Grade by Grade
E. Spatial Sense · Shapes, Position and Measurement

Matching Halves (Symmetry)

E1.3About 30 minutes
Learning goals
  • I can tell when a shape has matching halves.
  • I can find a line that splits a shape into two matching halves.
  • I can build or draw a shape that has matching halves.

Words to know

half
One of two equal parts of something.
matching halves
Two parts that are exactly the same size and shape, like mirror pictures of each other.
line of symmetry
A line that splits a shape into two matching halves. If you fold on it, the two halves fit right on top of each other.
mirror image
What you see in a mirror. It looks the same but flipped.

Look at a butterfly. Its left wing and right wing look exactly alike. Look at your face in a mirror. You have an eye on each side! When a shape can be split into two parts that match exactly, we say it has matching halves.

matching halvesmatching halvesNOT matching
The heart and the triangle can be folded on the dashed line so the halves match. The L-shape cannot.

How to check for matching halves

The best test is the fold test:

  1. Draw or cut out the shape.
  2. Fold it along a line.
  3. If the two parts fit exactly on top of each other with nothing sticking out, the shape has matching halves. The fold line is called a line of symmetry.
Worked example

Does a heart have matching halves?

Cut out a paper heart. Does it have matching halves?

  1. Fold the heart from the top dip straight down to the bottom point.
  2. Look at the edges. The left half sits exactly on top of the right half.
  3. Nothing sticks out, so the halves match.

Yes. The fold line down the middle is a line of symmetry.

Some shapes have more than one line

A square is special. You can fold it in more than one way and still get matching halves!

up and downside to sidecorner to corner
Three of the ways to fold a square into matching halves. (There is one more corner-to-corner line. Can you find it?)

Be careful

Matching halves must be the same size and the same shape. If one part is bigger, they are not halves.

NOT matchingMatching halves
On the left, the line splits the rectangle into a small part and a big part, so they are not matching halves. On the right, the line is in the middle, so the halves match.
Worked example

Finish the picture

Here is half of a shape. The dashed line is the line of symmetry. How do you finish it?

  1. Look at the half you have. Start at the top of the dashed line and go left 30, then down, then left again, then down to the bottom.
  2. Now do the same moves on the other side, but going right instead of left, as if it were a mirror.
  3. Check by imagining folding along the dashed line. Both sides should land on each other.

The finished shape looks the same on both sides of the dashed line, like a picture and its mirror image.

Finish theother half!
Half of a shape. Copy it on paper and draw the matching half.

Matching halves in 3D objects

Solid objects can have matching halves too. A cup, a ball, a cereal box and a toy car (from the front) can often be cut down the middle into two matching parts. In nature, look at leaves, butterflies, ladybugs, and snowflakes. A maple leaf, like the one on the Canadian flag, has matching halves. The flag of Canada has matching halves when you fold it down the middle!

Thinking tip

Some shapes look like they match but do not. Always try the fold test or use a small mirror on the line to check.

Just for fun

Why did the paper heart love the fold test?

Because it found its perfect matching half!

Hands-on activity

Blob butterflies and block buildings

Blob butterfly: fold a piece of paper in half and open it. Put a few blobs of paint on ONE side only, close to the fold. Fold it closed and press gently. Open it up. You made matching halves! Where is the line of symmetry?

Block buildings: with blocks or LEGO, build a building where the left side matches the right side. Then ask a grown-up to build half and you build the matching half.

Mirror hunt: stand a small mirror on a picture of a letter, like A, H, M, T, B or C. Can you make the whole letter by showing half of it in the mirror?

Your turn!

1

Does a circle have matching halves?

2

You fold a paper shape and one part sticks out past the other. Are the parts matching halves?

3

Name 2 things in nature that have matching halves.

4

Does the capital letter A have matching halves? Where is the line?

5

Does the capital letter F have matching halves?

6

A rectangle that is not a square: how many lines of symmetry does it have?

7

Draw a house with matching halves. Where is your line of symmetry?

More practice: warm-up

1

True or false: matching halves must be the same size and the same shape.

2

Does a square have matching halves?

3

Fill in the blank: the fold line that makes matching halves is called a line of ___.

4

Does the capital letter H have matching halves?

5

What is a good way to check if a shape has matching halves?

More practice: on your own

1

Does the capital letter T have matching halves? Where is the line?

2

Does the capital letter L have matching halves? How do you know?

3

Tom cuts a square sandwich from one corner to the opposite corner. He gets two triangles. Are they matching halves?

4

How many lines of symmetry does a square have?

5

Look at this bead pattern: 🔴🔵🟢🔵🔴

If you fold it at the 🟢 bead, do the two sides match?

Challenge

1

Find the mistake! Liam wants a bead string with matching halves. The fold goes in the middle. The left half is 🔴🟡🔵. He made:

🔴🟡🔵🔴🟡🔵

What went wrong? Fix it.

2

Which of these capital letters have matching halves: A, B, F, M, R? Tell where the line is.

3

Make a shape with matching halves using exactly 4 square blocks (touching side to side). Draw it and show the line of symmetry.

Check your understanding

Quiz

1.

Which shape has matching halves?

2.

What do we call the fold line that makes matching halves?

3.

Ella cut a sandwich into two pieces. One piece is much bigger. Are they matching halves?

4.

Which of these has matching halves?

5.

Which letter has matching halves?

6.

How many lines of symmetry does a square have?

For parents and teachers

What your child is learning: recognizing, building and drawing 2D shapes and 3D objects with matching halves (symmetry) (Ontario Grade 1, E1.3). The words "line of symmetry" are introduced, but the main idea is "two parts that match exactly".

Common mistakes:

  • Saying any two pieces are "halves" even if they are different sizes. Use food: "Would you be happy if I gave you this smaller half?"
  • Drawing the missing half going the same direction instead of flipped (like a copy rather than a mirror). Use a real mirror to show the flip.
  • Thinking a square has only one line of symmetry. Let them fold a paper square in many ways.

How to help: fold paper, cut paper snowflakes, make blob paintings, and point out symmetry in faces, cars, leaves, and Indigenous beadwork or quill designs where many patterns are balanced on both sides. Ask "How can you check?" and let your child test with folding or a mirror rather than giving the answer.