You will learn
- Split a composite figure into rectangles.
- Add the areas.
- Subtract a missing part.
- Check the answer.
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 figure into rectangles.
- Find each area and add.
- Or find a big rectangle and subtract a missing part.
- Check your answer.
Words to know
A shape made of simpler shapes.
Divide into parts.
Total of parts.
Remove a part.
1. Discover: an L-shaped garden
An L-shaped garden is made of an 8 m by 5 m rectangle and a 4 m by 3 m rectangle. What is its total area?
2. Understand: composite figures
Split the figure into rectangles, find each area and add.
- 8 × 5 = 40 m² and 4 × 3 = 12 m². Total = 40 + 12 = 52 m².
- Or subtract: a 10 by 6 rectangle with a 4 by 2 corner removed: 60 − 8 = 52 m².
Idea 1: Add parts
12 by 5 plus 6 by 3: 60 + 18 = 78. L-shape of 9 by 4 and 3 by 5: 36 + 15 = 51.
Idea 2: Subtract
10 by 8 minus 3 by 3: 80 − 9 = 71.
Idea 3: Add areas
Areas 24 and 18 give 42. Areas 30, 20 and 10 give 60.
Why split? We know how to find the area of rectangles.
3. Worked examples
Example 1 (I show you): Add
12 by 5 plus 6 by 3
- 60 and 18.
Answer: 78
Example 2 (We do it together): Subtract
10 by 8 minus 3 by 3
- 80 and 9.
Answer: 71
Example 3 (You try): L-shape
9 by 4 and 3 by 5
Show the steps and answer
- 36 and 15.
Answer: 51
Did you know?
Architects split floor plans into rectangles to find areas.
Why this matters
Composite figures are floor plans, gardens and fields.
4. Explore: split
You need squared paper.
- Draw an L-shape.
- Split it in one way.
- Find each area and add.
- Split another way to check.
Think about it: what did you notice?
Same total.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I split it into ___ and ___.
- The areas are ___ and ___.
- I add / subtract to get ___.
- The total area is ___.
Guided practice
Question 1. 40 + 12?
52.
Question 2. Area of 10 by 6 minus 4 by 2?
52.
Question 3. Why split into rectangles?
We know how to find rectangle area.
Independent practice
Level 1: Start
- Areas 24 and 18
- 12 by 5 plus 6 by 3
- 10 by 8 minus 3 by 3
- L-shape: 9 by 4 and 3 by 5
- Add 30, 20 and 10
Level 2: Grow
- 5 by 4 plus 3 by 2
- 8 by 8 minus 2 by 2
- Areas 15, 25 and 10
Level 3: Stretch
- L-shape of 12 by 3 and 4 by 6
- 14 by 9 minus 4 by 3
- Ana subtracts 3 from 80 for a 3 by 3 hole and gets 77. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A hall is made of rooms 12 m², 18 m² and 20 m². Total area?
Show a sample answer
50 m².
Another one. A garden is 12 m by 8 m. A pond 3 m by 2 m is in it. What is the area of grass?
Show a sample answer
12 × 8 = 96 and 3 × 2 = 6, so 90 m².
7. Common mistakes
Fix: Split without overlapping.
Fix: Find the area of the missing part first.
Fix: Find each area, then add.
8. Lesson summary and revision card
- I can split a composite figure.
- I can add areas.
- I can subtract a missing part.
- I can check the answer.
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.
- Add or subtract.
- Check another way.
11. Next lesson
Next lesson: Time intervals. 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.
- Add the areas 24 and 18. [1 mark]
- Find 12 by 5 plus 6 by 3. [3 marks]
- Find 10 by 8 minus 3 by 3. [3 marks]
- Find the area of an L-shape made of 9 by 4 and 3 by 5. [3 marks]
- Ben says 30 + 20 + 10 = 50. Is he right? Explain. [2 marks]
Total: 12 marks.
Marking guide and model answers
- 42 [1]
- 12 × 5 = 60 [1]; 6 × 3 = 18 [1]; 78 [1]
- 80 [1]; 9 [1]; 71 [1]
- 36 [1]; 15 [1]; 51 [1]
- No [1]. 30 + 20 + 10 = 60 [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
- 24 + 18
- 12 by 5 plus 6 by 3
- 10 by 8 minus 3 by 3
- L-shape 9 by 4 and 3 by 5
- 30 + 20 + 10
- 8 by 5 plus 4 by 3
- 10 by 6 minus 4 by 2
- 12 by 5 plus 6 by 3
- 10 by 8 minus 3 by 3
- Rooms of 12, 18 and 20 total
Homework
Draw an L-shaped room and find its area.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 24 + 18 | 42 | 2 |
| 12 by 5 plus 6 by 3 | 78 | 2 |
| 10 by 8 minus 3 by 3 | 71 | 2 |
| L-shape 9 by 4 and 3 by 5 | 51 | 2 |
| 30 + 20 + 10 | 60 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 42; 2 78; 3 71; 4 51; 5 60.
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 52; 8 78; 9 71; 10 50.
Independent practice answers. Level 1: 1 42; 2 78; 3 71; 4 51; 5 60. Level 2: 1 26; 2 60; 3 50. Level 3: 1 60; 2 114; 3 The hole has area 3 × 3 = 9, so 80 − 9 = 71..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Split a composite figure 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 Add the 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 |
| O3 Subtract a missing part | 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 answer | 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 the overlap twice. Split without overlapping.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Draw rectangles on a grid.
- 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 shapes made of rectangles. You do not need to be good at mathematics to help.
- Sketch a floor plan and find the area.
- Ask: how can we split it?
- Check by splitting in a different way.
- 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 a composite figure into rectangles; add the areas; subtract a missing part; check the answer.
Prerequisite knowledge. Lesson 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? Do I 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 the overlap twice. Split without overlapping.
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. Draw rectangles on a grid. 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 4 » 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.7d and 4.MD.A.3; Cambridge Primary Mathematics Stage 5 (area of compound shapes). These sources informed the lesson.