How do I help my 6 year old with place value and partitioning??

[SandyChick]

My ds is 6 (yr2).

He's a brilliant kid and always tries his hardest but he is struggling with the basics when it comes to maths. We are doing lots at home to help (his teacher is great). The problem is I don't know how to 'teach' him.

He is struggling to add numbers that are larger than 10 as he counts on his fingers. So 35+12 etc. How do I help him to understand place value etc so that he can break down the sum?

Buy a graph paper book of 1cm squares, colour in single squares, strips of ten and squares of 100. Photocopy them onto card then cut them out. You can then set them out in columns on the table to correspond with the sums. Dc can then swap ten single squares with you for a strip of ten when adding up when you get to more difficult sums.

You can also show 10 units making a strip of 10 and 10 strips of 10 making 100.

Make sure you are helping them to do the sums themselves rather than just showing them; a child learns much more by doing than by being shown. Also stop as soon as the child wants to as maths needs time to "sink in". When they return to it, they will find it easier.

I've been doing quite a lot of this at home with DD.

First is he confident adding and taking off 10 to/from any two digit number?

At school DD was practising starting at 2, 7 or 99 for example and then adding or subtracting 10, so 2, 12, 22 or 7, 17, 27, or 99, 89, 79 etc. This needs to be secure and a 100 square is useful for showing this too as you just move up or down the columns.

Second partitioning the numbers. Does he understand tens and units yet? Have you explained that units are all the numbers to 9 - once you get to ten you have 1 in the tens column and 0 in the units column. Have you explained why 20 is written as a 2 and a 0 etc.? This is worth explaining fully because it will make column addition easy to understand in the future.

There are free resources on-line and apps as well that are visual, i.e. they show blocks of ten and then single blocks for units, showing how 27 is 'made' from 2 blocks of ten and seven single blocks. Obviously real blocks / Lego are also good for this.

He may need to do this with blocks or visual representations for a while before he can tell you that 12 is made with 1 ten and 2 units in his head so that he instantly knows that 35 + 12 = 35 + 10 + 2. Modelling how to write the equivalent sums out will help him too.

I've found that DD finds 35 + 23 = 35 + 20 + 3 easier than 28 + 7 = 28 + 2 + 5 because the 'break' is easier to see - therefore practice is also key!

get him an abacus - it is very visual and physical - you swap 10 on one row for one on the next - really reinforces place value.
Also show that when you take 2 off 11 for example - you have to change the 10s back to 10 units and then take off your 2.

You can play with adding and taking away 10s - and show that the units stay the same - and then move up (or down on the abacus) to hundreds etc.

Can also have a lot of fun going up to very large numbers :)

I was taught with Lego - big blocks represented ten, little ones represented one.

All the suggestions on the thread are about making it physical though - literally substituting to get used to the idea before you try to substitute in your head.

My DSs are visual learners and once they 'saw' the working out they understood it better.
They started with pictures of apples - bags of 10 apples, and single apples. First they needed to understand place value - 23 is 2 bags and 3 single apples, 45 is 4 bags and 5 single apples etc etc

Then they added on small single numbers 45 + 5 for example - still using the pictures to see it happening.
Then bigger ones so they 'went over' the 10 eg. 45+6
Then adding up 2 2 digit numbers e.g. 25+32 . Because they could see the 2 bags of 10 and the 3 bags, and then the individual apples of 5+2 it made much more sense to them. So they worked out
20+30=50
5+2=7
50+7

or do it with money - using 1 pennies and 10p and £1 coins

I give you 10p for every 10 pennies you give me - make up numbers with coins.

Thank you all so much.

Lots of really good ideas.

He just doesn't get tens and units yet. I'm trying lots of different ways to explain it but it just isn't clicking for him. We had a bit of a breakthrough this morning with a game on topmarks. It has a row of tens - 10, 20, 30 etc up to 90 then 0-9. It will give a number eg 84. You need to select the tens and units. To start with ds was selecting 8 & 4 rather than 80 + 4.

Until he understands tens and units etc I don't want to confuse him with partitioning just yet. Going to really focus on this for now.

He still struggles with written down numbers eg 13 & 30, 14 & 40. He can count past these numbers but when they are written down he's not as confident.

Mine had a total mental block about that at that age - and through to yr3 and yr4 as well. Now at 12 he is capable of GCSE level maths and more (on a good day - on a bad day 2+2 baffles him ).

Give him time and lots of practise with different applications and he will get there.

I would tend to steer away from coins.You want something that consolidates the idea that each ten is ten units.
just squared paper cut into individual quares for units, strips of 10 squares for tens and 10 by 10 squares for hundreds.

Yes think I'm going to try the squared paper. Money & coins are a whole other storey. He really doesn't get that either. He can do a sum eg 25 + 5 but if you put a p after each number it completely throws him.

He'll get there it's just trying to think of fun ways to help it stick.

He loves printing stuff and laminating it so going to make a number square at the weekend and some flash cards.

you need to get him used to the idea that the number isn't related to the thing.

10 rabbits is the same as 10 pens is the same as 10p - there are still 10 of them - regardless of what they are.

The idea that you can count anything with the same numbers.