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Chinese multiplication

magazine article | Published in TES Newspaper on 3 May, 2002 | By: Wendy Fortescue-Hubbard, Math Agony Aunt

Q

I am a support assistant. The class teacher has allowed the pupils to do long multiplication in a new way they have been taught at primary school. They get the right answer by filling in a diagonal grid but I haven't a clue how.

A

There are several methods that use a grid. Here I demonstrate the Chinese one. I have found this particularly helpful for dyslexic pupils as errors in calculation or incorrectly written digits can more easily be identified.

Before multiplying, by whatever method, make an estimate to ensure the answer is about the right size. For this, simplify the numbers, so if we are calculating 689 x 17 we round 689 up to 700 and 17 up to 20. Now we have 700 x 20 = 14,000 - a five-digit number.

689 has three digits and 17 has two. Draw the grid (figure 1) three squares wide and two squares deep. Draw a diagonal line from the bottom left-hand corner to the top right-hand corner through each square. The direction is important.

The idea of the grid is to multiply each digit on the top by each digit on the side:6, 8, 9 x 1 and 6, 8, 9 x 7.

Figure 2 shows 8 x 7 = 56. The "tens" (5) is placed in the top triangle of the square and the "units" (6) in the bottom. For 1 x 9 = 9, place 0 in the "tens" position and a 9 in the units position - so 9 is written 09.

Complete the grid for all of the digits (figure 3) and extend the diagonals outside the grid. This is where the answer is to be written. The next step is to add the numbers in the diagonals together (figure 4). This is always begun in the bottom right-hand corner. The first diagonal has only one digit (3) so a 3 is written below as shown. In the next diagonal the sum is 6 + 6 + 9 = 21, write down the units (1) below this diagonal and carry the 2 into the adjacent diagonal on the left. The digits in the next diagonal are added, 0 + 8 + 5 + 2 + (the "carried" 2) = 17. As before the units (7) is written below the diagonal and the 1 is carried into the next diagonal. This next diagonal gives 0 + 6 + 4 + "carried 1" = 11. Write down 1 at the bottom of the diagonal and carry the 1 into the last diagonal. This last diagonal gives 0 + the "carried 1" = 1. The solution is 11,713 (this has five digits as we estimated).

Good tip: colouring the diagonals in alternate colours helps pupils see clearly the numbers in each diagonal that have to be added.

The grid I have shown is for a three-digit by two-digit number. For a five-digit number by a four-digit number a grid 5 squares by 4 would be used, and so on.

When multiplying decimals, the position of the decimal point in the answer is found by estimating the size of answer expected. For example for 6.89 x 1.7, simplify 7 x 2 = 14. So we expect an answer in the tens and the decimal point is placed between the 1 and 7 giving 11.713 Q

I am a French teacher and recently had to cover a maths lesson. One of the pupils asked me "what is the difference between mass and weight?" I didn't know how to explain it. Can you help?

A

Mass and weight are related by gravity. The mass of an object is an expression of the amount of matter in it and remains unchanged, wherever it may be. The weight of an object is the force experienced when gravity acts on it. As gravity changes so does an object's weight.

I got this letter on the day we had a digger in to move soil for a parking space. It moved 18 tonnes of soil. Now imagine putting it all into a bag and squeezing it so tight it has half its original volume. We have changed the way it looks, but we know we still have same amount of soil, in other words the same mass and weight. Now put the soil into a rocket and blast it into space where there is no gravity. We would still have all the same soil but it would have zero weight.

As weight is a force we should use units of Newton (symbol N). On Earth the soil has a weight of 180,000 N, but in deep space the force (weight) is 0 N.

Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.Email your questions to Mathagony Aunt at teacher@tes.co.ukOr write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX


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