Some pictures feel balanced before we can explain why. One side seems to answer the other.
In this lesson, you are going to become a symmetry detective: looking for hidden mirror lines, testing shapes, and deciding when a match is exact — and when it is only almost exact.
Find the line of symmetry
A straight line has already been drawn across the picture. Rotate the line until you think it splits the figure into two matching mirror halves, then check your answer.
When you think you have found the line, imagine folding the picture along it. If every point on one side lands exactly on a matching point on the other, you have found a mirror line.
Mirror lab
Now make your own symmetric picture. Draw on one side of a mirror line and watch what happens when every mark is reflected.
Draw with a mirror
Draw anywhere on the left side. Every stroke is reflected across the purple mirror line.
Brush size: 8. Start drawing on the blue half.
Now give the idea a name
A shape has reflection symmetry if it can be reflected across a line and still match itself exactly. That line is called a line of symmetry.
You can also think of the line of symmetry as a fold line. If the two halves land exactly on top of each other, the fold works.
Go on a mirror-line hunt
If you have a small mirror, stand it upright on top of a shape. Move it around until the reflection completes the shape.
Try a square, rectangle, equilateral triangle and a shape of your own.
How many different places can you put the mirror and still make the whole shape? Make a prediction before you test each one.
How many mirror lines?
Some shapes have one line of symmetry. Some have several. Some have none at all. Make a prediction for each shape before opening the answer.
A different kind of symmetry
A shape does not always need a mirror line to match itself. Sometimes it matches again after it has been turned around a centre.
The starfish
Imagine turning the starfish around its centre. After about one fifth of a full turn, another arm moves into almost the same position.
Because it is a living object, the match is only approximate — but it shows the idea clearly.
A shape has rotational symmetry if it can be turned around a fixed centre by less than one full turn and still match itself exactly.
The smallest turn that makes the shape match again tells us how the symmetry repeats. For a perfect five-armed design, that would be one fifth of a full turn.
Mini projects for craft-loving learners
Choose one, two or all three. Each project opens on its own page, so you can keep this lesson short and come back to the practical activities whenever you like.
Paper snowflake
Fold, cut and unfold a design, then investigate the mirror lines you created.
Two-mirror star
Change the angle between two mirrors and watch repeated reflections build a star-like pattern.
Open project →Build a kaleidoscope
Make a simple kaleidoscope and investigate reflection and rotational symmetry inside it.
Open project →
Lesson 3: Symmetry detectives
Download the combined booklet with the Lesson 3 handout, activities and extra practice exploring reflection and symmetry.
Get the Lesson 3 resources →What did you think?
Whether you explored this together or worked independently, we would love to hear from both learners and parents. Tell us what you enjoyed, what was confusing, or what you would like to see next.
Share your feedback
The form is short and you do not need to give your name.
Next we will take the same ideas and make them move: slide, turn and flip.