Year 6 maths - when can they use a calculator?

[WoodenCat]

DS has maths homework to work out percentage increases. He has been given and understands the method of multiplying by 1.xx where xx equals the percentage.

He doesn’t know if he may use a calculator. Any teachers able to advise please? He has 20 questions and it will take ages if he has to sit and work out eg 215x46% or 89x17% - unless I’m missing an easier method?

Seems perverse to just plug it all into a calculator and like torture to write it all out!

Hi,

I am a TA and no they will not be allowed a calculator in the sats papers. Your DS should have been taught that if he can work out 10% and 1% then he can work out everything in between from those. E.g 46% work out 10% then multiply by 4, then work out 1% and multiply by 6. Add the 2 answers. Another way for 46% would be to work out 50% or 1/2 and then take away 4X1%.
.

No calculators in yr 6

Just do 215 x 46 and divide by 100.( move 2 decimal points to the left.) is the quickest way, I think.

As a year 6 teacher, the best way I've found, that gives the children in my class the fewest mistakes, is to chunk it into different percentage amount of the number.
E.g. 215 x 46%

Divide 215 by ten to get 10% = 21.5

Double 10% to get 20% = 43

Double 20% to get to 40% = 86
(Or just multiply 10% by 4)

Halve 10% to get 5% = 10.75
divide 10% by 10 to get 1% = 2.15

Then add the 40%, the 5% and the 1% together.

This has the added bonus of getting them to consider what a percentage of an amount actually is.

prometheus , is that really best way to calculate the percentage?
I think it's very good way for children to understand the concept.
But when question you need to answer is something like 215 x 46%, doesn't that cause children with less grasp of it make even more mistakes?
If the child can halve 21.5 easily, they must be able to do multi column multiplication easily than following all those steps of devide by 10, multiply by 4 etc and add up 40% + 5% +1% in the end?

irvineoneohone

You would think that, but actually children with less grasp of mathematics tend to make more mistakes when following a method with no understanding of why (in my experience). I've shown the children in my class both methods and they tend to find the idea of dividing the number by 100 and then multiplying by what they're trying to find very confusing (e.g. to do 215/100 x 46). Unless they are drilled in the method, they forget it easily, and then added to that you need to know they're secure in multiplying decimals - another area they can easily make mistakes).

You could do 215 x 46 and then divide by 100, but the conceptualisation for why that works is very advanced.

And halving 21.5 with busstop is fairly straightforward compared to doing 2.15 x 46

irvineoneohone

You would think that, but actually children with less grasp of mathematics tend to make more mistakes when following a method with no understanding of why (in my experience). I've shown the children in my class both methods and they tend to find the idea of dividing the number by 100 and then multiplying by what they're trying to find very confusing (e.g. to do 215/100 x 46). Unless they are drilled in the method, they forget it easily, and then added to that you need to know they're secure in multiplying decimals - another area they can easily make mistakes).

You could do 215 x 46 and then divide by 100, but the conceptualisation for why that works is very advanced.

And halving 21.5 with busstop is fairly straightforward compared to doing 2.15 x 46

Thank you.
When my ds started doing decimal multiplication, he got confused. I mentioned it on one of the thread and noble(secondary maths teacher) suggested doing it as whole number and move decimals and it has worked perfectly. There was no confusion.
Also dividing by 100 is the concept they need to know, isn't it, since percent means per 100? So when you see 46%, they need to know it's same as 46/100, or 0.46?
Just thought simple 215 x 46 / 100 is easier than finding out 10% and them multiplying by 4 to get 40%, and finding out 5 % and 1 % and adding everything together. It's great skill to have, and children should know that, but I don't think it's very practical when you have 20 questions to do.

I understand the ease of the method is tempting, but I do prefer my students to understand why. Your son can do the method but does he know why the digits move? Does he understand that 215 x 46 then you can divide it by 100 is the same as doing 2.15 x 46? He may do, but many don't.

Understanding that 46% = 0.46 and 46/100 is indeed something they need to know (and why I teach them to do 215/100 and then multiply by 46, as this is how you would find a fraction of a number). However, being able to understand that 46% is a percentage of another number is different (in my opinion) than knowing it is the same as 0.46 of a whole.

I've taught both and found that segmenting sticks in their heads better than the more streamlined method.

I understand the ease of the method is tempting, but I do prefer my students to understand why. Your son can do the method but does he know why the digits move? Does he understand that 215 x 46 then you can divide it by 100 is the same as doing 2.15 x 46? He may do, but many don't.

Understanding that 46% = 0.46 and 46/100 is indeed something they need to know (and why I teach them to do 215/100 and then multiply by 46, as this is how you would find a fraction of a number). However, being able to understand that 46% is a percentage of another number is different (in my opinion) than knowing it is the same as 0.46 of a whole.

I've taught both and found that segmenting sticks in their heads better than the more streamlined method.

