Symmetry and reflection on the whiteboard

What it does on screen

The first pill in the row picks one of four boards. Each one is a different way into the same idea: one half is the other half flipped over a mirror line. The black bar at the foot of the board holds the buttons you press during the lesson, and the pen in the header writes over any of them.

• Freehand. A white board with a dashed mirror line. Draw on one side and it appears on the other as you draw. Pick an upright line, a line across, both at once, a diagonal, or a six or eight-way pattern round the middle. With one line you can drag it somewhere else or turn it with the round handles.
• Squares. Squared paper, 6, 8 or 10 squares across, with an upright, across or diagonal mirror. One side has a coloured pattern. The class fills in the other side and Check marks it.
• Coordinates. A shape on a coordinate grid, reflected in the y-axis, the x-axis or any upright line. Show distances counts each corner to the mirror on both sides, and a table lists the coordinates before and after.
• Lines of symmetry. A Fold panel and six shapes to look at. Draw a line across a shape and fold it to test it. Turn test counts how many times it fits in a full turn.

Freehand: drawing with a mirror

Pick a colour and a pen and draw. Thick is good for the back of the room. Fill floods a closed space and its reflection at the same time, so the spots on a butterfly's wings are two taps. If the space has a gap it won't fill, which is a handy way to show a shape isn't closed.

Hide other side is the most useful button here. It hides the reflection, so you draw half a picture and the class says (or sketches on their whiteboards) what the other half will look like. Then press Show. Turn on Grid if you want squares to count against.

The six and eight-way patterns draw in every slice at once, like a kaleidoscope. They make a lovely five minutes at the end of a lesson, and a good way in to talking about how many mirror lines a pattern has.

Squares: complete the pattern

Random gives a few coloured blocks on one side, not a scatter of single squares, so there's something to talk about. A pupil picks a colour and taps squares on the other side. Tap a square again to clear it. Check puts a tick on each square that's right and a cross on each one that isn't, and the card says how many are right, how many to fix and how many are still to go. Show answer fills the rest in faintly if you want to go through it together.

The diagonal mirror is the one children find hardest, because they want to count straight across. The tip card says it plainly: count to the mirror square by square. You can tap the given side yourself to make your own pattern, which is handy if you want a particular shape like the ones in a test paper.

Coordinates: reflect in a line

Random shape puts a triangle or a four-sided shape on one side of the mirror. Or press Plot my own, tap the corners, then tap A again to close it. Press Reflect and the shape folds over the line rather than just appearing on the other side.

Show distances draws a dotted line from each corner to its image, with the number of squares written on each half: 6 and 6, 2 and 2. That's the whole idea in one picture, and the class sees it rather than being told it. The table lists A, B and C before and after, and for the y-axis the Notice card says x flips sign and y stays the same, which they can check against the table. Hide image takes the reflection away so they can work the coordinates out first.

You can pick one, two or four quadrants. One quadrant has no room past the y-axis, so it uses a line like x = 6 instead. The x-axis needs all four quadrants, so picking it opens them.

Lines of symmetry: fold and turn

Tap a card to put its shape in the Fold panel. Drag a line across the shape and press Fold. One half lifts and flips over the line. If it lands exactly on the other half, it says so and the line stays drawn in lilac. If it doesn't, you can see why, because the flipped half sticks out. A line drawn very close to a true one snaps onto it, so nobody needs a perfect hand on the board.

The cards hide their number of lines behind a lilac pill. Ask the class first, then tap the pill or press Reveal. Regular, Irregular, Letters and Mixed change the six shapes. The letters are plain capitals, so H has two lines, E has one, and S, N and Z have none.

Turn test is a stretch for Year 6. A copy of the shape turns round the middle and the board counts how many times it fits before it's back where it started. That count is the order of rotational symmetry.

How to use it in a lesson

1. Start with Freehand. Draw half a butterfly with the other side hidden. Ask what it will look like, then Show.
2. Move to Squares. Do one together on the upright mirror, then hand the pen to a pupil for the next one and press Check together.
3. Try the diagonal. Expect mistakes. Use Check to find them, then count square by square to the mirror.
4. Go to Coordinates for Year 5 or 6. Hide the image, ask for the new coordinates, then Reflect and Show distances.
5. Finish with Lines of symmetry. Show the gallery with the answers hidden and let them argue about the rectangle and the parallelogram. Then fold them.

Ideas by year group

• Year 2. Freehand with the upright mirror. Draw half a face or a house and ask what's missing.
• Year 3. Squares on the upright and across mirrors, size 6 or 8.
• Year 4. Lines of symmetry with the Regular and Irregular sets, and Squares with the diagonal mirror.
• Year 5. Coordinates on two quadrants, first the y-axis and then a line like x = 2.
• Year 6. Coordinates with the x-axis on four quadrants. Then Turn test on the Letters set: which letters have rotational symmetry but no lines of symmetry?

The misconceptions it helps with

Every diagonal is a line of symmetry. Fold a rectangle or a parallelogram along a diagonal and the flipped half clearly doesn't fit. It's the most common wrong answer, and now they can see why.

A diagonal mirror reflects straight across. On the diagonal squares, Check marks a square counted straight across as wrong, and the tip says to count to the mirror square by square.

A reflection is just a slide. Show distances makes it clear: each corner ends up as far past the mirror as it started in front of it, so the shape faces the other way.

Reflecting in the y-axis changes the y. The table and the Notice card show x flipping sign and y staying the same, with the numbers right there.

Frequently asked questions