Interactive 2D shapes and polygon explorer for the whiteboard

What the polygon explorer does on screen

It draws one shape big in the middle of the board on faint squared paper. The top row is the setup: how many sides, and which shape. The black bar along the foot holds everything you switch on and off mid-lesson, so nothing is buried while you are still talking to the class.

• Sides. The minus and plus buttons step between three and twelve. Every regular shape sits on a flat base, and the odd-sided ones point upwards, so the pentagon looks like a pentagon and the square looks like a square.
• The shape family. At four sides you get Square, Rectangle, Rhombus, Parallelogram, Kite and Trapezium; at three, Equilateral, Isosceles, Scalene and Right-angled. Press one and the corners glide across into the new shape.
• Regular. Glides the corners back to equal sides and equal angles from wherever they are. Take hold of a corner and the shape becomes irregular again on its own, so there is nothing to switch off first.
• Interior. A blue arc inside every corner with the size of that angle written beside it. On a dragged shape the numbers change as you move, and they always add up to the sum in the line underneath.
• Angle sum. Writes the angles out adding up, 108 + 108 + 108 + 108 + 108 = 540, under the shape.
• Hide angles. Keeps the arcs but blanks every number, so the class works them out before you show them.
• Lengths and Perimeter. Each side labelled in grid squares, and the total added to the line underneath. A regular four-sided shape measures six squares along every side.
• Marks. The usual ticks on sides that are equal and arrows on sides that are parallel, one pair getting one mark and the next pair two, the way a textbook draws it.
• Exterior. Each side carries on as a red dashed line, and the exterior angle is drawn and labelled between that extension and the next side. That is the only honest way to show what an exterior angle actually is.
• Symmetry. Every line of symmetry, drawn right across the shape. Regular shapes only, because a dragged one may well have none.
• Triangles. Dashed orange lines fan out from one corner to every corner it is not already joined to, cutting the shape into triangles so the angle sum can be counted instead of recited.
• Diagonals. Every diagonal at once, in purple dashes, which is how you count them for real.
• Right angles. Puts the usual small square into any corner within two and a half degrees of ninety, which a finger on a board can actually hit. With it switched on, the corner you are dragging is pulled the last bit of the way onto exactly ninety and holds there.
• The line underneath. It names what is on the board rather than what you last pressed: how many sides, which sides are equal, how many pairs are parallel, how many right angles, and the angle sum. Drag a square about and it will start calling itself a trapezium, then a kite, then an irregular quadrilateral.

How to use it in a lesson

Turn on one thing at a time. With interior angles, exterior angles and every diagonal showing at once the shape turns into a spider's web and the idea you wanted is lost in it.

1. Name it before it appears. Press plus and pause before the class can read the line underneath. Nine sides, what do we call it? Then let the readout settle the argument.
2. Build the angle sum instead of giving it. Turn Triangles on and step through four, five, six and seven sides. Count the triangles each time, multiply by 180, and check against the sum in the readout before you move on.
3. Break the shape on purpose. Drag one corner right in towards the middle and ask whether the angle sum has changed. It has not, and a lot of children expect it to have.
4. Walk the quadrilateral family. Four sides, then Square, Rectangle, Rhombus, Parallelogram, Kite, Trapezium in turn with Marks on. The ticks and arrows do the explaining: what changes, and what stays.
5. Prove exterior angles make 360. On a regular shape, read one exterior angle and multiply by the number of sides. Then drag it about and check the claim still holds.
6. Hunt the right angle. Four sides, Right angles on, and send a child out to drag a corner until the little square appears. It clicks into place when they get close, so the shape holds still while the class checks it.
7. Print the board if you want the same shape on paper, with whatever you switched on still switched on.

One thing worth knowing before the board is live: if you drag a corner past its neighbours the sides cross over, and a shape that crosses itself reports angles that will not mean what a child expects. Pressing Regular glides it straight again.

Ideas by year group

• Year 1. Regular on, all the angle buttons off, and step from three to eight. How many sides, and how many corners? Is it always the same number?
• Year 2. Four sides, then press Square and Rhombus one after the other. Same four equal sides, and only the corners have moved. So which one is the diamond, and why is that not a name?
• Year 3. Four sides, Right angles on. Drag a corner until the square appears, then ask whether a four-sided shape can have two right angles.
• Year 4. Regular on, Symmetry on, stepping from three to ten. How many lines has each one got, and what do you notice about that number?
• Year 5. Interior, Angle sum and Triangles on, five to eight sides. How many triangles fit inside, and what does that make the sum? Then drag a corner and check the total has not moved.
• Year 6. Diagonals on for a pentagon, a hexagon and a heptagon. Five, nine and fourteen. Where is that pattern going next, and can you say why?
From the classroom

I had a Year 4 girl who was adamant that a shape had to be regular to be a pentagon. She had a point, in a way, because every pentagon in her book and on my display was the same neat one, point up and flat along the bottom. So I took hold of one corner in front of the class and dragged it a long way down and to the left, into something that looked like a squashed house. I asked what it was now. Half the room said it was not a shape any more. The readout underneath said pentagon, five sides, and it was still counting them. We dragged it about for another couple of minutes and she got there in the end, but what convinced her was not the name, it was that the sides still counted to five however ugly it got.

The misconceptions it helps with

A square turned round becomes a diamond. Press Square, then Rhombus. Four equal sides both times, and the only thing that changed is the corners. Tilting a square does not make it something else, and having the two side by side is the quickest way to settle it.

A squashed shape must have squashed angles. Drag a pentagon into something lopsided and the sum stays at 540. The individual angles all change, the total does not, and seeing both at once is the whole point.

Muddling the interior and the exterior angle. Showing both at one corner makes it plain that the two sit on a straight line and add to 180, which is worth more than memorising either of them.

Counting diagonals by guesswork. Draw them all and count them for real on a pentagon, a hexagon and a heptagon, and the jump from five to nine to fourteen becomes something to chase.

Frequently asked questions

Is there a free interactive 2D shape tool for the whiteboard?

Yes. This one opens on the board from one button, with no sign-in and nothing to install, and it works on an interactive whiteboard, a laptop or a tablet.

Can I make an irregular polygon?

Yes. Every corner is a handle, so just drag one and the shape becomes irregular. The angles move with it and the line underneath renames the shape as it changes, so a dragged square starts calling itself a trapezium the moment one pair of sides is parallel.

How do I show the interior angle sum of a polygon?

Turn Triangles on and the shape is cut into triangles from one corner. Count them, multiply by 180, and compare with the sum printed under the shape. Stepping up a side at a time builds the rule rather than announcing it.

Why will Symmetry not turn on?

Symmetry only draws on a regular shape, because a dragged shape may have no lines of symmetry at all. Press it on a dragged shape and it says so. Press Regular, the corners glide back into place, and the lines appear.

Does the square sit flat or stand on its point?

Flat. Every regular shape sits on a flat base, so four sides looks like the square the readout says it is, the hexagon is flat-bottomed and the triangle has its base down. The pentagon keeps its point at the top, which is how children expect to see it.

Can I show a kite or a trapezium?

Yes. Step the sides to four and the quadrilateral family appears by name: Square, Rectangle, Rhombus, Parallelogram, Kite and Trapezium. Press one and the corners glide into place. Three sides gives Equilateral, Isosceles, Scalene and Right-angled the same way.