What it shows
Each rod carries the multiplication table of one digit written in split boxes. Laying rods for 4 and 6 side by side and reading row 7 gives 7 times 46 = 322 by adding along the slanted lines, a 400-year-old calculating tool.
The science
A rod for digit d lists d, 2d, 3d up to 9d with the tens and ones separated by a diagonal. Placing rods for 4 and 6 together and reading row 7 shows 28 and 42. The diagonals line up tens of one product with ones of the next, so reading diagonally adds 280 + 42 = 322, which is 7 times 46. The rods do the multiplying and you only add.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- 11 flat ice-cream sticks or card strips 2 cm wide
- A fine permanent marker
- A ruler
- A card frame with a numbered column 1 to 9 on the left
- A small box to store the rods
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.
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.
Divide each stick into nine equal boxes and draw a diagonal from top right to bottom left in every box.
Label the top of the sticks 0 to 9, and on each stick write the multiples of its digit from 1 times to 9 times, tens above the diagonal and ones below.
Make an index stick numbered 1 to 9 down its length and glue it to the left edge of the frame.
To find 7 times 46, place the 4 stick and the 6 stick next to the index stick.
Look along row 7: the boxes show 2/8 and 4/2. Add along each diagonal from the right: 2, then 8 + 4 = 12 (write 2, carry 1), then 2 + 1 = 3. The answer is 322.
Check with a calculator, then try 8 times 375 using three rods: the answer is 3,000.
For 46 times 37, find 46 times 30 and 46 times 7 from rows 3 and 7, then add 1,380 + 322 = 1,702.
Store the rods in digit order so the right ones are quick to find at the exhibition.
What you should see
The rods give 7 times 46 = 322 and 8 times 375 = 3,000, and reading two rows with a shift multiplies two-digit numbers correctly.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1Who invented these rods?
John Napier, a Scottish mathematician, in the early 1600s. He also invented logarithms.
2Why are the boxes split by a diagonal?
So the tens of one small product line up with the ones of the next, making the diagonal sum a correct place value addition.
3What is 7 times 46?
322.
4How would you multiply by a two-digit number?
Read one row for each digit, shift the tens row one place left and add.
Take it further
Make a second set and use both to multiply numbers with repeated digits, such as 44 times 6.
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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