Area (I): Count squares
FoundationCount squares. Each is 1 cm².
After this lesson, you can:
- Area = how much flat space a shape covers
- The unit is cm², a 1 cm × 1 cm square
- Measure by counting squares on grid paper
1Summary 重點摘要
Count squares. Each is 1 cm².
2Vocabulary cards Vocabulary
a
area面積
How much flat surface a shape covers.
s
square centimetre (cm²)平方厘米（cm²）
The area of a 1 cm by 1 cm square; the unit of area.
g
grid / square grid方格紙
Paper ruled into equal squares, used to count area.
f
full square滿格
A square completely inside the shape; counts as 1 unit.
h
half square半格
A square half covered by the shape; two halves make 1.
c
count squares數方格
The basic way to measure area: count the squares.
c
cover鋪滿
To tile the whole shape with unit squares.
p
perimeter vs area周界與面積
Perimeter is the border length; area is the space inside — different things.
3Step by step Steps
- Part 1: Area is how much spaceArea measures how much surface a shape covers. Compare a notebook cover with a bookmark: which takes up more space? That is a question about area. Area differs from length: length tells how long, area tells how much surface.
- Part 2: Squares as the unitSquares are used as the unit for area. Tile the shape completely with 1 cm × 1 cm squares; however many squares fit, that is the area in square centimetres, written cm². One square is one square centimetre, so counting squares is measuring area.
- Part 3: Count full squaresStart by counting full squares. A rectangle 4 cm long and 2 cm wide has 4 squares in each row and 2 rows: 4 + 4 = 8 squares, so the area is 8 cm². Count row by row so nothing is missed.
- Part 4: What about halves?The border of a shape can cut a square into two halves. Two half squares join to make exactly 1 full square. For example, a shape with 4 full squares and 2 half squares has 4 + 2 ÷ 2 = 4 + 1 = 5, so the area is 5 cm².
- Part 5: More than half?What if the covered part is not a half, say 34 of a square? It can be paired with a 14 square to make one whole. In Primary 3 most questions use only full and half squares; harder cases will be worked out by multiplication in Primary 4.
- Part 6: Area is not perimeterArea is not perimeter. For a 3 cm by 2 cm rectangle, the perimeter is the length all round the edge: 3 + 2 + 3 + 2 = 10 cm. The area is the number of squares inside: 6 cm². One counts the edge, the other counts the surface, so do not mix them.
4Diagrams Diagrams
5Worked example Example
Example: a shape on grid paper has 6 full squares and 4 half squares. What is its area?
- Count the full squares first: there are 6, so note down 6.
- Work out the halves next: 4 half squares equal 4 ÷ 2 = 2 full squares.
- Add them together: 6 + 2 = 8 squares.
- Each square is 1 cm², so the area is 8 cm².
- Answer: Answer: the area of the shape is 8 cm². Two half squares must be joined to count as one full square, so never count each half as a whole. Count the full squares first and then the halves, and mistakes can be avoided.
6Common mistakes Mistakes
✗ Counting every half square as 1
✓ Two halves make 1: four halves = 2 squares
✗ Writing area in cm
✓ Area uses cm² (square centimetres); cm is for length
✗ Confusing perimeter with area
✓ Perimeter is the border (cm); area counts squares inside (cm²)
✗ Missing border half squares when counting
✓ Count full squares first, then walk the edge slowly for halves
7Quick check Quick check
Q1What is the unit of area?
Answer: Square centimetres (cm²)
Did you get it right?
Q2Two half squares together make?
Answer: 1 full square
Did you get it right?
Q3Area of a 3 cm × 2 cm rectangle in cm²?
Answer: 6 cm²
Did you get it right?
Q45 full squares + 2 halves = ? cm²
Answer: 5 + 1 = 6 cm²
Did you get it right?
Q5Perimeter measures what around a shape?
Answer: The border length (cm)
Did you get it right?
8Recap Recap
- Area = how much flat space a shape covers
- The unit is cm², a 1 cm × 1 cm square
- Measure by counting squares on grid paper
- Two half squares = 1 full square
- Area (cm²) and perimeter (cm) are different measures