What it shows
Rubber bands stretched round nails on a square grid make triangles, rectangles and other polygons in seconds. Counting the unit squares inside a shape gives its area, and a rectangle 3 by 4 always has area 12 and perimeter 14 wherever it is placed.
The science
The nails sit on a grid with equal gaps, so the gap is one unit of length and each small square between four nails is one unit of area. Area is how many unit squares a shape covers and perimeter is how many units of band go round it. A right triangle made by cutting a rectangle in half along its diagonal has exactly half its area, which is why the area of a triangle is half the base times the height.
Materials
Cost: under Rs 50. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A plywood board 25 cm by 25 cm
- 36 small nails with flat heads in a 6 by 6 grid, 4 cm apart
- Coloured rubber bands
- A pencil and ruler to mark the grid
- Dot paper for recording shapes
Safety
For this project: An adult must hammer the nails. File any sharp heads and keep rubber bands away from eyes.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Mark a 6 by 6 grid of dots 4 cm apart on the board and hammer a nail at each dot, leaving about 1 cm standing.
Stretch a band round nails to make a rectangle 3 units by 4 units and count the squares inside: 12.
Count the band length round the rectangle: 3 + 4 + 3 + 4 = 14 units of perimeter.
Add a second band along a diagonal of the rectangle to make two triangles, each of area 6.
Make a square of side 2 and then side 4, and record how the area changes from 4 to 16 when the side doubles.
Make as many different shapes of area 4 as you can and draw each one on dot paper.
Make a shape with a bigger perimeter than a 3 by 4 rectangle but a smaller area, such as a long thin 1 by 5 rectangle.
What you should see
The board gives area 12 and perimeter 14 for a 3 by 4 rectangle, area 6 for each half triangle, and shows that doubling the side of a square makes the area four times bigger.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is the area of a right triangle with legs 4 and 3 on the board?
6 square units, half of the 3 by 4 rectangle.
2Can two shapes have the same perimeter but different areas?
Yes. A 1 by 5 rectangle and a 3 by 3 square both have perimeter 12 but areas 5 and 9.
3What happens to the area when you double the side of a square?
It becomes four times bigger.
4What is one unit on the geoboard?
The gap between two neighbouring nails.
Take it further
For class 9 and 10: count the boundary nails B and inside nails I of any shape and check Pick's formula, area = I + B/2 take away 1.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
Science projects
Maths Working Models and Activities
Make maths visible: models for number, geometry, algebra and data
Science projects
Science Projects for Class 6 to 8
Working models matched to middle-school science topics