Please can you advise me on this numeracy

[bananasatsuma]

I have a feeling the way dc are taught to add and subtract 3 digit numbers has changed since i was at school. Just want to check i am telling my ds the right way.

by doing the units, 10s and 100s seperately (I think)
so
367-113 = (300-100)+(60-10)+(7-3)=254
but i am not sure what happens with 322-162,

Thanks for the reply. That was my exact problem! I have always been rubbish at maths.

My dd has been taught the colum way, as above, but doing the units first, then the tens and then the hundreds.

Also the empty number line method, but I can't explain that without a pen and paper.

the obvious thing would be

322-162 =(300-100)+(20-60)+(2-2)=200+(-40)+0 = 200-40 = 160
but can they understand this without knowing about negative numbers

You would do it as

322-162 = (300-100) + 22 - 62 = 200 + 22 - 62 = (220-60) + 2 - 2 = 160 + 2 - 2 = 160

(actually in that example you might actually take the 2 off first).

It's basically the way you would do maths in your head

Wow. Thanks for that. I will try to get my brain to absorb that now.

One way my dd has been taught is to look at the difference between numbers so often a subtraction will look like it is done in an addition way e.g.

162 to 170 = 8
170 to 300 =130
300 to 322 = 22

Answer = 8 + 22 + 130 = 160

By the time it gets to 322-162, then it is easier to chunk it. So, 322-100=222, 222-60=162 then 162-2=160.

The way suggested by witch is how we start off teaching the idea as it reinforces place value. However the way I've shown it above makes it easier on e bridging of tens or hundreds becomes involved. 222-60 isn't that difficult once they have sound place value knowledge and understand the concept of taking away multiples of 10!

Oh and the empty number line as aurra has suggested can also be used but is considered an earlier more informal method than the one I've suggested. With the number line you draw a blank number line and put the smaller number at the start. You are effectively jumping up towards the higher number in obvious chunks. So for 322-162, you would start with 162 and add on until you reach 322. We teach children to first take it to the next multiple of 10 so 170. Above it they would record the steps so in this case, +8, then they would make the easy jump from 170 to 200 and record +30 above it. Then they'd take that to 300 then to 320 then to 322 recording the 'jump' amounts each time. As they become more confident with the method they may chose to jump to 200 then record a jump of 122 all the way to 322, if that makes sense? After reaching the larger number they add up their jumps so 8+30+100+20+2=160

Hope that makes some sense?

I had NO idea they'd changed it from when we were at school. Who the heck is supposed to teach me these methods so that I can help dd? I currently do maths in my head using a complicated abacus and a basket of bricks.

The way treas has mentioned is the same as the numberline concept and children often start recording it this way once the numberline way makes complete sense to them.

It is basically teaching them that subtraction is the difference between the two numbers and that this can also be worked out by adding on. It also reinforces the idea that subtraction is the opposite of addition. We do lots of 7+5=12, so 12-5=7, so 12-7=5 sort of thing to help them understand how it works.

I was stressed about this so I bought a book called something like Maths for Mums and Dads. I'm glad I did - it is so different to how I was taught.

I did a 10 hour course last year at school all about how they teach maths in school these days. Its changed loads since I was at school (Im in my early 30s). Subtraction and addition, are taught in numerous ways. They start with a number line, (foundation/yr1,) move onto a blank number line, (yr1/2,) then using the long method, as witch described (ks2) & then usually around year 5/6 they'd be taught to put them above each other in the traditional sum we'd recognise. Basically, they like to give them lots of different ways to manage numbers. My own ds (yr3 but working at yr5 level,) would work out eg 127+335 by adding 127 & 300 & then adding 35 (in his head). Dd (yr1,) is just getting to grips with counting on, but with smaller numbers has just started to use a blank number line.

Maths for Mums and Dads is brilliant! A Dep Head who lectures on maths to Primary PGCE students recommended it. Great examples, clear explanations and common misconceptions resolved. Fab!
www.amazon.co.uk/Maths-Mums-Dads-Rob-Eastaway/dp/0224086359/ref=sr_1_1?s=books&ie=UTF8&qid=1320363421&sr=1-1

Just out of interest, does anyone know why the 'carry over' method involving lots of crossing out zeroes and replacing them with nines that I remember being taught in the 70s has been replaced?

I'm not 'pro' it, just interested in why thinking about numeracy teaching had changed.

Academy, the concept of borrowing and carrying confused many children because really, you aren't borrowing at all. It also didn't help children understand the concept of place value. So even for a simple subtraction involving no 'exchanging', say, 365-142, we alway would have said 5-2 then 6-4 then 3-1. But this is wrong as it isn't 6-4 at all. It's 60-40. The newer methods show the value of each digit much clearer so when a child is doing a calculation such as the one above they are actually visualising it as 60-40 rather than 6-4 and 300-100 rather than 3-1.

I started teaching a few years before the original numeracy stategy came in. With it's advent I saw a dramatic difference in the level of understanding shown by young children. The emphasis on oral and game playing early on, followed by informal jottings meant that it was all about understanding what they were doing and why rather than just leaning how to do it.

More able kids will always learn whichever method they are exposed to but the newer methods mean that many children who would previously have struggled now have a greater understanding of basic arithmetic.

Thanks. Our school does various parental involvement sessions to help us support our kids in the methods they've been taught at school. If these aren't enough, I'll definitely look at Maths for Mum and Dad.

I've been told today that I'm teaching subtraction next week on my PGCE placement - time to get the book out!

I have seen that many people recommend Maths for Mum and Dad. We have maths works books at home for 5-6 year-olds. Would this be sufficient to understand the modern maths methods or should I still buy Maths for Mum and Dad? I like work books because you can write in them.

"Maths for Mums and Dads" will explain the method that the children are being taught, why it works and how it's used. Workbooks usually don't have that background info, though that obviously depends on the workbook. It'll also last you many years of maths.

Thank you EcoLady. That is very useful to know.