Throughout their time at school your child will be exposed to many different methods of doing addition. Some will be written methods and others will be what we call mental methods - worked out in your head or using jottings. As a parent the best way you can help your child with their addition is to build up their ability to do addition in their heads - what I would call mental addition.
This will build your child's understanding of addition in a much better way than through using pencil and paper methods. To be able to do maths in your head you have to be able to understand what you are doing. Doing the mental methods will really build your child's knowledge and understanding of numbers. The danger with using pencil and paper methods is that your child doesn't fully understand what they are doing and can't do it in their heads and so ends up relying on a method they don't quite understand and therefore does not have the knowledge to recognise if they have gone wrong. I have seen it many times when children are working through sums. They bring me them to mark and several are obviously wrong if you look at the numbers but these children, because they are relying on the method, are not actually looking at the numbers. They are just putting them through a formula and not even looking at or thinking about what is coming out the other end so can't spot their mistakes. Giving your child a really secure mental knowledge and understanding is the best thing you can do for them.
So, now you know what to do here's how to do it.
As with everything start easy and build up. Easy builds the confidence.
When doing addition, your ultimate aim is for it to be done in the head or with simple jottings but you need to teach your child what to do in their head first. So, when doing the activities below you need to have something to write on so all practise can be done modelling what is going to be going on in the head and then, as time goes on, you can gradually take away how much is written down.
Level: Single digit addition progressing to 2-digit add 1-digit numbers
Find an object that you have many of! This could be crayons, books, duplos, cars............
Create a sum on the floor with your objects ie two small piles of cars. With your small child ask them how many cars there are and then how many cars there are in total and count them out together. One thing that is really good to do is to count the individual piles and then count the cars altogether and then start with one pile and say something similar to this:
'OK, I have 4 cars on this pile and 2 on the other pile. If I add them together I can do it by starting with the first number and then adding on the second. I know I have 4, so I don't need to recount them, I just add on the next two. So, 4, 5, 6. I have 6 in total.' Basically you are demonstrating that you don't need to count all the cars every time.
Once you have done the sum then swap the sum round so instead of it being 4 cars add 2 cars make it 2 cars add 4 cars.
After doing these sums write them out or encourage your child to help write them out so they can start to see how we write sums out. I would always try and use something fun for the writing like a whiteboard, a window or chalk, just makes it more fun for your child.
Once you have established basic addition you need to ensure they are starting to understand that:
- You don't have to count each time
- Addition sums can be done either way round and give the same answer
- Their fingers can help them - our number system is base 10 so having ten fingers works really well for addition
Level: 2 digit add 2-digit numbers
When it comes to adding two 2-digit numbers together you need to start encouraging your child in a very visual method so they can start to internalise this and use it within their heads.
I teach this by writing the sum across the page and then drawing a loop on top of the sum from one units number to the other, adding them in my head and writing the total above the loop. Initially I write the sum above the loop too. Then I draw a loop under the sum from one tens number to the other and then, write the total of these under the loop. Again I start by writing the sum. Please, please write the full tens number of 20 or 30 etc. please don't just write 2 or 3 to show the number of tens. They really need the visual of the full tens number to help internalise that understanding. Once I have added the units and then the tens (please always try to demonstrate by doing the units first) I then write after the sum a new sum of the tens add the units with the answer. This is very visual and can really help your child to see and understand the process they need to go through to add numbers together. Although I encourage children to add the units first (this will help them with bigger numbers and when holding numbers in their heads) when they write the new sum I encourage them to write the hundreds number first, then the tens and then the units as this can help them see the numbers fit / add together.
6 + 3 = 9
eg. 26 + 13 = 30 + 9 =39
20 + 10 = 30
Once you have shown this method you will need to stay visual for a while but as your child increases in confidence and ability the next step is to slowly take away the visual and encourage them to do this within their heads.
1. Stop writing the sums on the loops, just write the answers
2. Next step is to take away the end sum where you add the tens and units, encourage them to do that sum in their heads and just write the answer.
3. Then the loops need to be dropped. As these are dropped you may want to use the final sum again, as a way of recording the answers to the mini sums eg.
26 + 13 = 30 + 9 = 39
Obviously the final step is then to drop that final sum and for all those steps to be done in the head.
The above process is not quick, it will take a lot of time and practice but eventually your child will get there and will have a fab understanding of numbers.
What you may find happens, is that every time you increase the level of the sum you will need to re-use some of the stepping stones above just to re internalise but also give your child the tools and time to learn to cope with bigger numbers.
Level: 3-digit numbers add 2- digit numbers
For these sums you need to use exactly the same visual as above. All you are doing is adding in a simple 100's element. You should still have 2 loops but when you write out the second sum you will have hundreds in there too. eg.
147 + 83 = 100 + 120 + 10 = 230
This is going to require lots of practice as there are many areas that can confuse a budding mathematician.
- Suddenly they are dealing with three numbers
- They may have hundreds in more than one number in their second sum and tens in more than one number.....
- They have to go into much higher numbers
eg. 147 + 83 = 100 + 120 +10 = 200 + 30 = 230
Level: 3-digit numbers add 3-digit numbers
As with above you need to take this step by step and steadily.
Use the same method as above but this time you will need to add a third loop to add the hundreds numbers together. Likewise, add in the loop, do lots of practice and then slowly take the visual elements away until your child can add these numbers confidently in their heads.
Level: Bigger numbers!
I could go on describing the gradual increase with 3-digit add 4-digt etc. but I think you should understand what you are doing by now. Your child should also understand. If the previous levels have been taught slowly and steadily then by the time you hit 4-digit numbers your child should be able to manage very easily in his / her head without having to go through the written / visual process to practice.
The basics you need for teaching mental addition is paper and pencil and some objects if you have a young mathematician.
As with many aspects of maths this part of maths does initially require some sitting down and learning but we can make it more fun and interesting
Dice - use these to create your sums. Each dice throw represents another digit in the sum (yes, the dice only go to 6 but this can work great when moving up a levle as it keeps the sums a little simpler)
Number cards - your child may love making some numbers cards 0 - 9 which you can then use to help you pick the numbers for your sums
Race - children love racing / working against an adult. Write a sum and both of you race to do it
Taking it in turns - write sums for each other. So you write one for your child to do, they write one for you to do. (establish rules for the sums if you do this ie. 2 digit numbers etc.)
Timer - this can be used in several ways: how many sums in 1 minute or you could set a target of 'can you do 3 sums in one minute.
Obviously there is lots of progression that can be made with this topic. My advice is to find your childs level and with that to improve it a little and then do lots of practice around it. Then in a few weeks come back to it and move them on again. Go slowly and steadily. There is no rush. The most important thing here is that you are developing a clear understanding of addition in your child.
Once you have done the sitting down teacher bit you need to practice. Again, this can be done in may ways.
Sitting down practice - every few days sitting together and working through some sums
Random - every so often just ask your child what the answer to a sum is eg. What's 7 + 26 . This can be quite fun if you just add it into your everyday life.
Hide and seek numbers - hide some numbers (these need to be full numbers at the level you're working at) around a room / the house. Get your child to find 2 and add them together. Hide them again and then they need to find another 2 and add them.
Bribery games - some children may need more of an incentive and you could score points for every sum they get right doing the activities suggested above. When they have so many points they could earn something. Generally with my daughter when she earns something it's craft time with me or a day out of her choice (within budget) etc.