Calculating percentage

[user789653241]

When you are calculating 39% of 89, I always thought the way was to 89 x 0.39.
I just saw a suggestion, do 89 x 39, then divide by 100. It seems very logical, but never occurred to me. (I don't have a maths brain.)
This method seemed to me a great one, since you don't need to involve decimal multiplication, and all the children doing this should know divide by 100 means moving 2 decimal points to the left.
Is this a valid method in UK?

[spanieleyes]

Yes, of course!

[KP86]

If I was doing it that way, I would teach the other way around. Divide by 100 (to get one per cent) then multiply by percentage needed.

[user789653241]

Thanks, spaniel.

KP, if you divide 89 by 100 to get 1%, it will still involve decimal calculation. 0.89 x 39 and 89 x 0.39 isn't so different. But doing 89 x 39 and move 2 decimal points afterwards seemed less confusing to me.
But of course, I know they needs to understand what they are doing in the first place.

[OurBlanche]

Moving the decimal place, that place jump we all learned and used so well, is frowned upon these days. I was informed that we don't teach tricks we explain why...

... cart and horse I thought!

[user789653241]

OurBlanche, I didn't know it was frowned upon! My ds knew it, so I assumed they taught it in UK. He learned a lot of maths through US websites, maybe he picked it up from them. But I think he understands logic behind it.

[OurBlanche]

I have no idea why, or how widespread the dislike is. It seems daft to me. I still use most of the 'tricks' I was taught - and I taught Functional Skills maths for a few years

[KP86]

I see what your saying, but my logical brain wants to find the 1% first.

In reality I would always just multiply by the % if using a calculator. (Eg 89 * 0.39), as you said.

If I was doing it in my head I would divide by 100 and multiply back out as I find it easier to work in smaller numbers.

[noblegiraffe]

If you were finding 39% of 89 you would most likely be using a calculator so typing 89 X 0.39 is more efficient than typing 89 X 39 / 100

If you are finding percentages by hand then we wouldn't expect a student to do 89 X 0.39, we would expect them to break it down e.g. Finding 10%, 1% then multiplying 10% by 4 to get 40% and subtracting 1% to get 39%.

[spanieleyes]

It's not moving the decimal place, it's increasing the place value! ( although the effect is the same, the understanding isn't!) So children are taught that multiplying by ten moves the digits one place to the left as we use base ten,.
Similarly we don't "add a zero" when multiplying by ten, we again move the digits one place to the left ( because of the confusion that can be caused when multiplying decimals by 10, simply adding a zero doesn't work!!)

[user789653241]

So noble, you don' do it manually at all in secondary?
I only ask because ds was doing these questions on maths website, and I told him he can use calculator(the title said "percentage-calculator") , but he was adamant he wasn't allowed to used it in school.
And when I was browsing through percentage problems on other sites, I came across those suggestions.

[OurBlanche]

Thanks spaniel... it is more widespread than just were I used to work then

[user789653241]

"Finding 10%, 1% then multiplying 10% by 4 to get 40% and subtracting 1% to get 39%." seems to take even more work than just doing 89 x 0.39.
It seems too complicated for me.

[spanieleyes]

We don't use calculators in primary as the children are expected to be able to calculate percentages of amounts without one. Noble's method ( of finding 10%, then 1% and using these to find all other percentages) is the usual one. Multiplication of decimals can cause children conceptual problems so is best avoided

[user789653241]

spaniel, that sound very logical and better than teaching them to move decimal place. thank you.

[noblegiraffe]

In secondary, on a non-calculator paper, the students would be expected to find a percentage by breaking it down to 10%, 5%, 1% and build up the required percentage from these easy building blocks.

In the olden days when VAT was 17.5%, pupils were taught to find 10%, halve it to get 5%, halve it to get 2.5%, then add the percentages together. They would not be taught to multiply by 0.175.

He won't be allowed a calculator in school because he's in primary and they've now got rid of all calculator assessments. If he is accessing secondary teaching material, then they will expect him to be able to do both non-calculator (breaking down the percentage) and calculator (multiplying by a decimal) methods, because finding a percentage could appear on a non-calculator or a calculator paper (2 out of 3 of the new GCSE papers will allow a calculator).

