Why is the area written as a fraction?

Because on a geoboard it is one. Any shape with corners on the pegs has an area that is a whole number of squares or a whole number and a half, so 4½ is the exact answer and 4.5 is a decimal approximation of something that was never a decimal.

Why does the perimeter sometimes have a ≈ in front of it?

Because a diagonal side is not a whole number of units. A side from one peg to the one diagonally next to it is the square root of two, about 1.41, and no number of decimal places makes that exact. The sign is there so nobody teaches a child that 1.41 is the answer.

Can I have more than one band?

Yes, up to six, each in its own colour. Close one and the next tap starts another. The measurements follow the newest band, and Remove takes the newest one off.

Why will it not tell me the area of my shape?

If the band crosses itself, it does not enclose one area, so there is nothing honest to report. Take the crossing corner off and it will measure it.

Geoboard

Shape & Space · Year 2–Year 6

Stretch bands between pegs. Reads off area and perimeter, or hides them.

Loading…

About the geoboard

Tap one peg, then the next, and a band stretches between them. Tap back on the corner you started at to close the shape. There is no mode to be in and nothing to pick up first, and every tap is one step of Undo, so a wrong corner costs a tap to put right.

The area is exact. A geoboard's whole point is that a triangle on it covers exactly four and a half squares, so the area is written as 4½ rather than as 4.5 and never as a rounded decimal. The perimeter cannot always be exact, because a side across the diagonal of a square is the square root of two, so when it is not exact it says so with a ≈ rather than pretending 13.66 is the answer.

Turn the measurements off and the board holds a shape and a question. That is how a geoboard is used: make a shape with an area of six, or two different shapes with the same perimeter. Turn them back on to check.

A band that crosses itself reports no area at all, and says why. The usual formula gives a bow tie an area of nothing, which is a confident wrong answer to a shape a class can see, and a tool that does that is worse than one that declines.

How to use it on your whiteboard

1Tap peg to peg to stretch a band round the corners of a shape.
2Tap the ringed peg, where you started, to close it.
3Tap the last peg again to take that corner back off.
4Pegs switches between a 5, a 9 and a 13 board.
5Turn Measurements off to ask the class before showing them.

Questions

Why is the area written as a fraction?: Because on a geoboard it is one. Any shape with corners on the pegs has an area that is a whole number of squares or a whole number and a half, so 4½ is the exact answer and 4.5 is a decimal approximation of something that was never a decimal.
Why does the perimeter sometimes have a ≈ in front of it?: Because a diagonal side is not a whole number of units. A side from one peg to the one diagonally next to it is the square root of two, about 1.41, and no number of decimal places makes that exact. The sign is there so nobody teaches a child that 1.41 is the answer.
Can I have more than one band?: Yes, up to six, each in its own colour. Close one and the next tap starts another. The measurements follow the newest band, and Remove takes the newest one off.
Why will it not tell me the area of my shape?: If the band crosses itself, it does not enclose one area, so there is nothing honest to report. Take the crossing corner off and it will measure it.