You will learn
- Split into rectangles.
- Subtract a cut-out.
- Add areas.
- Check the total.
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
- Split a composite shape into simple shapes.
- Add areas of the parts.
- Subtract a cut-out or hole.
- Area is in square units.
Words to know
Made of simpler parts.
Divide into parts.
Take away a part.
Surface covered.
1. Discover: L-shaped room
An L-shaped room is made of an 8 m by 5 m rectangle and a 4 m by 3 m rectangle. What is its area?
2. Understand: composite figures
- Split: 8 × 5 = 40 and 4 × 3 = 12, total 52 m².
- Subtract: a 10 × 6 board with a 3 × 2 hole has area 60 − 6 = 54.
- Always check each part’s measurements.
- A rectangle plus a triangle (base 6, height 4): 6 × 5 + 12 = 42.
Idea 1: Add
L-shape: 8 × 5 = 40 and 4 × 3 = 12, total 52. 6 × 5 + ½ × 6 × 4 = 30 + 12 = 42.
Idea 2: Subtract
10 × 6 − 3 × 2 = 60 − 6 = 54. For a hole you subtract.
Idea 3: Units
Area is measured in square units, for example m².
Why split? We know the area of simple shapes.
3. Worked examples
Example 1 (I show you): Add
8 × 5 + 4 × 3
- 40 + 12.
Answer: 52
Example 2 (We do it together): Subtract
10 × 6 − 3 × 2
- 60 − 6.
Answer: 54
Example 3 (You try): Mixed
6 × 5 + ½ × 6 × 4
Show the steps and answer
- 30 + 12.
Answer: 42
Did you know?
There is often more than one way to split a shape.
Why this matters
Rooms, gardens and plots are rarely simple rectangles.
4. Explore: split
You need squared paper.
- Split the shape.
- Find each area.
- Add or subtract.
- Write m².
Think about it: what did you notice?
52 m².
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I split the shape into ___.
- The area of the first part is ___.
- I add / subtract ___.
- The total area is ___.
Guided practice
Question 1. 8 × 5?
40.
Question 2. 4 × 3?
12.
Question 3. Total?
52 m².
Independent practice
Level 1: Start
- 8 × 5 + 4 × 3
- 10 × 6 − 3 × 2
- 6 × 5 + ½ × 6 × 4
- Add or subtract for a hole?
- Unit of area
Level 2: Grow
- 6 × 4 + 3 × 2
- 9 × 5 − 2 × 3
- Unit for the area of a floor in metres
Level 3: Stretch
- Frame 20 by 15 cm with a 14 by 9 cm picture. Area of the frame only
- 8 × 3 + ½ × 8 × 5
- Ben says area is measured in cm. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
L-shaped room: 8 × 5 plus 4 × 3. Area?
Show a sample answer
52 m².
Another one. An L-shaped room is a 10 m by 4 m rectangle with a 3 m by 2 m rectangle added. Find its area.
Show a sample answer
46 m²
7. Common mistakes
Fix: Split without overlap.
Fix: Subtract a hole.
Fix: Use square units.
8. Lesson summary and revision card
- I can split into rectangles.
- I can subtract a cut-out.
- I can add areas.
- I can check the total.
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
- Split the shape.
- Add or subtract.
- Use square units.
11. Next lesson
Next lesson: Volume of rectangular prisms. 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 8 × 5 + 4 × 3 for an L-shaped room. [3 marks]
- A 10 by 6 rectangle has a 3 by 2 hole. Find the area. [3 marks]
- A 6 by 5 rectangle has a triangle with base 6 and height 4 on top. Find the area. [3 marks]
- Do you add or subtract the area of a hole? [1 mark]
- Ali says area is measured in cm. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 8 × 5 = 40 and 4 × 3 = 12 [1]; add them [1]; 52 [1]
- 60 and 6 [1]; subtract [1]; 54 [1]
- Rectangle 30 [1]; triangle ½ × 6 × 4 = 12 [1]; 42 [1]
- Subtract [1]
- No [1]. cm measures length [1]. Area uses square units such as cm² [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 8×5 + 4×3
- 10×6 − 3×2
- 6×5 + ½×6×4
- Hole: add or subtract
- Unit of area
- 8 × 5 + 4 × 3
- 10 × 6 − 3 × 2
- 6 × 5 + ½ × 6 × 4
- For a hole you
- Unit of area
Homework
Find the area of an L-shaped floor you know.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 8×5 + 4×3 | 52 | 2 |
| 10×6 − 3×2 | 54 | 2 |
| 6×5 + ½×6×4 | 42 | 2 |
| Hole: add or subtract | subtract | 2 |
| Unit of area | square units | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 52; 2 54; 3 42; 4 subtract; 5 square units.
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 52; 7 54; 8 42; 9 subtract; 10 square units.
Independent practice answers. Level 1: 1 52; 2 54; 3 42; 4 subtract; 5 square units. Level 2: 1 30; 2 39; 3 m². Level 3: 1 174 cm²; 2 44; 3 cm is length. Area uses cm²..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Split into rectangles | 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 Subtract a cut-out | 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 Add areas | 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 Check the total | 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: Counting an overlap twice. Split without overlap.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Area of rectangles.
- 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 composite figures. You do not need to be good at mathematics to help.
- Find the area of an L-shaped room.
- Ask: can I split it?
- Draw the pieces.
- 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: split into rectangles; subtract a cut-out; add areas; check the total.
Prerequisite knowledge. Lessons 3 and 4.
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. How can I split it? Add or subtract?
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. Counting an overlap twice. Split without overlap.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-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 of rectangles. 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 6 » Ratios & Proportional Relationships; Grade 6 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 6.G.A.1 and 3.MD.C.7d; Cambridge Primary Mathematics Stage 6 (composite area). These sources informed the lesson.