What it shows
On a 10 by 10 chart of 1 to 100, counting in twos, fives and tens makes straight columns, counting in nines makes a diagonal and counting in threes makes slanting stripes. Patterns appear because the chart has ten numbers in each row.
The science
Each row of the chart holds ten numbers, so moving down one row adds 10. Multiples of 10 and 5 line up in columns because adding 10 keeps the last digit. Multiples of 9 step down one row and back one column each time, because 9 is 10 minus 1, so they form a diagonal. Multiples of 3 land at 3, 6, 9, 12, 15 and so on, shifting by 3 along each row and giving slanted stripes.
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 chart paper ruled into a 10 by 10 grid, numbers 1 to 100
- Transparent plastic sheets from old folders
- Coloured permanent markers
- Tape or clips to hold the overlays
- A ruler
Safety
This project uses safe, everyday materials. Still, read the rules below with a parent before you start.
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.
Step 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.
Rule the chart with 1 at the top left and 100 at the bottom right, ten numbers in every row. Write the numbers big enough to read from a metre away.
Cut four clear plastic overlays the same size as the chart.
On the first overlay colour every square that holds a multiple of 2. Hold it over the chart to check you have columns.
On the second overlay colour the multiples of 5, and on the third the multiples of 3.
On the fourth overlay colour the multiples of 9 and look at the slanting line from 9 down to 81; 90 and 99 start a second short diagonal at the right edge.
Fix the overlays with clips so a visitor can flip them one at a time or stack two together.
Stack the twos and threes overlays: the squares coloured twice are the multiples of 6. Write this discovery on a label.
Add a small card explaining why 9 makes a diagonal: each step is one row down and one square back.
What you should see
Flipping the overlays shows columns for 2, 5 and 10, stripes for 3, a diagonal for 9, and the twos and threes together pick out exactly the multiples of 6 (6, 12, 18 up to 96).
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01Why do the multiples of 10 make one column?
Every row has ten numbers, so adding ten moves straight down one row.
02Which numbers are coloured on both the twos and the fives overlays?
The multiples of 10.
03How many multiples of 9 are there up to 100?
Eleven: 9, 18, 27 and so on up to 99.
04What pattern would multiples of 11 make?
A diagonal going down and to the right, since 11 is one row down and one square forward.
Take it further
Make an overlay that colours only the prime numbers and count them: there are 25 primes below 100.
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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