[OurBlanche]

And I still use the Noble thing now... it is easy to do in your head. One of the good tricks... though finger bends to get x9s is best. Or the 11 sandwich

[educatingarti]

Maths tutor here. Students are taught both methods in KS 3 - ie the x 0.39 by calculator and the mental/paper and pencil method of find 40% via 10% then subtract 1%. If he understands it, there's no reason why he shouldn't do 39 x 89 / 100 but this is harder to do mentally than the 40-1 method.

[noblegiraffe]

It seems too complicated for me

Long multiplication involving decimals is not easy.

If they are finding a percentage without a calculator, it will often be numbers were they could do these calculations in their head, so 15% of 30 for example. Find 10% and 5% and adding is a lot easier than 0.15 X 30.

[user789653241]

Thank you everyone. I think follow on to noble's method would be the best way forward for my ds. He needs to expand his way of thinking. It maybe easy to learn to be able to calculate 89 x 0.39, but doing it more efficient way in your head would be more valuable. I'm just finding it so eye opening because I was never good at maths! I really appreciate all the input. Thank you again!!!!!

[mrz]

Noble they have to be able to do it without a calculator in primary ...no calculator allowed in SATs.

[noblegiraffe]

I know. It's a pain in the arse, we just had a bunch of Y7s mess up their end of year exams because they insisted on doing their calculator paper without using their calculator. It's going to be something that we will have to majorly focus on in secondary transition.

[MrR2200]

I teach Year 6 and, at primary, most percentage questions are in 5% or 10% jumps and you wouldn't tend to get answers to two decimal places. Therefore, I agree that (89 x 39)/100 is probably the most efficient method in this case and the mental method is potentially quite complicated.

However, as you say, irvine, the real aim is to expand thinking. The point of the new curriculum especially (with its non-calculator approach to primary maths) is to develop a conceptual understanding of number as opposed to just techniques for dealing with particular problems.

If I were working it through with a Y6 student and trying to make it less complicated... well, first off, I'd start with 30% of 350, 85% of 470 and 40% of 3 because these require fewer steps.

But sticking to your question, I'd make sure they use jottings and their wider maths knowledge. So jot down:

10% of 89 = 8.9
1% of 89 = 0.89

Now, to find 40% do 8.9 x 4. You can do this mentally if you know that 8.9 is the same as 9 - 0.1. So four times that is 36 - 0.4 which is 35.6.

So I'd jot: 40% of 89 = 35.6.

Now you need to take 1% from 40% which means calculating 35.6 - 0.89 .

Because we're going into decimal places and we're subtracting, I'd probably draw a blank number line as a prompt -- this is what children use lower down the school and, although you can do it without, it's still a useful prompt to iron out misconceptions such as whether you're counting up or down.

So I know -0.89 is the same as -1 and then +0.11 (which I know because 11 is the complement to 100 of 89 and therefore 0.11 is the complement to 1.00 of 0.89).

35.6 - 1 = 34.6 -- that'll take me to the left-hand side of the number line. Then add 0.11 (a jump part-way to the right on the number line) to get 34.71.

What I'm trying to show is that, to work through this question, there's a lot of conceptual understanding needed. The child needs to know how to tackle percentages. How to subtract decimal numbers which are to different decimal places. How to simplify expressions to make them easier to calculate. Knowing complements to 100 in different powers of 10. And not to be fazed by needing a few steps to get an answer.

Children should have all this by Year 6 if they're working at the standard. And none of the individual calculations are very complex. So if the child is missing a step, you can work out which one they're missing.

And if you've found something they're missing -- THAT'S the gap you plug first because it's obviously a more fundamental gap than calculating percentages.

By the way, once you've shown both methods, the extension of this would be to ask the child to use their reasoning skills to compare the two approaches. Is (89 x 39)/100 the same as the above method? Prove it -- check. What's similar and what's different between the methods? How do you know? Which is more efficient and why? Is it the one with the fewest steps or the simplest calculations along the way? Which would be the best method to use with a calculator? Which would be the best method if you were estimating in your head?

It's more involved than just having the one strategy but it's less about teaching "the way to do it" and more about developing a deeper understanding of how to manipulate numbers in lots of different ways to reason and problem-solve.

[user789653241]

Wow, thank you MrR2200. I was really blown away by your post. It makes calculating 39% of 89 so much more interesting than just doing actual calculation. Especially the proving bit, it will show if ds has understood the concept fully or not. It really made me to start to appreciate what teachers are saying about deepening and mastering.
Thank you for your help.