What it shows
Each rod of the abacus stands for a place: ones, tens, hundreds and thousands. Ten caps on one rod are worth exactly one cap on the next rod to the left, so the number 2,346 is 2 caps, 3 caps, 4 caps and 6 caps from left to right.
The science
Our number system is a base-ten place value system. A digit is worth ten times more every time it moves one place to the left, so 10 ones make 1 ten and 10 tens make 1 hundred. The abacus turns this rule into something you can hold: when a rod collects ten caps you take them all off and add one cap on the next rod. This is exactly what "carrying" means in column addition.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A shoebox lid or a piece of plank for the base
- Four wooden skewers or pencils as rods
- 40 plastic bottle caps with a hole punched in the centre
- Four labels: ones, tens, hundreds, thousands
- Glue or clay to fix the rods
- A sketch pen
Safety
For this project: An adult must punch the holes in the caps with a hot nail or a drill, and cut the skewer points off so nobody is poked.
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.
Fix the four rods upright in a row on the base, about 5 cm apart, and let the glue or clay set.
Label the rods from right to left: ones, tens, hundreds, thousands. Right to left is the common mistake, so check it twice.
Put ten caps on each rod so you have enough to show any digit from 0 to 9, with one spare set for carrying.
Show the number 2,346 by placing 2, 3, 4 and 6 caps on the rods, reading from the thousands rod.
Now add 8 to it: put 8 more caps on the ones rod, so it holds 14 caps.
Take off ten caps from the ones rod and put one cap on the tens rod instead. Read the new number: 2,354.
Try subtracting 9 from 2,354: there are only 4 caps on the ones rod, so borrow by removing one tens cap and adding ten ones caps, then take 9 away.
Write each step as a column sum in your notebook next to a drawing of the abacus, so a visitor can match the two.
What you should see
The abacus shows any number up to 9,999 and acts out carrying and borrowing: 2,346 + 8 gives 2,354 and 2,354 take away 9 gives 2,345 on the rods and on paper.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1Why do we remove ten caps and add one cap on the next rod?
Because one cap on the next rod is worth ten caps on the rod before it. That is place value.
2What is the biggest number this abacus can show?
9,999, with 9 caps on every rod.
3What is the value of 7 caps on the hundreds rod?
700.
4What happens if you put 12 caps on the hundreds rod?
You must change ten of them into one cap on the thousands rod, leaving 2 on the hundreds rod.
Take it further
Add a fifth rod for ten-thousands and show the population of your town or village on the abacus.
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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