Fun with Symmetry
Lines of symmetry, paper folding and cutting, mirror images of numbers and words, and tiles that fit together without gaps.
- What a line of symmetry is
- Predicting shapes made by folding and cutting paper
- Mirror images of shapes, numbers, and words
- Tiling: repeating shapes with no gaps or overlaps
- Symmetry in nature
🎨 Let’s Begin: The Ink Butterfly
Pinky puts a few drops of paint on one half of a paper, folds it, and presses. When she opens it, both halves are exactly the same, like a butterfly!
The fold line divides the design into two matching halves. It is called the line of symmetry.
🪞 Part 1: Lines of Symmetry
A shape is symmetrical if you can fold it so that one half lies exactly on the other.
| Shape | Lines of symmetry |
|---|---|
| Heart, kite, arrow, butterfly | 1 |
| Rectangle, envelope | 2 |
| Equilateral triangle | 3 |
| Square | 4 |
| Circle | Countless! |
✅ A rectangle has only 2 lines: across the middle (up–down and left–right).
✂️ Part 2: Fold and Cut
- Fold a paper once and cut a shape on the fold → you get the shape doubled when you open it.
- Fold twice (into four layers) and cut a corner → the cut shows up 4 times.
- To cut a hole in the centre, fold twice and cut the corner where the two folds meet.
🔢 Part 3: Mirror Images
A mirror flips things. Only symmetrical things look the same in a mirror.
- Digits that look the same in a side mirror: 0, 1, 8
- With the mirror kept below the number: 0, 1, 3, 8
- Numbers like 181, 808, 1881 look the same with the mirror at the side, and 1331, 8030 look the same with the mirror below.
Why is AMBULANCE written backwards on the front of ambulances? So drivers ahead can read it correctly in their rear-view mirror and make way quickly!
🧱 Part 4: Tiling
Floors and walls are covered with tiles that fit together with no gaps and no overlaps. Squares, rectangles, triangles, and hexagons work well.
A tile can be slid, turned, or flipped to make beautiful patterns. Look for the repeating unit: the smallest part that repeats again and again.
Cut-and-slide trick: Cut a piece from one side of a square and tape it to the opposite side. The new odd-shaped tile still fits perfectly with its copies!
✏️ Practice Time
Try these on your own first, then check your answer below each question.
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Pages 164–165 · Ink design and paper planeLines of symmetry
Challenges
Challenge 2: Fold once and make two cuts in the middle from the fold. When opened, you get a shape with 4 sides (a diamond or rectangle hole, depending on the cuts).
Challenge 3: Fold twice and cut a small square at the corner where both folds meet (the centre of the paper). 2 cuts are needed to cut out that little square.
Symmetry in shapes
Mirror placement and numbers
(b) Circle both 181s. 686 does not stay the same, because 6 flips.
Digits with the same side mirror image: 0, 1, 8. 4-digit examples: 1001, 1881, 8008, 8118, 1111, 8888 (mirror at the side) · 1331, 3003, 8338 (mirror below).
Guess my number: 118 (mirror kept below the number: 1, 1, and 8 are all symmetric top-to-bottom) or 111 (mirror at the side).
Ambulance and mirror writing
Sides and lines of symmetry
Create your own
👨👩👧 Tips for Parents
- Make ink-blot butterflies and paper cut-outs together.
- Write your child’s name in mirror writing and let them read it with a mirror.
- Look at floor tiles at home and find the repeating pattern.