Teaching Column Addition and Column Subtraction

This is my lovely place value teaching tool. It was custom-made for me by my brother at Sen Clock and my dad. Prior to this I’d been using a paper sheet and laminated tokens, but I was fed up with them sticking together and getting lost. This magnetic version is much more practical.

I find this really useful because we if stick the tokens to the board, children have visual proof that once there are 9 tokens in a column there is no room for any more, so if they wanted to add another One in, it’s time to exchange 10 Ones, which won’t fit, for 1 Ten, which will. Physically clearing out the column, exchanging 10 One tokens for 1 Ten token really helps them to understand what happens when I want to add 1 to 109.

It’s great for subtraction too. When presented with – calculation lots of children will try to do 3-1. With this place value board, they can see that we only have one counter so we can’t take away 3. Then we can physically exchange 1 Ten for 10 Ones. I’ve made the column wide enough to accommodate them and the children can then see that they have enough in the column now to subtract 3, and that the tens column has one less token than it had before. I find this works really well side by side with a written column subtraction to iron out any misconceptions and to understand how the written method works.

Numeracy in a School for the Deaf

From the time I spent observing and teaching in a school for the Deaf, I found that maths lessons were the ones most like lessons in a mainstream school. The main difference is the fact that because class sizes are so much smaller (between 5 and 9 children), lesson objectives are more targeted for each individual child rather than having the same objective for a whole class or whole set.

There is also more support – two to three TAs in each classroom – so during independent activities each group still has an adult to support them. The children are mainly below the level of their peers in mainstream schools, because of their delay in language acquisition. However, teachers still have high expectations and lesson plans have both age-expected learning objectives, to make sure that staff bear in mind where these children *should* be, as well as realistic objectives.

To help the children catch up, they have two maths lessons a day – an hour-long one in the morning in their own class,  and a 15 minute ability-grouped one in the afternoon which focuses on particular areas of weakness such as mental calculations and maths vocabulary.

Teaching is, obviously, very visual and kinaesthetic and happens mostly in English with signs to support.

In the lower school, children can choose whether they record their maths in figures or pictures. Some  are happy to write 4 + 3 = 7, but many prefer to show this as   4+3=7

and either is considered acceptable. Higher up the school they record their work in figures only.

One thing I became very aware of during maths lessons, is that for some children, having BSL as their first language hinders their maths. For example, hearing people naturally count on both hands whereas counting in BSL is done on one hand only: you start with your thumb for one and put up an extra finger for each number up to 5; then you come back down again, so 6 is represented by just the little finger, 7 by the little finger and ring finger together and so on. Now imagine trying to do 7 take away 2 on your hands: you put up two fingers to show 7, and then take away 2……  Hardly surprising that 7-2=0 appears so often in their books…

With so many extra obstacles in their way of their learning, it’s a true testament to their perseverance, and their teachers’ dedication that they manage to learn.

Related posts: Literacy in a School for the Deaf    Deaf Studies in a School for the Deaf

A Multisensory Approach to Reading

A while ago a parent contacted me for help because her child was struggling with reading. He hadn’t picked up phonics in Reception with the rest of his class, and so now his Year 1 teacher wanted to send him back to Reception for another dose of letters and sounds.

His mother was concerned about the effect this would have on his self-esteem and also couldn’t understand how repeating a year of something that clearly hadn’t worked was going to help him move on. She asked if I had any idea for things she could work on at home with him that might help him progress.

My first thought was that if phonics lessons at school hadn’t worked at all, he was possibly a purely kinaesthetic learner. This line of reasoning was backed up by the fact that he learnt more physical activities easily: he had learned to ride his bike without stabilisers with no problems at all, and he was already quite accomplished at several sports. These were all things he would have learnt kinaesthetically. Phonics in school is taught in a visual and auditory way (see the letter, listen to the sound it makes). I know that some people claim that kinaesthetic learners are catered for because there are actions to go with the letters and sounds, but I’m a kinaesthetic learner myself and I know for a fact that tapping my arm whilst saying “a-a-a”, or holding a finger in front of my mouth to pretend I’m blowing a candle out whilst saying “b-b-b” wouldn’t have helped me to recognise either of those letters.

I suggested helping him experience the letters in a different way. He started getting to know the letters by using wooden ones (magnetic ones would do just as well) that he could pick up so he would be able to feel the shape of each letter. He explored which letters had straight edges, which had curved edges and which had sharp angles, and as he picked each one up we said together the sound the letter represented.

From there, I stayed with the idea of 3D letters but we moved on to making them. By using straws, rulers, pens, bits of string, blu-tack, sellotape, etc he was able to make his own 3D letters. With his mum he made some dough, which he fashioned into letter shapes and they baked them. Eating the letters afterwards brought in taste alongside sight, hearing and touch for a truly multi-sensory experience.

Now it was time to start relating these 3D letters to the 2D ones on the page. Again I wanted to bring in as many senses as possible so I used stencils to write out the letters on sandpaper so that he could trace his fingers over the rough surface to feel the shape of the letter. I drew big letters in chalk in his back garden so that he could walk around the shapes, and I got his mum and dad to take chalk to the park so that they could write even bigger letters for him to ride his bike round. Finally we looked at printed letters on paper. While he looked at each letter and we said the sound the letter makes, using my finger I drew the letter on his back so that he could feel the shape of it.

By the time we started looking at printed letters on the page without the additional extra-sensory support, he was so familiar with the shape of each letter that he was able to associate them with the sounds they represented without difficulty.

