Bridging 10 in subtraction questions

[teafor1]

I've been teaching my son about 2 digit subtraction such as 45-23=22 using the method of splitting the numbers into tens and units. He's got that. He can add two two-digit numbers and knows to add the extra 10 into the ten spot if the unit spot is larger than ten. Subtraction where you have to "steal" a ten from the ten spot is trickier to explain. What year would the kids normally learn this and how would it be taught?

My DD would tackle this as 'counting on' from 23, first in tens then units. She is y2.

I would teach it in a number line in year 2, first jumping back in 10s then the units. I've also done it (with year 3) using lolly sticks and elastic bands. I made a big place value chart (HTU columns) then put the lolly sticks into bundles of 10 with the elastic bands. For your expletive I would put four bundles of ten in the tens column and then five loose ones in the units column. It then becomes obvious that you can't take away more than you've got, so you take a bundle from the tens column, take the elastic band off and put them in the units column. Then you've got enough to do the subtraction. (Hope that makes sense - on phone)

First this is really important - can he do this on a number-line yet? If he can't do number-line then work on that before going more 'abstract'.

I think otherwise you are broadly trying to do column subtraction, which both my DDs managed y3-y4. For both my DDs I used physical coins £1, 10ps 1ps and used the 'going to the bank' analogy.

ie 42-17
You have 4 10ps, and 2 1ps. You need to give me first 7 1ps.
You can't so you go to the bank and change a 10p into 10 1ps
You now have 3 10ps and 12 1ps.
You can now give me 7 1ps and then 1 10p.
You now have 2 10ps and 5 1ps = 25p.

Once they can do this with coins, I write it down as column subtraction whilst they are doing it.
Then swap to do on paper mirroring with coins
Then just paper.

Also works with addition.

Thanks everyone. He hasn't been using number lines at home but I assume he does at school. I don't hear much about what he learns at school though! I also like the idea of bundles of things plus loose ones to really give some realness to it.

What year is he?

Number lines were a new thing for me (maths degree) when my DDs arrived, but I am a complete convert as I think they really help the child visualise stuff. Otherwise they can learn the mechanics without really having a solid foundations of how everything fits together, and they end up without a good grasp of the reasonableness of answers later on.

He's in year 1. Number lines are also new for me so I hadn't thought of using it to be honest! At the last parent evening the teacher talked briefly about place value (tens and unit spots) so I went down that route. As I said he is good with addition, even carrying the 1, but subtraction is just too abstract I think. Especially for his age. I am keen to start using the number line with him and get him really comfortable with it because it does seem like a great way to visualize things. Dont't worry he just does a tiny bit of maths out of school to keep him on top of things, I'm not a tiger mum!

Are you trying to teach the formal written calculation or calculating mentally. I'm not sure number lines are a pre-requisite for either, they are just a useful tool to help some children calculate or as another representation of numbers. I would make sure he:

a) understands the number order and that each number when you count backwards is one less than the number before - use towers of blocks for this, starting by building a tower of 10, then 9 etc. You can extend to using a number line but this can be a bit abstract for some children of this age.
b) has a basic understanding of subtraction using objects, understanding that subtraction involves taking objects away and seeing how many are left.
c) can use objects to subtract by counting back. So something like 9 - 3 by starting with 9 objects and counting back as you take 3 objects away 1 at a time.
d) understands place value - this is the key part. The formal written calculation is all about understanding of place value. He might need a lot of practical experience of grouping objects in bundles of 10s and counting numbers as sets of 10s and some 1s. He'll need lost of experiences of swapping ten 1s for a ten and vice versa.

Once he can do that, use toomuchicecream's method of using a place value chart and objects to show how the calculation works, so he can physically move a set of ten into the ones column and can see what is happening.

We had a number line lesson this morning and ds is fine counting up or down by ones but not at all confident making jumps of ten. So a question he would be fine with using a quasi column method was difficult using the number line. Interesting! For our weekend maths lessons from now on we'll practice jumping by tens and then ones using the number line.

I suspect if he can add ones using a number line but not tens, that place value is his problem, not the number line. Can he count up and down in tens from 0 or any other number and explain what happens to the digits?

He is able to count by tens and add multiples of ten to another number. I suspect it's just the different representation of the sum and the process of it. He's never been introduced to jumping by tens on a number line so totally new stuff. It will be good to get him comfortable with it.

What about a 100 square? They are really important for year 1 to get their head round the fact that if you keep adding 10 to, say 14, you get 24, 34, 44 etc etc etc. To add 10 you go down one square, to take away 10 you go up 1 square, to add you go across 1 to the right and to subtract you go across 1 to the left.

Lots of work on this will show them that if you add or take away 10 the units digit never changes. You could have one up on the wall somewhere - there's so much to talk about. For example, all the numbers in the same column have the same number of units but the 10s digit changes. Or all the numbers in the same row have the same tens digit but different numbers of units. If you say a number to him, how quickly can he find it? If you say 73, does he scan across from the top or start looking in the bottom left hand corner? If you cover a number over, can he tell you what number is missing? If you cover a whole column, can he tell you what would be in a given square?

