Transcript

INSTRUCTOR:

I am going to find the result of multiplying 74 by 36 first of all by using the grid method. This links to finding the area of a rectangle 74 units long and 36 units wide. I'm going to partition 74 and 36 into that tens and units, which will mean splitting the length of the rectangle into 70 and 4 and the width of the rectangle into 30 and 6. I'm now then to find the areas of the four parts of the rectangle. So the top left, 30 times 70, three 7's are 21.

So 30 times 70 is 2,100. Top right, 30 times 4 is 120. Bottom left six times 70 is 420. 6 times 4 is 24. So the area of the rectangle is the area of those four parts added up. I'll work out some of the numbers on the top row, that's 2,220. And the bottom row will be 444. And if I add those two up, I'll get the answer to 74 times 36 which is 2,664.

The beauty of the grid method is that the learner works out four products for a two digit by two digit calculation. And if any mistakes are made, it is easy to check where those mistakes are. The learner is also dealing with those numbers as the sum of their parts, 70 and 4, 30 and 6 in this case.

Another method of working out the same multiplication would be to use the standard column method. This is the traditional method, which has been taught for decades. So you would think that every adult would be proficient at it but surveys show that very few people in the general population are proficient at using the standard column method. So we'll look at that method now.

The numbers are written one underneath the other, 74, 36, and I put a multiplication at the side to remind us that that's what we're doing. We're going to have three lines of working. First of all, I'll multiply 74 by 6. Six 4's are 24. So I'll put down the 4 and carry the 2 very small in the next column. six 7's are 42 plus the two that I carried makes 44.

Then I come to multiply by the 3, remembering that it is actually 30. So to multiply by 30, I put down the 0 then carry on as if I were multiplying by 3. Three 4's are 12. So I put down the 2 and carry the 1 very small into the next column. Three 7's are 21 plus the one that I carried makes 22. And if I add those two lines up I got 2,664, the same as I did for the grid method. You might notice that they've got the same lines of working.

Now the standard column method is neat and quick if the learner knows how to do it correctly. However, for many learners, this method is fraught with difficulties. It treats each number as a string of digits, unlike the grid method which treats each number as the sum of its parts. This can mean the learner operates the standard column method according to the set of rules, and they can be easily forgotten or confused.

Some of the procedural problems I've seen are learners not knowing what to do with the carrying figures or forgetting to put down the 0 or not putting it in the units column but putting it at the side and getting lost during the working as they don't know their multiplication tables and need to work them out, whereas in the grid method, they still have to work out the multiplication table facts, but at least the other three boxes can wait for them. And there are no carrying figures to worry about.