Geoboard
Stretch rubber bands between pegs to make shapes, then see each shape's area and perimeter. Copy shapes from the challenge cards or make your own.
Geoboard · free from Fieldbook Learning
How to use it
Click a peg to start a rubber band, then click more pegs to stretch it from corner to corner. The band follows your pointer until you click the first peg again to close it. Choose a colour before you start, or select a band and pick a colour to change it. Drag any corner to another peg to reshape a band, click inside a band to select it, and use Undo, Remove band or Clear all to tidy up. The board comes in 5 by 5, 7 by 7 and 10 by 10 pegs, with or without faint grid lines.
The panel shows the selected band's number of sides, a name for the shape when there is a simple one (right triangle, square, rectangle, parallelogram, trapezoid, kite, pentagon, hexagon and more), its area and its perimeter. Challenge cards ask for shapes like a rectangle with an area of 6 or a tilted square with an area of 2; build it, select it and press Check. On a keyboard, tab to the board, move with the arrow keys and press Space to place a peg. It works with a mouse, a touch screen or a projector in full screen.
The math: squares, half squares and tilted sides
Area is how many unit squares fit inside a band. Count the whole squares first, then the pieces: a square cut corner to corner makes two halves, so two half squares make one more whole. For a slanted side, draw the rectangle around it; the triangle it cuts off is half of that rectangle. The tool works the area out exactly with the shoelace formula, so you will see answers like 4½ square units.
Perimeter is the distance around the band. Straight sides along the grid are whole numbers. A slanted side is longer than it looks on the grid: the diagonal of one square is about 1.4 units, not 1. The tool gives the perimeter to one decimal place with ≈ and, for older students, the exact form such as 4√2. That is how a square can have an area of 2: tilt it so each side is the diagonal of one square.
For grades 5 and 6, turn on peg counts. Pick's theorem says that for any band that does not cross itself, area = pegs inside + half the pegs on the band − 1.
- How many different rectangles with an area of 6 can you make? Do they all have the same perimeter?
- On a 5 by 5 board, how many different sizes of square can you make, counting tilted ones?
- Make a triangle with an area of 2. Now move one corner along a line parallel to the opposite side. What happens to the area?
- Check Pick's theorem on three shapes of your own. Does it work for a band that crosses itself?
Free to use, no account needed. It runs in your browser: nothing you type, and no sound from your microphone, is sent to Fieldbook.
Hands-on lessons to pair with Geoboard
Ready-to-teach units, each lesson a printable teacher guide and student sheet. Your first three lessons are free.
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Three full lessons, free
Make a free account and download any three Fieldbook lessons, from any grade or subject, as printable PDFs. No card needed.
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