Area with Grids

Overview

In this first lesson of a two-lesson unit, students develop area as the amount of surface covered by equal-sized square units. They estimate, measure and compare rectangles and right-angled triangles using 1 cm² grids, then connect rectangular arrays to multiplication and investigate different dimensions that produce the same area.

Learning intentions

Students will:

• estimate and measure area using square centimetres;
• use a 1 cm² grid and rows × columns to calculate rectangular area;
• determine the area of right-angled triangles by counting squares or relating them to half a rectangle;
• create and compare rectangles with equal areas;
• explain strategies using diagrams, mathematical language and number sentences.

Success criteria

• I can use a 1 cm² grid to measure area.
• I can calculate the area of a rectangle using rows × columns.
• I can find the area of a right-angled triangle on a grid.
• I can explain how rectangles with different side lengths can have equal areas, using an array and square centimetre units.

Curriculum links

• Area — estimate, measure and compare surfaces using square centimetres and the grid structure.
• Two-dimensional shapes — compare and describe rectangles and right-angled triangles.
• Transformations and composition — recognise a right-angled triangle as part of, or half of, a rectangle.
• Multiplicative relations and Working Mathematically — use arrays, multiplication, reasoning, estimation and clear mathematical communication.

Lesson structure (75 minutes)

1. 0–5 min · Hook and estimate. Open with the hook and estimation slide showing two rectangles that look different but may cover the same area; students silently estimate which has greater area, then justify their first idea to a partner. Teacher explains that area measures the surface covered, not the distance around a shape, and introduces the investigation question: “Can rectangles with different side lengths have the same area?”

2. 5–20 min · I do: model grids, arrays and triangles. Use the modelling slides and display a rectangle on a 1 cm² grid; model counting the rows and columns, connecting the array to length × width, and recording the answer with the unit cm². Explicitly teach and display square centimetre, rectangle, triangle, grid, array, length, width and area. Teacher then models a right-angled triangle on a grid by counting covered squares and by enclosing it in a rectangle where the triangle is half the rectangle; students show estimates and calculations on mini-whiteboards, including “What is the area and how do you know?”

3. 20–28 min · Guided example and checking. Present two rectangles, 3 × 8 and 4 × 6, using the equal-area discussion slide. Students calculate both areas, draw matching arrays on squared paper and discuss whether different side lengths can produce the same area. Teacher checks that students distinguish length from area and always record square centimetres, addressing common errors such as counting only the boundary or adding the side lengths.

4. 28–45 min · We do: paired shape investigation. Place students in pairs with square-centimetre grid overlays, rulers, shape cards, tiles and squared paper. Distribute the paired area investigation sheet for estimates, diagrams, calculations and explanations. Pairs rotate through shape cards, first estimating, then overlaying or sketching a grid and finding each area by efficient counting or multiplication; for triangles, students count covered squares or use a related rectangle. Teacher circulates, asks “How could you check?” and selects examples for discussion.

5. 45–53 min · Equal-area construction. Students use tiles or squared paper to build at least two rectangles with an area of 24 cm², recording each dimension and number sentence on the equal-area recording section. Teacher pauses the class to compare examples such as 3 × 8 and 4 × 6, reinforcing that the dimensions may change while the total number of square centimetres stays the same.

6. 53–65 min · You do: Area Detective. Students independently complete the Area Detective task: calculate several rectangle and right-angled triangle areas, then design two or more rectangles with an area of 24 cm². They must include an array diagram, a multiplication number sentence and a written explanation. Teacher conferences with selected students, checking estimation, accurate grid use, efficient strategies and appropriate units. Students who finish early investigate whether they can find every whole-number rectangle for 24 cm² and justify how they know none are missing.

7. 65–75 min · Plenary and exit assessment. Use the plenary and exit-ticket slide to display three questions: calculate the area of a 5 × 7 rectangle; find the area of a right-angled triangle shown on a grid; and give two different side lengths for a rectangle with an area of 18 cm². Students complete the questions independently on mini-whiteboards or the final section of the exit-ticket section, then share one strategy. Teacher collects responses to identify students requiring further support in Lesson 2.

Resources

• the area introduction and modelling deck
• the area investigation and exit-ticket worksheet
• Square-centimetre grid overlays
• Centimetre grid paper and squared paper
• Rulers
• Rectangle and right-angled triangle shape cards
• Square tiles or centimetre grid tiles
• Mini-whiteboards, markers and erasers
• Board or visualiser

Assessment

• Observe estimates, grid counting, use of arrays and mathematical vocabulary during modelling and paired investigation.
• Check worksheet diagrams and calculations for correct units, efficient strategies and explanations of equal areas.
• Use the exit ticket to assess rectangular area, triangular area and construction of equal-area rectangles; group students for the next lesson according to identified needs.

Differentiation

• Support students with pre-drawn 1 cm² grids, tiles, smaller dimensions, partially completed arrays and the sentence starter: “The area is ___ cm² because ___.”
• Allow students to physically build arrays before recording multiplication, and pair students strategically for discussion and checking.
• Provide enlarged grids, high-contrast resources and reduced visual clutter for students requiring additional visual or fine-motor support.
• Extend confident students by asking them to find and justify all whole-number rectangles for a given area, compare their factor pairs and explain why rotations represent the same dimensions.