Mental Arithmetic - Just going into Y2 - What should DD be able to do?

[Elsashmelsa]

DD is just finishing Y1.

I have no idea what they are supposed to be able to do in regards Mental arithmetic...

We have some of the Carol Vorderman books (which she actually asks to do because she enjoys them) and she doesn't struggle at all with the Age 5/6/7 maths in those because there are always numberlines etc, but she does seem to struggle doing these things in her head.

But I have no clue what she is supposed to be able to do in her head, if anything!

We were doing something the other day and I asked her to do 5+3 and she could only do it using her fingers. Should she be able to do that in her head easily by now?

We haven't had her report yet but I know that she is currently in the top set for Maths, although I don't think she's as confident in her Maths as she is in her reading/phonics/spelling.

Is there anything to help her with mental arithmetic and if so, what sort of numbers should we be talking about? I have a friend who is a teacher. Her DS is in DD's class. She says that he easily adds sums like 16+17 because he knows the 'strategies' to use. Can anyone shed any light where we might find things to help DD (if indeed you think she needs help...).

It is the same we found with DS2, he is going to finish year 2 now. In class, he is top of the class, can do big sum using number line. But for mental math, he can only slowly doing 100-22=78, 16+17=33 etc. I think in year 1, he was not secure at 5+3 in mental math either. I forgot when did he stop to use his fingers.

Anyway, I think it is because DC didn't have much chance to practice. In class, they go through the concept quickly, once DC master it, they would move forward. Although DS2 has moved to big sum with 3 digits, he is not able to do the small sum quickly.

So I think you don't need to worry, it is common. But meanwhile, maybe let her practice a bit during summer holiday? I found monopoly is useful, as there are 2 dices, you need to add up to play. DS2 likes this game, so we played a lot. Or simple shopping game, buy one item 3 pound, the other one 6 pound etc.

Thanks Cloud. That's a good idea. We also have a game called 'Sum Swamp' which is similar. There are two die with numbers and one with three sides with '-' and three sides with '+'. The objective of the game is to throw the three die together and then they will do the sum. She manages these Ok but I can see her mouthing the words for workings for example if she gets 6+7 she mouths:

"6 in my head, add one is seven, add two is eight, add three is nine..." etc up to 7..

I think you may find the following document helpful.

The second part is all about teaching mental strategies for calculation. The first part is less useful as it relates to the old curriculum.

HTH

We are in Wales and DS3 is going into year 2, he is considered slightly ahead, but I imagine with England's new curriculum he wouldn't be.
He can add numbers up to 100 e.g. 37+45
Or take them away can easily do something like 59-34 but would have to be concentrating to do 54-39 but can do it.
He knows that if doing a subtraction and the numbers are close together it is quicker to count on, or to subtract if they are far away.
He can do fractions of numbers e.g. what is 1/4 of 16 as long as the answer is a whole number - wouldn't be able to do 1/4 of 15 for example.
Knows his 2,4,5 and 10 times tables, some of the 3s.

Thanks Diamondage for the document, I will have a look through.

LittleMissGreen, I would imagine that's far and away much more advanced than the average year 1. They haven't even covered numbers up to 100 in Y1 yet (other than counting up to 100 in 2s, 5s and 10s), so I don't think that's a representation of what is required.

I'm more concerned with strategies on how I can help DD to do mental arithmetic so thank you for your comments on that, I will use those .

I also need to understand whether they would actually be 'expected' to do sums in their heads or whether they will use a number line? I guess some of this I will ascertain from reading her report that is due out this afternoon. That may give me some insight as to whether she is doing what she needs to do or not...

Diamond, I've just looked at that document. That is exactly what I needed to see in terms of where she needs to be. Other than the adding '9' which she may have done but we haven't talked about, everything else she is already doing, plus some of the Y2 stuff aswell.

I am going to work on the adding '9' over the holidays. The explanation of how to do that is exactly what I needed to see. I'm very conscious of teaching her to do things and then finding that they teach them in a very different way at school. I may even see if I can have a word with one of her teachers before she finishes because the last thing I want to do is confuse her. They may say to leave it to them as she's absolutely fine!

Thanks again.