My year 1s have done a lot of work with 100 squares but much less with number lines at this stage. They are a very bright bunch, but I only started them with drawing their own number lines for calculations after February half term. It's quite a big mental leap to go from a pre-printed line with every number on to drawing a blank line and putting in the numbers you need. It's another huge jump to move from counting on or back in 1s to making jumps of more than 1.

In your situation I would do lots of jumping up to the next multiple of 10 too - it uses the number bonds to 10 they spend so much time learning. So - put your finger on 23. What's the next 10s number/number which ends in 0/multiple of 10? (adjust vocabulary as appropriate). Can you put your finger on it? How many more do we need to jump on to get to it? You'll know you're getting somewhere when he doesn't need to count - he just knows it's 7! It really helps to move on from the idea of counting on in 1s the whole time.

Numbers are very abstract. The aim is to provide the children with a whole range of strong mental/visual images to support them as they move from the concrete (ie things to count) to the abstract digits which represent them. The more you can do of this at year 1 age, the better the foundation your child will have for the future.

Thank you toomuchicecream! A number square sounds like a great idea and you are right, there are so many games we can play with it. I really want him to have a solid understanding of things.

Hi tea for 1 -

I haven't read all the answers in the entirety but I think what may be missing (although not completely clear) is whether your son appreciates place value. That the numbers in the right most column represent units - and those numbers can only be 0 - 9, that the numbers in the next column to the left represent tens, the next column to the left hundreds, etc... - and that in each column you can only use the numbers 0 - 9.

in effect this is teaching base 10. That to represent ten of something in this counting system is indicated by a 0 in the units column and a 1 in the tens column.

10 in base 2 (where you only have 0 or 1 - binary code) would be 1010 - more info here: www.mathsisfun.com/binary-digits.html

Visually we explained this by having bigger and smaller objects of similar type - so duplo blocks for tens and lego blocks for units/ grapes for tens and raisins for units.

This way taking 23 from 45 becomes two plates:

45 = 4 grapes and 5 raisins
23 = 2 grapes and 3 raisins

5 raisins take away 3 leaves 2 raisins

4 grapes take away 2 leaves 2 grapes

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So when it comes to a more tricky problem involving borrowing -

say 43 - 25 - get out your plates again

plate 1 (43): 4 grapes and 3 raisins
plate 2 (25): 2 grapes and 5 raisins

Well fairly immediately your child can see that they can't take 5 raisins from 3 raisins. So they're going to need more raisins.

They have lots of grapes and 1 grape = 10 raisins. So cash in one of the grapes (of the 43 - 4 grapes) and convert it to 10 raisins.

Now you have 13 raisins take away 5 raisins = which gives you 8 raisins.

Then you can deal with the grapes:

3 grapes (remember we converted one of the grapes to raisins from the 43) take away 2 grapes = which gives you 1 grapes.

so 1 grape + 8 raisins = 10 + 8 = 18.

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Woodlands junior school has a lot of links for place value practice.

The abacus bead game (bead numbers - midway down on the right hand side) helps you to really visualise what each column of a number stands for (so the number 138 = one hundred, 3 tens and 8 units). The spooky sequences games are also really helpful.

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Finally - it may seem odd - but playing blackjack or '21' is brilliant practice for carrying with small numbers and mental addition. It really does help with adding numbers >10 and breaking through 20. After that it's a lot easier. We played open handed. Ace = 1, 2 - 9 as numbered, Jack/ Queen/King = 10. The object is to get as close to 21 or exactly 21 if you can - but if you go past 21 you're 'bust' and out of the game.

Each player is dealt two cards. They have to total their cards and then let the dealer know if they want another.

So say you are dealt a Jack and a 3. That's 13. So that's a long way off from 21 so you ask for another card.

If it's a 7 - that's brilliant you're on 20. Pretty close to 21 and so you may opt to stay there.

If it's a 9 - that's 22 and you've passed 21 and are now bust and out of the game.

once our DD1 was good with the counting - we played it the traditional way with no cards showing but the dealers.

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With DD1 this was a painfully tricky stage and I had to work hard to be supportive and patient. But keep telling yourself they'll get there in the end. Our solution was to keep trying things in different ways until something worked for DD1.

HTH

PastSellByDate I love the Blackjack idea! I could do it with both of my kids using premade number lines.

A tiny update for those who care (most likely nobody) but a week later we did some sums this morning and my ds was way more confident making the jumps of 10 and then by ones on the number line. I made one up to 70. He is way quicker just looking at the numbers and adding or subtracting the 10s and ones but I really think the number line work will solidify things. I'll worry about bridging the 10 in subtraction without apparatus when he is older.

Also interested in this. Is there a good place to teach myself how to go about using number lines so I can help DD?

NumptyNu I have Maths for Mums and Dads and find it useful.

Is that an app or a website ?

Sorry, it's a book.

www.amazon.co.uk/Maths-Mums-Dads-Rob-Eastaway/dp/0224086359/ref=sr_1_1?ie=UTF8&qid=1399152641&sr=8-1&keywords=maths+for+mums+and+dads