In this post, I will be continuing on from my previous post about maths. It’s often the case that us parents look at maths homework and realise that things are taught differently nowadays. In part 1 I looked at addition and subtraction so in this second part it will all about multiplication and division.
Before reading on, have you read part 1 yet?
Multiplication and division can be the Achilles heel of any student, young or old. Let’s work through some examples to learn how I was taught versus how it’s taught in my daughters’ primary school.
Before really getting into this, I can’t stress enough how important it is for children to learn their times-tables. I might often wonder if I’ll ever use algebra in my daily life, but simple multiplication is almost a skill I use daily.
Schools today reinforce the message that multiplication is repeated addition:
Let’s now look at how the school would calculate a tricker multiplication like 58 x 4.
It’s all about place value. The school encourages children to split numbers into their place value groupings. This helps to simplify the maths.
I can see how this will help kids to simplify the equation and make it easier to calculate. But, is this so different or better than long multiplication?
The same question done as long multiplication works in exactly the same way. To me is easier to understand too. With long multiplication, you multiply the 4 by the unit value of 58 (8) and then tens value of 58 (50) and then add the two answers together. As the multiplications get more difficult the method expands in a logical way.
Long multiplication of two 2-digit numbers is quite simple when you break it down. It’s requires nothing more than knowing you times-tables to 9 and knowing how to multiply by 10, 100, 1000 etc. These are 5 steps to achieving the above:
- Multiply the unit value of 24 by the unit value of 58
4 x 8 = 32
- Multiply the unit value of 24 by the tens value of 58
4 x 5 = 20
Because there was a tens value multiply this by 10
20 x 10 = 200
- Multiply the tens value from 24 (2) by the unit value from 58 (8)
8 x 2 = 16
Because there was a tens value multiply this by 10
16 x 10 = 160
- Multiply the tens value from 58 (5) by the tens value from 24 (2)
5 x 2 = 10
Because both numbers are from the tens column you multiply by 10 then that answer by 10
10 x 10 = 100
100 x 10 = 1000
- Finally, you all these answers together
32 + 200 + 160 + 1000 = 1392
There’s a huge emphasis on place value in the current teaching. It’s clear that the newer methods that are being taught to calculate are reliant on this thorough understanding of place value. I can’t argue with that. However, you had to understand this for the older methods too.
Of the four mathematical operations, division was always my least favourite at school. This implies I had a favourite, I didn’t I just didn’t like division.
When I first came across how division is taught now I had to admit something. I admitted that I liked it. Long division was, still is, a nightmare for me. Hate it with a passion. But, this post is about comparing the old with the new. So first we will use the method called division by chunking to solve 8640 ÷ 15.
Division by chunking
At first glance, division by chunking may look a bit long-winded. But, once you grasp the concept it really does work. The principle is that kids learn to multiply (yes I know we’re dividing but go with me here) simply numbers and by multiples of 10, 100 etc. So division by chucking uses this to help break, or chunk, the number down.
Start with the number you are dividing at the top. Down the left take your divisor number (15) and do asimpley multiplication that you know will result in a number less than the top number, in this case, 15 x 100 = 1500. Take the 1500 away from 8640 to get 7140. Now repeat this process until you have to multiply 15 by a lower number and so on. Once you have reach zero at the bottom, add up all the numbers you multiplied the 15 by and you get 576.
To prove in this case that the new method, for me, beats the old method I’ll go back into the pain cave and work through long division.
- 15 doesn’t go into 8, so we look at the next digit.
- 15 goes into 86 five times, so put a 5 above the 6.
Take the 75 away from 86 to get your remainder.
- Next, carry the 4 down to make 114.
15 goes into 114 seven times, so put a 7 above the 4.
Take the 105 from 114 to get your remainder.
- Carry the 0 down to make 90.
15 goes into 90 exactly 6 times, so put a 6 above the 0.
Even now, this method baffles me. I see now that there’s no logical use of place value here and that’s why kids get confused with it. Division by chunking may look less formulated when written down, but it works.
I’ve enjoyed this little exercise in comapring how I was taught maths and how primary schools to it today. I’m not a teacher so maybe I’ve missed something and I’d be happy if someone commented to point that out. Every day is an education and we never stop learning.
Thanks for reading.
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