From then on his reading improved quickly and it wasn’t long before he caught up with the rest of his class. We avoided the knock his self-esteem would have taken by having to go down a year, and his confidence grew because he was no longer the only child in his class who couldn’t read. And that’s why I really love my job!

For maths and English tutoring in the north Birmingham, Sandwell and Walsall areas, visit www.sjbteaching.com. For links to other interesting education related articles, come and Like my Facebook page.

Related posts: Teaching the Times TablesA Multisensory Approach to Spelling  

Teaching Number Bonds

Number bonds. We all use them in our adult life without even realising it. When adding up items in our basket at the supermarket, we know that 3p and 7p is 10p, and that 2x 50p is £1. When we buy something for £5.60 at the market and hand over a £10 note, we know that £5.60 + 40p is £6 and another £4 makes £10, so we know to expect £4.40 change. Knowing our number bonds is extremely useful, but a lot of children struggle to learn them.

Over the years I have successfully taught many children how to remember their number bonds. As with times tables, the key is to find multi-sensory ways to teach, and to make practising fun.

Some children respond very well to visual clues, and to help these I use colour strips. These are strips marked out in 10 sections and coloured in contrasting colours, so that children can see clearly that 2 red squares plus 8 green squares equals 10 squares altogether, and that 8 green squares plus 2 red squares also equals 10 squares altogether. They are small enough to hold in the hand, and I tend to use them in conjunction with other methods. The children I tutor find them really useful to refer to during games.

Snap and pelmanism are always popular games, and I have made two sets of cards for this. The first set is colour-coded, so when the children turn the cards over there is a visual clue as to whether the two cards add up to 10. When they turn over the first card, I encourage them to work out what number they need to find to make 10. When the children are a little more confident I switch to the black and white ones to remove the visual clue, but we still play the same games to keep some familiarity.

Another card game I play is Imprison the Villain, which is played in the same way as Old Maid/Donkey/Chase the Ace. I use these lovely monster cards, which I downloaded from Primary Resources. I coloured mine in for added attraction and laminated them for durability.

Bengali - number bonds to 10I have one last set of number bonds cards which I made especially for one boy. He was struggling with number bonds, and as his home language was Bengali not English, as an experiment I found the numbers in Bengali on the internet and made him a set of dual language numbers cards. They have the numbers in words and figures in Bengali and English. They worked! When he saw them his eyes lit up and he pointed excitedly saying “I know these numbers!” The cards really increased his motivation and it didn’t take him long to learn them.

There are also a couple of fun number bonds games on Sue Kerrigan’s Let Me Learn website. I have Number Bombs and the similar but seasonal Elf Splat. There are two game boards for each of these games, one for addition and one for subtraction, which are both versatile enough to use for number bonds to 10 and 20. I haven’t tried this game with any girls yet, but the boys love it, and now I get greeted with “Are we going to play Number Bombs today?” My answer is always “We don’t need to now – you already know your number bonds to ten!”  However because it is so popular we do sometimes play it at the end of a session as a reward for good work!

Another game that children seem to love is ping pong. I can’t remember where I first heard about this game, but it’s played like a game of table tennis except that you bounce numbers backwards and forwards instead of a ball. I begin by establishing a rhythm – I say ‘ping’ and the child replies ‘pong’. Then I start calling numbers from 1-10 and the child gives me the corresponding number that adds to 10.  As we speak we swing an imaginary table tennis paddle to hit the numbers. For extra fun and an exercise involving whole body movement, stand opposite sides of the table with real paddles.

dominoesFor progression to 20, I have found a dominoes game which you will find if you follow the link to Primary Resources and type dominoes in the search box.  It takes a little practise because many children don’t know how to play dominoes, but once they get the hang of it, it proves quite a popular game.

For moving children on and helping them to see that when they know their number bonds to ten, and understand the pattern for making twenty, it’s quite easy to use this knowledge to find bonds for any multiples of ten, Sue is developing some resources based around football which highlight the patterns for making 30. I have been lucky enough to trial these resources. There is a write-on wipe-off card which explains how to use your knowledge of number bonds to make 30, and then a booklet to practise in.   There is also a game to play – similar to Number Bombs, but with the added excitement that if you land on certain squares you can get ‘sent off’ and you have to remove one of your counters. I have only recently starting trialing this game, but it is proving popular so far. Finally, the set includes a match report card, where you can tick off each goal as you achieve them: working out number bonds to 10 on fingers, knowing number bonds to 10 from memory etc.

Games are fun, but sometimes children need other ways to make those numbers stick, and word association is often helpful. I have found a few number bonds rhymes on the internet, but I find it works better when the children write their own. I have helped children to write their own rhymes, such as “5 plus 5 like to go for a drive” or “7 plus 3 go to Devon for their tea”. They then illustrate each of the rhymes with pictures such as two number 5s in an open top car, or the numbers 7 and 3 having a picnic under a sign saying Devon.

One Year 6 girl I worked with found it really hard to remember which numbers added to ten, and she was really down-hearted at being so far behind her classmates. We used this word association method and she found that she could remember her own poem and the pictures really easily. To begin with she said her rhyme every time before deciding which numbers went together. Eventually the numbers became so well embedded that she was able to dispense with the rhyme.

By the time she moved on to secondary school, she was still behind her classmates, but she now knew that she could achieve in maths which really increased her confidence. And that’s why I really love my job.

Related posts: Teaching the Times Tables    A Multisensory Approach to Reading