ rows, __ squares in each row, so its area is __ square units.” Use the build-and-talk instruction slide. Circulate, rebuilding arrays with students who need concrete support and checking vocabulary frequently.

4. 25–35 minutes – Record and apply Distribute the arrays and rectangles worksheet. Students draw or complete rectangular arrays, label rows and columns, and calculate area by counting and multiplication. Read instructions aloud and allow students to explain answers orally before writing. Pause halfway for a whole-class check using one example. Ask: “Would 4 × 3 give the same area as 3 × 4? What changes in the picture, and what stays the same?”

5. 35–41 minutes – Same area investigation Use the same-area challenge slide. Give each pair a target such as 12 or 24 square units. Students find as many different rectangular arrays as possible, using tiles first and then drawing them. Invite pairs to share, for example, 2 × 6 and 3 × 4. Emphasise that the side lengths differ but the area is the same. Early finishers can find rectangles for a larger target.

6. 41–45 minutes – Plenary and assessment Display the reflection slide. Students respond orally or on the final worksheet prompt: “A rectangle has 5 rows and 3 squares in each row. Its area is ___ because ___.” Select two students to explain their reasoning. Revisit the WALT and ask students to self-assess against the success criteria using a verbal response or simple finger signal.

Resources

• the complete lesson slide deck
• the arrays and rectangles worksheet
• Square tiles, counters or linking cubes
• Large grid paper and thick coloured pencils
• Whiteboard and markers
• Prepared arrays or enlarged grid examples
• Mini-whiteboards or scrap paper
• Visual word prompts: row, column, array, area, square unit

Assessment

• Observe whether students make rectangular arrays accurately and distinguish rows from columns.
• Listen for correct explanations linking repeated addition or multiplication to area.
• Check worksheet responses, especially the use of square units and the same-area investigation.

Differentiation

• Support learners with concrete tiles before drawings or symbols; provide partially completed arrays and ask one question at a time.
• Colour-code rows and columns, use large grid paper, and keep language consistent: “rows go across; columns go down.”
• For dyslexic students, provide oral rehearsal, clear sans-serif print, minimal written text, enlarged examples and extra processing time.
• For the student with Down syndrome, use a peer model, repeated two-step instructions, choice of smaller arrays, hand-over-hand support only when appropriate, and frequent encouragement and checks for understanding.
• Extend confident learners by asking them to find all rectangular arrays for 24 square units and explain why a square is also a rectangle.