You will learn
- Use length × width.
- Find area with decimals.
- Find area of composite figures.
- Convert square units.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Area is the surface a shape covers.
- Rectangle area = length × width.
- Split composite shapes into rectangles.
- 1 m² = 10,000 cm².
Words to know
Surface covered.
Unit for area.
Made of rectangles.
Longer side.
1. Discover: a floor
A floor is 8.5 m by 4 m. How many square metres of tile?
2. Understand: area
- 8.5 × 4 = 34 m².
- Square of side 7.5: 7.5 × 7.5 = 56.25.
- 1 m² = 100 cm × 100 cm = 10,000 cm².
- L-shape: 10 × 6 + 4 × 3 = 60 + 12 = 72.
Idea 1: Rectangle
12 by 7: 12 × 7 = 84. Square side 7.5: 7.5 × 7.5 = 56.25. 2.5 × 2.5 = 6.25.
Idea 2: Composite
9 by 4 plus 5 by 2: 36 + 10 = 46.
Idea 3: Units
1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm².
Why 10,000, not 100? Area multiplies two lengths.
3. Worked examples
Example 1 (I show you): Area
12 by 7
- 12 × 7.
Answer: 84
Example 2 (We do it together): Composite
9 by 4 plus 5 by 2
- 36 + 10.
Answer: 46
Example 3 (You try): Convert
1 m² in cm²
Show the steps and answer
- 100 × 100.
Answer: 10,000 cm²
Did you know?
Area is always measured in square units.
Why this matters
Area tells us how much paint, carpet or land we need.
4. Explore: area
You need squared paper.
- Draw 8.5 by 4.
- Multiply.
- Write the unit.
- Convert to cm² if needed.
Think about it: what did you notice?
34 m².
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- Area = ___ × ___.
- I split the shape into ___.
- The areas add to ___.
- The unit is ___.
Guided practice
Question 1. 8.5 × 4?
34 m².
Question 2. 1 m² in cm²?
10,000.
Question 3. L-shape 10×6 + 4×3?
72.
Independent practice
Level 1: Start
- Area 12 by 7
- Area of a square side 7.5
- Area 2.5 by 2.5
- 1 m² in cm²
- Area 9 by 4 plus 5 by 2
Level 2: Grow
- Area 15 by 4
- Square side 6
- Area 3.5 by 2
Level 3: Stretch
- Area 6.4 by 5
- L-shape: 10 by 6 plus 4 by 3
- Ben says 1 m² = 100 cm². What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A floor is 8.5 m by 4 m. How much tile?
Show a sample answer
34 m².
Another one. A room is 5.5 m by 4 m. What is its floor area?
Show a sample answer
5.5 × 4 = 22 m²
7. Common mistakes
Fix: Area needs square units.
Fix: Multiply for area.
Fix: Write m² or cm².
8. Lesson summary and revision card
- I can use length × width.
- I can find area with decimals.
- I can find composite areas.
- I can convert square units.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- l × w.
- Square units.
- Split composites.
11. Next lesson
Next lesson: Volume. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Find the area of a 12 by 7 rectangle. [2 marks]
- Find the area of a square with side 7.5. [2 marks]
- Find the area of a 2.5 by 2.5 square. [2 marks]
- How many cm² are in 1 m²? [3 marks]
- Ali says the area of 9 by 4 plus 5 by 2 is 9 × 4 × 5 × 2. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 12 × 7 [1]; 84 [1]
- 7.5 × 7.5 [1]; 56.25 [1]
- 2.5 × 2.5 [1]; 6.25 [1]
- 1 m = 100 cm [1]; 100 × 100 [1]; 10,000 cm² [1]
- No [1]. Add the two areas [1]. 36 + 10 = 46 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Area 12 by 7
- Square side 7.5
- Area 2.5 by 2.5
- 1 m² in cm²
- 9 by 4 plus 5 by 2
- Area of 8.5 m by 4 m:
- Area of a square, side 7.5:
- 1 m² =
- Area 12 by 7:
- L-shape 10×6 + 4×3:
Homework
Find the area of three rooms.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Area 12 by 7 | 84 | 2 |
| Square side 7.5 | 56.25 | 2 |
| Area 2.5 by 2.5 | 6.25 | 2 |
| 1 m² in cm² | 10,000 | 2 |
| 9 by 4 plus 5 by 2 | 46 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 84; 2 56.25; 3 6.25; 4 10,000; 5 46.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 34 m²; 7 56.25; 8 10,000 cm²; 9 84; 10 72.
Independent practice answers. Level 1: 1 84; 2 56.25; 3 6.25; 4 10,000 cm²; 5 46. Level 2: 1 60; 2 36; 3 7. Level 3: 1 32; 2 72; 3 100 × 100 = 10,000 cm²..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use length × width | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Find area with decimals | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Find area of composite figures | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Convert square units | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Using cm instead of cm². Area needs square units.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Area by counting squares.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child finds the area of rectangles and composite shapes. You do not need to be good at mathematics to help.
- Find the area of a room.
- Ask: what are the length and width?
- Compare m² and cm².
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: use length × width; find area with decimals; find area of composite figures; convert square units.
Prerequisite knowledge. Lesson 2.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need squared paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. What are the lengths? Do I split the shape?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Using cm instead of cm². Area needs square units.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Area by counting squares. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 5 » Measurement & Data. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.MD.C.7 and 5.NF.B.4b; Cambridge Primary Mathematics Stage 5 (area). These sources informed the lesson.