Geoboard

A square peg board with four colors of rubber band. Tap pegs to make a shape, close it, and read its name, area in square units and perimeter, on a board of 6 by 6, 8 by 8 or 11 by 11 pegs.

How to use it

Choose a board size, then tap pegs one after another to stretch a band round them. Use the arrow keys and Enter to do the same from the keyboard.
Tap the first peg again, or press Enter, to close the band. The shape's name, area and perimeter appear beside the board.
Press a color to start a band in another color and make a second shape on the same board. Press Z to undo a peg and R to clear the board.

Ideas for class

Ask the class to make a rectangle with an area of 12 square units and find all the different rectangles they can: 1 by 12 does not fit, but 2 by 6 and 3 by 4 do.
Make a square, then a tilted square that uses diagonals, and compare their areas. The tilted one is a good puzzle for older students.
Show a right triangle with legs 3 and 4 and ask for its area, then double it into a rectangle to show why the area of a triangle is half of a rectangle.
Ask for two shapes with the same area but different perimeters, and discuss what the numbers say about long thin shapes and compact ones.
Build an L-shape by closing a six-peg band and ask students to find its area by splitting it into two rectangles.
Make a band that crosses itself on purpose and discuss why the tool says the area means nothing.
Ask students to make a parallelogram that is not a rectangle and to find the base and height that give its area.

Questions

What is a geoboard?

A board with pegs on a square grid and rubber bands that stretch round them. Students use it to make shapes, then compare their sides, angles, areas and perimeters, which makes geometry something they can build.

How does it find the area?

From the peg positions, using the area formula for any polygon given by the coordinates of its corners. For shapes on a grid the answer is always a whole number or a half, and it matches counting squares.

Why is the perimeter sometimes written as about?

A side that runs diagonally across the grid is longer than a whole number of units, for example about 1.4 for one step across and one step up. The tool rounds such lengths to one decimal place and says so.

What if the band crosses itself?

Then it is not a single simple shape, and an area makes no sense, so the tool says so instead of showing a number. Undo a peg with Z and try again.

Is anything kept about what students make?

No. The bands live on the page until you reload it, and nothing is stored or sent. Only the size of the board you last chose is remembered, in this browser, on this computer.

Nothing you do here is sent to us. Names, lists and settings stay in this browser. No sign-in, no ads.

Using the geoboard in class

The geoboard is the place where area and perimeter stop being formulas and become something to see. Students who build a 3 by 4 rectangle and count twelve squares inside and fourteen units around it have the idea before they meet the formula. The tool reports the numbers so that students can check their own counting.

Begin with rectangles and squares, counting squares and sides by hand.
Then triangles, which are half of a rectangle on the grid.
Then shapes with diagonal sides, where perimeter is no longer a whole number.
Finish with open-ended challenges: the same area, different perimeters.

Common mistakes

Counting pegs and not the spaces between them. A band from one peg to the next is one unit long.
Confusing area and perimeter, giving the squares inside when the question asks for the distance round.
Treating a diagonal as one unit. A diagonal across a single square is longer than a side.