Thanks diamond as well; I also have a dd going into Y2 and in exactly the same boat.

Glad I'm not the only one Fiona, they are taught so differently to the way I learnt that I'm not sure how to explain things without confusing her!!

sorry! We hear so much about how the English curriculum has got really hard, I have come to believe we have been very left behind in Wales.
In terms of strategies, If DS was adding 25+35 he would add up in 10s - so either know 20+30=50 because 2+3=5, or would work it out 20+10+10+10 and then +5+5
If adding 9 he adds 10 then -1
If adding 8 he adds 10 then -2
Same with subtracting
to take away 9 then -10+1
to take away 8 then -10+2

Or if he was say doing 35-8 he would do 35-5 = 30 30-3=27
If he were doing 2 close numbers e.g. 35-27 then would do 27+3 = 30
30+5=35 3+5=8

Not to worry LittleMiss, sounds like your young man is doing fantastically well!!

Those strategies are great, thank you!!

From what I understand (as I said we all learnt so differently), once they have the strategies, the size of numbers shouldn't matter, so that's what I want to try and help DD with. Working out 'how' to work out the answer, IYSWIM.

You've got some very good suggestions already.

Sum swamp is a fantastic game for practicing quick mental maths. Also any other game where you can use two dice (e.g. snakes&ladders, ludo, etc).

I would say find out what she needs to know in terms of number bonds, and while playing with her check how well she knows them with instant recall. Start with pairs of numbers that add to 10, then 20, then 100 (although since you said they haven't covered numbers up to 100 she might not need these ones yet).

One game someone suggested in MN is to use normal cards from A to 10 (A equals 1), you shuffle the cards, then uncover the first one and the first person to shout the number bond gets the card (e.g. if the card is 8, she needs to say 2). I played this a lot with DS and he enjoyed winning the game because I was so "slow" and hardly ever got any cards for myself :)

Once she knows number bonds well enough, she can apply them to more complicated additions in her mind, like the examples LittleMissGreen posted (e.g. 24+6, she needs to see in her mind that 24 is like 20+4, the 4 pairs with the 6 to make 10, then she has 20+10 that equals 30).

Ellle, thank you for that!! She is very quick at doing her number bonds to 10 and 20 so I think we will work on applying those to bigger numbers over the holidays.

I got her report today and obviously the report has changed because they no longer do levels, so instead they have 'Made more progress than expected', 'Made the expected level of progress' and 'Requires Improvement'. Across the board for Maths and Literacy she got 'Made more progress than expected' so I don't think they're worried. Having said that, I don't know how that equates to the curriculum and that's what I need to understand...

But thank you for the brilliant suggestions. We've definitely got some ideas to work on during the holidays.

It's absolutely fine for a year 1/year 2 child to be using things to help them with mental calculations - that could be anything from grapes to number lines. They need a huge amount of practice at doing Maths in a practical way to help them develop really strong mental images to go with the numbers. If they get that firm grounding in KS1, they'll have the right foundations in place so they can thrive in KS2. In my experience, where children often come unstuck in KS2 is when they've rushed through the KS1 Maths and haven't properly secured their knowledge - they can sort of do it but aren't absolutely solid.

So in your position I'd have a 0-100 number line and have races to find a given number on the line. If you say 79, does your DC start from 0 and work all the way up, or do they start somewhere between 50 and 100? Use a 100 square - how quickly can they find a given number on there? Can they add or subtract 10 by going up or down 1? When you've done lots of that with the 100 square, can they do it without the 100 square? All of those things will help you to see if she has a solid understanding of place value.

These games are good: www.southwick.wilts.sch.uk/pdf/Bare%20Necessity%20KS1.pdf

Finally, if you're not confident about the Maths methods taught in school, I recommend getting hold of a copy of Maths for Mums and Dads - mine was 1p from Amazon!

It's absolutely fine for a year 1/year 2 child to be using things to help them with mental calculations - that could be anything from grapes to number lines. They need a huge amount of practice at doing Maths in a practical way to help them develop really strong mental images to go with the numbers. If they get that firm grounding in KS1, they'll have the right foundations in place so they can thrive in KS2. In my experience, where children often come unstuck in KS2 is when they've rushed through the KS1 Maths and haven't properly secured their knowledge - they can sort of do it but aren't absolutely solid.

