Area by counting square units

Primary 3 Area and Perimeter study guide: the whole chapter, step by step

About this subtopic

The idea in brief. Area counts the square units covered; two half-squares make one whole square. Count the area covered. Two half squares make one square unit. In the lesson. In the last chapter, you measured lengths in centimetres and metres. 1 centimetre is about the width of a fingertip. Today, we will find the area of a figure by counting square units. Area counts the square units a figure covers. Two half squares make one whole square.

Lesson video, with the working

Area

4 min 19 s

The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.

Watch on its own page

Today's question

Lin draws a tile pattern on a grid. Each small square has an area of 1 cm². Find the area of her shaded pattern.

  1. Whole squares = 2 + 4 + 2 = 8
  2. Whole squares from the half squares = 2 ÷ 2 = 1
  3. Squares covered = 8 + 1 = 9
  4. Area = 9 cm²

Ans: 9 cm²

Example 1 of 2

A walkway is covered with square tiles. Each tile has an area of 1 m². Find the area of the shaded part.

  1. Whole squares = 2 + 5 + 4 = 11
  2. Area = 11 m²

Ans: 11 m²

Example 2 of 2

Lin shades another figure on a grid. Each small square has an area of 1 cm². Find the area of the shaded figure.

  1. Whole squares = 4 + 3 + 2 = 9
  2. Whole squares from the half squares = 6 ÷ 2 = 3
  3. Squares covered = 9 + 3 = 12
  4. Area = 12 cm²

Ans: 12 cm²

How to solve it
  1. Each small square is 1 square centimetre, so the area is the number of squares the figure covers.
  2. Count the whole squares row by row and add them: 2 plus 4 plus 2 is 8.
  3. Count the half squares. 2 half squares make 1 whole square: 2 divided by 2 is 1.
  4. Add the whole squares: 8 plus 1 is 9 squares.
  5. Write the area with its unit: 9 square centimetres.

Area counts the square units a figure covers. Two half squares make one whole square.

Practice questions with worked solutions

Questions 1 and 3 are free to try. The other 6 open in the free trial, each with its solution film.

Intermediate

Challenge

Print this subtopic · included with a plan

6 more questions, each with its solution film.Answers checked, progress kept, wrong ones come back in revision. No card needed.

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Question 1 of 8 · Basic · free to tryEach small square in the grid has an area of 1 m². Find the area of the…Each small square in the grid…

Each small square in the grid has an area of 1 m². Find the area of the shaded figure.

m²

Show the working and the answer

Video solution · 1 min 10 s

Watch it in the free 7-day trial

Start the free trial

Working

  1. Whole squares = 2 + 5 + 2 = 9
  2. Area = 9 × 1 = 9 m²
  3. The area of the shaded figure is 9 m².

Answer: 9 m²

Question 3 of 8 · Basic · free to tryEach small square in the grid has an area of 1 cm². Find the area of the…Each small square in the grid…

Each small square in the grid has an area of 1 cm². Find the area of the shaded figure.

cm²

Show the working and the answer

Video solution · 1 min 14 s

Watch it in the free 7-day trial

Start the free trial

Working

  1. Whole squares = 1 + 3 + 5 + 3 = 12
  2. Area = 12 × 1 = 12 cm²
  3. The area of the shaded figure is 12 cm².

Answer: 12 cm²

For parents

How do you find area by counting squares in P3?

This is the first idea in the Primary 3 area chapter: area is the amount of flat surface a figure covers, and we measure it by counting equal squares.

What your child learns here

This is the first idea in the Primary 3 area chapter: area is the amount of flat surface a figure covers, and we measure it by counting equal squares. It comes before any formula, so your child sees what a square centimetre is before multiplying anything.

  • Area is how much surface a figure covers, measured in square units.
  • Each small square on the grid is one square unit, such as 1 cm² or 1 m².
  • Two half squares join to make one whole square.
  • The answer is a count of squares written with its unit, for example 14 cm².
Does the answer make sense?

The area cannot be less than the number of squares that are fully shaded, and it cannot be more than the number of squares the figure touches at all. Your child can count those two quickly; the answer should land between them, with a square unit written after it.

How to practise these questions

The Basic questions practise counting whole squares in a grid. The Intermediate questions add larger and more irregular shaded figures on the grid. The Challenge question asks for the shaded area of a shape with parts cut out of it, so the area to count is what remains. When counting squares is stuck, watch that question's solution film and try it again later from Revision.

Questions parents ask

What is a square unit in P3 maths? A square unit is a square used to measure area, such as a square with 1 cm sides (1 cm²) or with 1 m sides (1 m²). The Primary 3 syllabus asks children to measure area in square units, cm² and m². Changing between cm² and m² is left out at this level.

How do I explain half squares to my child? Cut a paper square in half along its diagonal and put the two halves back together. They make one whole square again, so two half squares on a grid count as 1 square unit.

Why does my child count squares instead of using a formula? Counting comes first because it shows what area means: the number of squares a shape covers. The rule length times breadth for a rectangle is built from that idea in a later subtopic of this chapter.