Virtual geoboard

What the geoboard does

A geoboard is a square board of pegs with rubber bands stretched between them. On this page, tap pegs to hook the current band around them; each new peg becomes the next corner. Drag a corner to move it to another peg, or tap a corner to unhook it. There are four bands in four colors, so a child can build several shapes and compare them.

The readout names the shape, such as right triangle, rectangle, parallelogram or concave hexagon, and gives its area in square units and its perimeter in units. A unit is the distance between two neighboring pegs. Slanted sides are longer than one unit, so a perimeter with slanted sides is shown as a decimal.

Why a geoboard helps with area

Area is the number of unit squares that cover a shape. On a geoboard a child can count those squares directly, and when a slanted side cuts a square in half, two halves make one whole. Triangles become half of a rectangle, and a tilted square can be found by drawing a bigger square around it and taking away the corner triangles. Pick's theorem gives another route for shapes with corners on pegs: area = pegs inside + half the pegs on the band − 1. Turning it on colors those pegs so a child can count them.

Common mix-ups

• Counting pegs instead of squares. A 3 by 2 rectangle touches 12 pegs but covers 6 squares. Ask the child to point to each square, not each peg.
• Thinking a slanted side is 1 unit long. The diagonal of a unit square is about 1.41 units, which is why the perimeter of a tilted shape is not a whole number.
• Believing a tilted square is not a square. A square can sit at any angle; it still has four equal sides and four right angles.
• Mixing up area and perimeter. Area is the inside, in square units; perimeter is the distance around, in units.

A 10-minute geoboard routine

• Make a 4 by 3 rectangle. Ask for the area and the perimeter before looking at the readout.
• Drag one top corner one peg to the side to make a parallelogram. Ask whether the area changed and why.
• Press Challenge. The numbers hide until the child turns them back on, so they count to solve it.
• With a second band color, make a different shape with the same area and compare the perimeters.
• Finish by making a square with area 2 or 5, which needs a tilt.

Where it fits by grade

• Grade 2: recognize and draw shapes with a given number of sides and angles (2.G.A.1).
• Grade 3: find area by counting unit squares (3.MD.C.6) and solve perimeter problems (3.MD.D.8). In England, Year 3 measures perimeter and Year 4 finds area by counting squares.
• Grade 6: find the area of triangles, special quadrilaterals and polygons by composing and decomposing shapes (6.G.A.1). In England, Year 6 calculates the area of parallelograms and triangles.

Learning more

Area and perimeter are on Eurekami's skill map, and Daily Practice brings them back when they start to fade. Lessons draw shapes live from the numbers in each question, and teachers can print worksheets with answer keys on the same skills.