Thank you. It's very interesting,
I find the concept not hard to understand, if you use the right tool to model percentage of something.
But I really don't know about how other children work out, since I only have one child.
I am not disageeing with you at all. I was just curious.

just to add, he shoudl be able to do 215 x 46 pretty quickly, long multiplication is somethign they shoudl be able to rattle off at year 6.

This is ridiculous.

89x17%

They should be being taught that is 89 x 17/100 so then they should be able to do 89x17 longhand then divide by 100.

Chunking it up into silly bits is time consuming and error prone and imo ultimately unhelpful. Fine if it is 20% of 150 but for 'odd' numbers I think it's daft (sorry teachers). My DD1 suffered from being taught all these fancy things and shortcuts but wasn't taught the one simple rule.

Now to the homework. 20 of these on the trot is, I agree, torture. I'd be tempted to make him do 5 long hand to show understanding, then use calculator for the rest.

Isn’t the conceptualisation for multiplying by 45/100 all part of the ks2 curriculum?

If they don’t know/understand that a percentage is a fraction out of 100 and 45% can also be written as 45/100 they probably aren’t ready to be finding a fraction of an number. And associating fractions with division is part of the ks2 curriculum

Multiplying a whole number by a fraction and long multiplication should have been taught earlier in KS2.

Chunking it up into silly bits is time consuming and error prone and imo ultimately unhelpful

The only reason to do the chunking is that it's easier (for most people) to be able to do it in their head, not that that is useful if you have a pencil...

sirfred Exactly. It is useful for something like 15% of 200 but not the examples given in the OP.

I also personally think that children shouldn't even be attempting 17% of 89 in y6 unless they properly understand percentages and thus can do it properly. It won't imo help them in secondary to go up with high maths SATs scores because they can do calculations like that without knowing why.

Prometheus You could do 215 x 46 and then divide by 100, but the conceptualisation for why that works is very advanced.

I'm interested by that statement. Do you not think that this is a flaw in the curriculum that they don't understand by the end of primary that the operations can be done in any order in that calculation?

I'm going to tag @noblegiraffe as I'd like her take on what she would see as a priority for pupils going up to secondary to understand / be able to do.

Teen - I hear where you are coming from, but I have had a student who just could not understand or do percentages. She had no problem understanding 10% x 4 though!
She needed to do that step in between, before progressing to the 'correct' version.

For students who just don't get it, you do need sometimes to stop and do something they can grasp first.

Ok in secondary for non-calc they'd be expected to chunk the percentage, find 10%, then 5%, add them up etc.
On the non-calc GCSE paper they'd be asked reasonable percentages like 15%, 40% etc where this method is appropriate. We don't teach them to do decimal multiplication probably because it's more prone to error.

Something like 17% of 89 would only come up on the calc paper, and it would be to check that they knew how to use multipliers (so type in 0.17*89).

Asking kids to do 17% of 89 by hand is crap because not only is it tedious, but it also makes them worse at using a calculator. It's hard enough to train them out of the mindset that calculators are cheating as it is. They should see that calculation and automatically reach for their calculator. It's really frustrating that 2/3s of the GCSE papers are calculator-allowed and yet kids who have access to a calculator would see that question and do 10%, 5% ... so many marks on the calculator papers are lost by kids bodging written calculations while the correct answers are a button-press away.

noble Do you have any view on how advanced understanding order of operations is?

I'm certain last years KS2 arithmetic test (non calculator) required children to calculate 7% of a number.

Why do they need to chunk it noble? Non-calc does not mean no pencil and paper, are they? Why do they need to do it more time consuming way like chunking when they can simply do 89 x 17 then /100?

You are the one suggested about moving decimals points for decimal multiplication 3/4 years ago to me I believe?

It was 7% of 500. Lots of ways of doing that one! 7% of 100 * 5 or 500% of 7, or 1% x 7, so pretty straightforward.

irvine chunking is easier than knocking up a grid and doing long multiplication, and usually quicker.
We teach removing the decimal point and putting back in for decimal multiplication, but we don't teach using decimal multiplication when there's a more straightforward method.

(I guess I am interested as to whether there is a disconnect in what is required for KS2 SATs in maths compared with y7/y8 in secondary, in the same way I perceive there to be for the G bit of SPaG.
I haven't noticed one, but threads like this think maybe that is just because DD wasn't very able.)

Teen Generally kids aren't at all confident with playing around with the order of operations. They know that they can do multiplication in any order, but usually stick to left to right when they see a string. Same with addition and subtraction, not many would switch -19+23 to 23-19.

What I think weird about teaching in primary maths is that they say they teach the kids several different ways to do things and let them choose. But they seem to prevent children to use most straight forward ways. At ds's school, they didn't allow column methods in KS1. Recently my ds said he was told off for using long division because they haven't taught them yet in class.