What it shows
Beads falling through seven rows of nails bounce left or right at random at each nail. With eight collecting slots at the bottom, the expected share of beads in each slot follows Pascal's triangle, 1, 7, 21, 35, 35, 21, 7, 1 out of 128, which draws a bell-shaped curve.
The science
At each nail a bead goes left or right with equal chance, like a coin toss. After 7 rows the slot it lands in depends on how many times it went right, from 0 to 7. The number of paths to each slot is a binomial coefficient, the row 1, 7, 21, 35, 35, 21, 7, 1 of Pascal's triangle, so the middle slots catch far more beads than the edges. With many rows the binomial pattern approaches the normal distribution, which is why so many measurements in nature make a bell curve.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A plywood board 30 cm by 45 cm
- 28 small nails in a triangle of seven staggered rows
- Thin card strips for eight collecting channels
- A clear plastic sheet from an old folder as the front
- About 200 mustard seeds or 5 mm beads
- A funnel at the top
- Tape and glue
Safety
For this project: An adult must hammer the nails and check none pokes through the back.
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
8 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 staggered rows of nail positions on the board: 1 nail in the top row, 2 in the next, up to 7 in the seventh row, with 2 cm between nails and each row offset by 1 cm.
Hammer the nails in, leaving 8 mm standing, and tap each so a bead cannot wedge between nails.
Glue eight card channels under the last row, one below each gap, each wide enough for a column of beads.
Fix the clear sheet over the front with tape, leaving the funnel open at the top.
Tilt the board to about 20 degrees so beads roll instead of bouncing, and drop 128 beads one at a time through the funnel.
Count the beads in each slot and write the expected counts beside them: 1, 7, 21, 35, 35, 21, 7, 1.
Repeat with 256 beads and compare; the shape should be closer to the prediction with more beads.
Draw a bar chart of the counts on the display board beside Pascal's triangle.
What you should see
The two middle slots hold the most beads and the edge slots almost none; with 128 beads the counts are close to 1, 7, 21, 35, 35, 21, 7, 1 and the columns form a bell shape.
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 chance a bead lands in the leftmost slot?
It must go left at all 7 nails: one half to the power 7, which is 1 in 128.
2Why do the middle slots collect the most beads?
There are many more paths that mix lefts and rights than paths that go all one way; 35 paths lead to each middle slot.
3What happens with more rows?
The shape smooths out towards a normal distribution, the bell curve.
4Name a real-life quantity that follows a bell curve.
Heights of adults, errors in measurements, or marks in a large exam.
Take it further
Bend some nails so beads go right with probability more than a half, and show the peak shifting to one side like a skewed distribution.
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.
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