What it shows
Lattice multiplication breaks a product like 23 times 47 into four small products (8, 12, 14 and 21) written in split boxes, then adds along the diagonals to give 1,081. The machine makes the method quick enough to race a calculator.
The science
Every two-digit number is tens plus ones, so 23 times 47 is (20 + 3) times (40 + 7). Multiplying out gives 20 times 40, 20 times 7, 3 times 40 and 3 times 7, which are the four cells of the lattice. The diagonal lines group digits with the same place value: ones with ones, tens with tens and so on, so adding along each diagonal is the same as column addition with carrying.
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 square of thick cardboard 30 cm by 30 cm
- Chart paper for the 2 by 2 lattice with diagonals
- Four strips of card that slide in slots along the top and the right edge
- A whiteboard marker and a clear plastic sheet to write on
- A cutter and ruler
Safety
For this project: An adult must cut the slots with the cutter.
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.
Draw a 2 by 2 grid of 8 cm squares on the chart paper and rule a diagonal from the top right to the bottom left corner of every square.
Cut slots above the grid and to its right, and make sliding strips with the digits 0 to 9 so any two numbers can be set.
Cover the grid with the clear sheet so products can be written and wiped.
Set 23 on the top and 47 on the right. In each square write the product of its column digit and row digit, tens above the diagonal and ones below: 08, 14, 12, 21.
Add along each diagonal starting from the bottom right corner: the first diagonal holds only 1; the second holds 2 + 4 + 2 = 8; the third holds 1 + 1 + 8 = 10, so write 0 and carry 1; the last holds 0 plus the carry, which is 1. The common mistake is to miss one of the three digits in a middle diagonal.
Read the answer around the left and bottom edge: 1,081, and check on a calculator that 23 times 47 = 1,081.
Try 56 times 89 and 99 times 99, writing the carries beside the lattice.
Time a classmate doing the same sum by long multiplication to compare.
What you should see
The machine gives 23 times 47 = 1,081 and 56 times 89 = 4,984, matching the calculator, and shows where every digit of the answer comes from.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What does the diagonal line in each box do?
It separates the tens digit from the ones digit of the small product, so digits of equal place value sit on the same diagonal.
2Why is lattice multiplication correct?
It is the distributive law: each digit of one number multiplies each digit of the other, and the diagonals add the place values correctly.
3What is 23 times 47?
1,081.
4What happens when a diagonal adds to more than 9?
You write the ones digit and carry the tens to the next diagonal, exactly as in column addition.
Take it further
Make a 3 by 3 lattice for three-digit numbers and multiply 123 by 456 to get 56,088.
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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