You will learn
- Count unit squares row by row.
- Count squares in rectangles and L-shapes.
- Avoid counting a square twice.
- Record area in 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
- Count unit squares row by row.
- Do not count a square twice.
- Count rectangles and L-shapes.
- Record the area in squares.
Words to know
A square of area one unit.
Squares side by side.
Squares one above another.
Say the numbers in order.
1. Discover: counting tiles
A wall has tiles in rows. How can you count all the tiles without missing any or counting one twice?
2. Understand: counting squares
To find area by counting, count the unit squares inside the shape.
- Count row by row, or count one row and use repeated addition.
- A rectangle with 3 rows of 4 squares has 4 + 4 + 4 = 12 squares.
- An L-shape is split into two rectangles: 3 + 4 = 7 squares.
Mark each square as you count it so that none is counted twice.
Idea 1: Rows
2 rows of 5 squares: 5 + 5 = 10 squares. 4 rows of 3 squares: 12 squares.
Idea 2: L-shapes
An L-shape made of 6 squares and 4 squares has area 6 + 4 = 10 squares.
Idea 3: No double counting
Mark each square as you count. 5 rows of 5 squares is 25 squares.
Why mark? A square counted twice makes the area too big.
3. Worked examples
Example 1 (I show you): Rows
2 rows of 5 squares.
- 5 + 5.
Answer: 10 squares
Example 2 (We do it together): L-shape
6 squares and 4 squares.
- 6 + 4.
Answer: 10 squares
Example 3 (You try): Square
5 rows of 5 squares.
Show the steps and answer
- 5 × 5.
Answer: 25 squares
Did you know?
Rows go across and columns go down.
Why this matters
Counting squares is the first step to measuring area.
4. Explore: count it
You need squared paper and a pencil.
- Draw a rectangle of 3 rows and 4 columns.
- Count the squares row by row.
- Draw an L-shape and split it into two parts.
- Add the parts.
Think about it: what did you notice?
Rectangle 12; L-shape 7.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- There are ___ rows of ___ squares.
- The area is ___ squares.
- I counted ___ + ___.
- I marked each square.
Guided practice
Question 1. A rectangle has 3 rows of 4. Squares?
12.
Question 2. An L-shape is 3 + 4 squares. Area?
7 squares.
Question 3. How do we avoid counting twice?
Mark each square.
Independent practice
Level 1: Start
- 2 rows of 5 squares
- 4 rows of 3 squares
- L-shape of 6 and 4 squares
- Rectangle 5 rows of 5
- L-shape of 2 and 8 squares
Level 2: Grow
- 3 rows of 4 squares
- 6 rows of 2 squares
- An L-shape of 5 and 3 squares
Level 3: Stretch
- 7 rows of 7 squares
- An L-shape made of 4 rows of 5 squares and 3 more squares
- Ben counts 4 rows of 5 squares and gets 9. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A floor has 4 rows of 6 tiles. How many tiles cover it?
Show a sample answer
24 tiles.
Another one. Draw an L-shape with area 11 squares and show how you counted.
Show a sample answer
for example 2 rows of 4 and 3 more squares: 8 + 3 = 11
7. Common mistakes
Fix: Mark each square as you count it.
Fix: Mark each square.
Fix: Multiply rows by squares in each row.
8. Lesson summary and revision card
- I can count unit squares row by row.
- I can count in rectangles and L-shapes.
- I can avoid counting twice.
- I can record the area in 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
- Count row by row.
- Split an L-shape into rectangles.
- Mark each square.
11. Next lesson
Next lesson: Area of rectangles using arrays. 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 2 rows of 5 squares. [2 marks]
- Find the area of 4 rows of 3 squares. [2 marks]
- An L-shape is made of 6 and 4 squares. Find the area. [2 marks]
- Find the area of 5 rows of 5 squares. [1 mark]
- Ali counts 3 rows of 4 squares as 7. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 5 + 5 [1] = 10 squares [1]
- 4 × 3 [1] = 12 squares [1]
- 6 + 4 [1] = 10 squares [1]
- 25 squares [1]
- No [1]. He added [1]. 3 × 4 = 12 squares [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 2 rows of 5 squares
- 4 rows of 3 squares
- L-shape of 6 and 4 squares
- 5 rows of 5 squares
- L-shape of 2 and 8 squares
- 2 rows of 5 squares =
- 4 rows of 3 squares =
- An L-shape of 6 and 4 squares =
- 5 rows of 5 squares =
- 4 rows of 6 tiles =
Homework
Draw three shapes on squared paper and count their squares.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2 rows of 5 squares | 10 | 2 |
| 4 rows of 3 squares | 12 | 2 |
| L-shape of 6 and 4 squares | 10 | 2 |
| 5 rows of 5 squares | 25 | 2 |
| L-shape of 2 and 8 squares | 10 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 10; 2 12; 3 10; 4 25; 5 10.
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 10 squares; 7 12 squares; 8 10 squares; 9 25 squares; 10 24.
Independent practice answers. Level 1: 1 10 squares; 2 12 squares; 3 10 squares; 4 25 squares; 5 10 squares. Level 2: 1 12 squares; 2 12 squares; 3 8 squares. Level 3: 1 49 squares; 2 23 squares; 3 He added 4 + 5. Count in rows: 4 × 5 = 20..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Count unit squares row by row | 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 Count squares in rectangles and L-shapes | 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 Avoid counting a square twice | 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 Record area in 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: Counting a corner square twice. Mark each square as you count it.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Count paper squares laid out on a table.
- 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 area by counting unit squares. You do not need to be good at mathematics to help.
- Count tiles on a floor.
- Ask: how many in each row?
- Draw shapes on squared paper.
- 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: count unit squares row by row; count squares in rectangles and L-shapes; avoid counting a square twice; record area in square units.
Prerequisite knowledge. Lessons 1 and 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 and a pencil. 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 many rows? How many in each? Did I count twice?
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 a corner square twice. Mark each square as you count it.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. Count paper squares laid out on a table. 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 3 » 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.6 (measure area by counting); Cambridge Primary Mathematics Stage 3 (area). These sources informed the lesson.