Measuring with Squares

Overview

Lesson 2 of 10 in Area and Squared Numbers. Students develop the idea that area measures the surface covered by equal-sized square units, using tiles to cover objects and rectangles accurately.

Learning intentions

• WALT measure area using square units accurately.
• WALT cover a surface with equal-sized square units.
• WALT record and explain how we checked an area measurement.
• WALT notice that rearranging the same square units does not change the area.

Success criteria

• I can place square units without gaps or overlaps.
• I can count and record the number of square units used.
• I can explain how I checked my answer.
• I can explain why rearranging the same square units keeps the area the same.

Curriculum links

• Measurement: estimate, measure and compare area using informal and standard square units.
• Number and Algebra: recognise equal groups and connect repeated rows of squares with multiplication.
• Geometry: describe and represent rectangles and their arrangement of square units.
• Key competencies: thinking; managing self; participating and contributing; using language, symbols and texts.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and connect

Open with the area introduction slides. Show a rectangle covered by squares, including an example with a gap and an overlap. Ask: “Which measurement would be trustworthy, and why?” Briefly revisit that area describes the amount of surface inside a shape, not the distance around it.

2. 5–11 minutes – Explicit teaching and modelling

Display the success criteria and model measuring a small classroom object or drawn rectangle with square tiles. Think aloud: place tiles edge to edge, leave no gaps or overlaps, count systematically, and record “__ square units”. Model checking by counting again in rows and then by adding the rows.

Introduce the idea that one tile is one square unit. If appropriate, show that 3 rows of 4 tiles can be counted as 4 + 4 + 4 or 3 × 4, preparing students for later work with squared numbers and area formulas.

3. 11–14 minutes – Pair task instructions

Distribute the square-unit area recording sheet to pairs and provide square tiles and selected small objects or drawn rectangles. Revisit the task directions on the pair investigation slides: choose a surface, cover it carefully, count the tiles, record the area, and explain the checking method.

Assign mixed-ability pairs with clear roles: placer and checker. Remind students to swap roles for the next object.

4. 14–30 minutes – Paired investigation

Pairs measure three or four classroom objects or pre-drawn rectangles. They record the object or rectangle, number of square units, a sketch or row arrangement, and how they checked their answer.

Circulate and ask: “How do you know there are no gaps?” “What will you count first?” “Could you organise the tiles into rows?” Provide verbal instructions, physical demonstration and a short numbered task card on the worksheet rather than expecting students to read a long explanation.

5. 30–38 minutes – Compare and discuss

Open the comparison and rearrangement slides. Select two pairs with different arrangements of the same number of tiles. Invite them to show their work and explain their checking method.

Give pairs a set number of tiles and ask them to make two different rectangles. Discuss: “Did the area change when the tiles were rearranged?” Establish that area stays the same when the same square units are used, provided every unit is counted once.

6. 38–45 minutes – Plenary and formative assessment

Students complete the final reflection on the check-and-explain section: draw or describe how they measured one shape and complete the sentence, “I know my answer is accurate because…”. Invite two or three students to share.

Revisit the WALT and success criteria on the plenary slides. Collect worksheets or photograph selected examples for the next lesson. Note students who still leave gaps, overlap tiles or count inconsistently.

Resources

• the area introduction and teaching slide deck
• the square-unit area recording sheet
• Square tiles, linking cubes with square faces, or paper square units
• Small flat classroom objects, such as books, whiteboards or pencil cases
• Pre-drawn rectangles on squared or plain paper
• Pencils, coloured pencils and rulers
• A demonstration rectangle and large square units
• Optional mini whiteboards for quick responses

Assessment

• Observe whether students place units edge to edge without gaps or overlaps.
• Check recording sheets for correct counting, the label “square units”, a drawing or row arrangement, and a clear checking explanation.
• Use questioning and the final reflection to identify understanding of conservation of area when units are rearranged.

Differentiation

• Provide pre-drawn grids, larger physical tiles, fewer and smaller surfaces, and mixed-ability pairs. Give the student with Down syndrome a consistent partner, a clear role, repeated modelling and the option to demonstrate rather than write.
• Use a dyslexia-friendly worksheet with a clear sans-serif font, generous spacing, short numbered instructions, symbols, visual examples and sentence starters such as “I counted…” and “I checked by…”. Give oral instructions, read prompts aloud and allow drawing, pointing or verbal recording.
• Support working memory by displaying the four task steps throughout: place, check, count, record. Use colour-coded rows and physically guide the first example if needed.
• Extend confident learners by asking them to make different rectangles with the same number of square units, predict the area before covering, and explain why rearranging the units does not change the area.