E. Spatial Sense · 3D Objects, Directions and Measurement

Square Centimetres and Square Metres

E2.9About 35 minutes

Learning goals

I can explain what a square centimetre and a square metre are.
I can measure area in square centimetres (cm²) by counting squares.
I can estimate the area of shapes with curved sides.
I can choose cm² or m² and compare areas.

Words to know

square centimetre (cm²)
The area of a square that is 1 cm on each side. It is about the size of your smallest fingernail.

square metre (m²)
The area of a square that is 1 m on each side. A few children can stand on one.

standard unit
A unit that is the same everywhere, like cm² and m². Everyone gets the same count.

row
A line of squares going across.

estimate
A thoughtful guess about a measurement.

Let's start with a problem

In the last lesson, Mark measured a table with cards and got 6, and Nia used sticky notes and got 24. Both were right, but it's confusing! People need units that are the same everywhere.

For area, we use standard units: the square centimetre and the square metre.

Square centimetres and square metres

A square centimetre is a square that is 1 cm long on each side. We write it 1 cm². It is about the size of your smallest fingernail. Use cm² for small areas, like a sticky note or a book cover.
A square metre is a square that is 1 m long on each side. We write it 1 m². Use m² for big areas, like a floor, a garden or an ice rink.

The little ² tells you it is a square unit for area, not a length.

A square centimetre (shown zoomed in) is 1 cm on each side. A square metre is 1 m on each side.

Measuring on centimetre grid paper

Centimetre grid paper is covered in 1 cm squares. Each square is 1 cm². To find the area of a shape drawn on it, count the squares inside.

For a rectangle, you can count by rows: count the squares in one row, then add the rows.

A rectangle on centimetre grid paper (drawing not actual size). It has 3 rows of 5 squares: 15 cm².

Worked example

Example 1: A rectangle

Find the area of the rectangle on the grid.

Each square is 1 cm².
There are 5 squares in each row and 3 rows.
Add the rows: 5 + 5 + 5 = 15.

The area is 15 cm².

An L-shape split into two rectangles: 2 by 4 (8 squares) and 3 by 2 (6 squares). 8 + 6 = 14 cm².

Worked example

Example 2: An L-shape

Find the area of the L-shape.

Split it into two rectangles.
Part 1 is 2 squares wide and 4 rows tall: 2 + 2 + 2 + 2 = 8.
Part 2 is 3 squares wide and 2 rows tall: 3 + 3 = 6.
Add the parts: 8 + 6 = 14.

The area is 14 cm².

Shapes with curved sides

Some shapes, like a circle or a leaf, don't cover whole squares. We can estimate:

Count the whole squares inside the shape.
Count the part squares (squares the edge cuts through).
Some parts are big and some are small. Two part squares make about 1 whole square. So add about half of the part squares.
Add them up and say "about ___ cm²".

A circle on centimetre grid paper (drawing not actual size). Green squares are whole squares inside the circle. Yellow squares are cut by the edge.

Worked example

Example 3: Estimate the area of a circle

Estimate the area of the circle on the grid.

Count the whole squares (green): 24.
Count the part squares (yellow): 28.
About 2 part squares make 1 whole. Half of 28 is 14 (because 14 + 14 = 28).
24 + 14 = 38.

The area of the circle is about 38 cm². It is more than 24 cm² (the whole squares) and less than 52 cm² (the whole squares plus all the part squares).

Worked example

Example 4: Square metres

Max's class taped sheets of paper together to make squares that are each 1 m by 1 m. They covered the carpet in the reading corner with 6 of these squares. What is the area of the carpet?

Each taped square is 1 m².
6 of them cover the carpet, with no gaps or overlaps.

The carpet has an area of 6 m².

cm² or m²?

Think about size:

A stamp, a photo, a book, a placemat: use cm².
A floor, a classroom, a garden, a playground, an ice rink: use m².

And remember: perimeter uses cm or m (a length). Area uses cm² or m² (squares).

Just for fun

A square centimetre is about the size of the tip of your little finger. A square metre is big enough for a few friends to stand on. Try fitting your friends on a square centimetre!

Hands-on activity

Square units at home

You need: centimetre grid paper (a grown-up can print some, or draw 1 cm squares with a ruler), a pencil, newspaper or wrapping paper, a metre stick or measuring tape, tape, and scissors.

Grown-up note: help with or supervise cutting.

Trace your hand on centimetre grid paper with your fingers together. Estimate its area: count whole squares, then add about half of the part squares.
Trace a coin, a cup bottom and a sticky note. Which has the greatest area?
Make a square metre: tape paper together and cut a square 1 m long on each side. Check each side with the metre stick.
How many family members can stand on your square metre?
Estimate how many square metres would cover your bedroom floor. Lay your square metre down to check part of the floor.

Math talk: "Why is it easier to compare areas when everyone uses cm²?"

Your turn

What is 1 cm²?

A rectangle on cm grid paper has 4 rows of 3 squares. What is its area?

Would you measure the area of a classroom floor in cm² or m²?

Would you measure the area of a sticky note in cm² or m²?

A shape covers 9 whole squares on cm grid paper. What is its area?

A leaf covers 10 whole squares and 8 part squares. Estimate its area.

Shape A is 20 cm² and shape B is 16 cm². Which has the greater area? By how much?

More practice: warm-up

How do you write "square metre" in short form?

On cm grid paper, how much area is one square?

A rectangle has 2 rows of 5 squares. Area?

Is 5 cm a length or an area?

Which is bigger: 1 cm² or 1 m²?

More practice: on your own

A square on cm grid paper is 4 cm on each side. What is its area? What is its perimeter?

An L-shape is made of a 3 by 2 rectangle and a 1 by 4 rectangle that do not overlap. What is its area?

A playground is covered by 5 rows of 8 square metres. What is its area?

Kai's hand covers 38 whole squares and 20 part squares. Estimate the area of his hand.

Rectangle P is 3 by 6. Rectangle Q is 4 by 4. Which has the greater area?

Challenge

Draw (or describe) two different rectangles that each have an area of 18 cm².

A rectangle has an area of 20 cm². It has 4 rows. How many squares are in each row?

A garden is 6 m long and 3 m wide. Grass seed for 1 m² costs $1. How much will it cost to seed the whole garden?

Check your understanding

Quiz

What is a square centimetre?

A rectangle has 3 rows of 4 squares on cm grid paper. What is its area?

Which unit is best for the area of a hockey rink?

A shape covers 12 whole squares and 6 part squares. About what is its area?

An L-shape is made of a 2 by 3 rectangle and a 2 by 2 square. What is its area?

Which is an area?

For parents and teachers

Big idea: Children use standard square units, square centimetres (cm²) and square metres (m²), to estimate, measure and compare areas, including shapes with curved sides (Ontario E2.9). In Grade 3 they find area by counting squares and adding rows. A multiplication formula for area comes in later grades.

Common difficulties:

Mixing up area and perimeter. Area counts the squares inside; perimeter counts the length around. Ask "Are we counting squares or edges?"
Forgetting the ² or writing cm for area. Praise using the right unit.
Curved shapes. Estimates will vary. An answer close to the count (whole squares plus about half the part squares) is great.

Safety: supervise scissors.

How to help: Make a 1 m² paper square together and see how many fit on a room's floor. Print centimetre grid paper and trace hands, leaves and cookie cutters.