So in your position I'd have a 0-100 number line and have races to find a given number on the line. If you say 79, does your DC start from 0 and work all the way up, or do they start somewhere between 50 and 100? Use a 100 square - how quickly can they find a given number on there? Can they add or subtract 10 by going up or down 1? When you've done lots of that with the 100 square, can they do it without the 100 square? All of those things will help you to see if she has a solid understanding of place value.

These games are good: www.southwick.wilts.sch.uk/pdf/Bare%20Necessity%20KS1.pdf

Finally, if you're not confident about the Maths methods taught in school, I recommend getting hold of a copy of Maths for Mums and Dads - mine was 1p from Amazon!

Oh - and what I expect my year 1s to be able to do (quick recall) is doubles and halves of numbers to at least 10 and often 20, then use what they already know to be able to work out other numbers ie if double 4 is 8, double 40 is 80. Counting forwards and backwards in 2s, 5s and 10s (the backwards bit is important). Adding and subtracting 1 or 10 from any 2 digit number (with a 100 square as a visual prompt if necessary). Knowing that 23 is made up of 2 tens and 3 ones/units. Number bonds to 10 and 20 (working out the bonds to 20 by using their bonds to 10 then adding 10 if necessary). Multiples of 10 to make number bonds to 100 (ie 70 & 30 - apply existing knowledge of 7 + 3 and make both numbers 10 times bigger). More able children know that they can find 1/4 of a number by halving and halving again. We've also been doing quite a bit of relating 1/2 and 1/4 turns to telling the time to the nearest 1/4 hour. (In fact - if you want to work on something at home, then telling the time is a really useful thing to do. Children need regular reinforcement, and it tends to come up once a term on the curriculum so doing a little bit every day or so helps them to not forget in between.) I'm sure there's more, but I can't remember it now...

Oh - and what I expect my year 1s to be able to do (quick recall) is doubles and halves of numbers to at least 10 and often 20, then use what they already know to be able to work out other numbers ie if double 4 is 8, double 40 is 80. Counting forwards and backwards in 2s, 5s and 10s (the backwards bit is important). Adding and subtracting 1 or 10 from any 2 digit number (with a 100 square as a visual prompt if necessary). Knowing that 23 is made up of 2 tens and 3 ones/units. Number bonds to 10 and 20 (working out the bonds to 20 by using their bonds to 10 then adding 10 if necessary). Multiples of 10 to make number bonds to 100 (ie 70 & 30 - apply existing knowledge of 7 + 3 and make both numbers 10 times bigger). More able children know that they can find 1/4 of a number by halving and halving again. We've also been doing quite a bit of relating 1/2 and 1/4 turns to telling the time to the nearest 1/4 hour. (In fact - if you want to work on something at home, then telling the time is a really useful thing to do. Children need regular reinforcement, and it tends to come up once a term on the curriculum so doing a little bit every day or so helps them to not forget in between.) I'm sure there's more, but I can't remember it now...

toomuch that is all so helpful thank you!! Taking various sections of your advice, she can count forwards and backwards to 100 in 1s, 2s, 5s and 10s. She also knows all her number bonds to 20 and knows how to add 10s, 20s etc. We have a 100 square at home so she tends to use that if she gets stuck. She can quickly find a number on a number line, going straight to it. She learnt to tell the time (at 5 minute intervals) about 3 months ago and we bought her a teacher watch for her birthday about a month ago which she uses every day.

We've also got a poster on the wall that shows 3,525 shown as 3 thousands, 5 hundreds, 2 tens and 5 units, she loves doing partitioning . She can also do her halves but I'm not sure about doing quarters so I might work on that with her...

I think part of the problem is that they have to get through so much that they don't get to spend long enough on each thing...

Thank you so much.

Then I really don't think you have to worry at all about covering anything new over the summer. Just keep her ticking over with what she knows already. Why not try using nrich maths to find challenges which enable her to apply her knowledge? That will really help to embed it. (Can she count backwards in 5s starting on any multiple of 5? That's the one which really stumps them!)

I will have a look at that, thank you!!!