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Showing posts with label Numeracy. Show all posts
Showing posts with label Numeracy. Show all posts

## Thursday, 19 December 2013

### Bidmas or Bodmas

 BIDMAS BODMAS not again!
BIDMAS or BODMAS, it doesn't matter which mnemonic you use, it always seems to cause problems for pupils. Below is an idea that is simple and works.

A student or class may be able to apply it to an exercise after your explanation. Give a few questions a week later and all is forgotten.

Either confusion reigns in the classroom when they try to apply it to problems that are outside the exercise specifically on BIDMAS or it is completely ignored by the pupils. Below is a an activity that will help.

## History and Maths

If you have ever read the book ' What is History?' by E. H. Carr you may have come across the idea that 'History stops here.' What this mans is that some historians in the past believed that the History that they wrote was the definitive view; there was no other interpretation. Of course History is constantly being rewritten in the light of current ideas, attitudes and data.

The way I was taught is the only way, 'numeracy stops here'. This is the view of many parents and teachers. They believe how they learnt to add, subtract, multiply and divide is the only correct method to use, anything else is ‘strange’, not ‘proper’ or at worst some kind of  trick being played upon their child. None of this is true of course. Each child has his or her own way of learning and remembering things and once confidence is gained using their own method they should continue using it.

## Subtraction

Jim, like many pupils could happily subtract when the sum which looks like this.

However as soon as we introduce something more complicated anxiety sets in, he had convinced himself that he couldn’t and never would be able to remember how to in his own words ‘do it when the number on top was smaller’. Such as in the example below. We have all been there as teachers or parents with our pupils or children wanting to subtract 7 from 3 because they can’t remember or don’t know why they have to do in effect 13 minus 7.

A succession of teachers had tried and failed to teach Jim how to do subtract using the traditional method and failed, his parents despaired also having failed to teach Jim how to subtract. He was now 16. Jim is a bright lad, a visual learner, he wanted to subtract so that he could pass his exams.

## Open number line

Jim was very comfortable with the open number line, so I decided to show him how to use it to subtract. First I drew the line like the one below and explained that we were at going to go from 17 to 43. I marked on the two numbers.

Now I asked Jim to jump to the nearest 10 from 17, he happily drew a line from 17 to 20.

How about jumping to the nearest 10 to 43 I asked. ‘What 40?’ he queried. He then drew the next jump and without prompting he then drew the final leap.

So how far have you jumped I asked him to which he replied 26. It was then only a small step to make the connection between this method and the subtraction su  set out in the traditional way. Jim was thrilled at being able to do subtraction with, as he termed it, ‘difficult take aways’. He successfully continued to use this method with ease and success, passed his exams and reduced his fear and anxiety when tackiling Maths.

Many of you may dismiss using this method as not being correct but it worked for Jim. It may not work for everyone but he was successful and solved problems so who is to deny him, or anyone that but adherence to other methods just because that was how they were taught.

## Tuesday, 14 May 2013

### Adding fractions - again and again and again ...

For years I taught adding fractions the traditional way. I taught it to the same pupils aged 11, I then taught it to them again aged 12. Yes you’ve guessed it 13, 14 , 15 and 16. Colleagues I worked with did the same, all with the same degree of success, or should I say failure, what is wrong with these kids we would say they just don’t get it. After a long, long time the ‘penny dropped’, it wasn’t them that didn’t get it, it was us Maths teachers.

Last night I taught a 15 year old to add fraction together in 15 minutes. She said ‘Is that it, it’s easy, for four years I was so confused and now … wow.’ I then had to teach her mum to add two fractions together who said why doesn’t everyone do that.

Most students can add two fractions together if the denominator is the same, this fact is easy to establish. You then need to tell them this is the only way to add two fractions if the bottom number is the same. Hopefully they agree. You then present them with two fractions like those below.

Now highlight one of the denominators and say you will use this to add the fractions. I find it really helpful to use colour, don’t dismiss this simple trick if you want to be successful and more importantly if you want the pupils to be successful.

Now say you are going to multiply the other fraction by the highlighted 4. Like this

Now highlight the other fraction.

Follow the same process. Multiply the other fraction by 3.

Finally complete the calculations like this

Point out the denominators are the same and then complete the sum.

After a couple of examples the pupils will happily be adding fractions. OK I know it isn’t perfect, such as when you have denominators of 2 and 4 but if you want them to be confident with adding fractions it is a really brilliant method. You have to tech pupils to cancel down so the problem of denominators of 2 and 4 is eventually tackled.

# Times tables - how can they stand it?

Have you ever struggled to find another way to teach multiplication or times tables? I have. It is never easy to find new ways to teach and/or practice multiplication tables. The kids are probably under pressure from home to learn them and in turn it increases the pressure on you, the teacher. Governments also use them as a handy measure of progress that the general public understand.

## A fun activity

This is great fun and can produce lots of laughter in the classroom. It is particularly  useful when the class is a bit sleepy, such as after lunch. (Or even when you are feeling a bit low on energy.) Equipment needed, NONE!

• Tell the class they have to stand. You are going to call out numbers in the three times table (for example). If the number is in the three times table they have to stay standing BUT if its not they have to sit.
• You say the number 9 staring intently at the class. No movement. 3, the same. 10 and the class sits down, or at least a few confident souls do and the rest follow. Once they have the idea you can continue, with the calling out of numbers becoming incresingly rapid. You can of course fool some by a slight bend of your knees as if you are about to sit down, even when you call out  number which is not a multiple of 3. Who follows your lead? Someone will. Continue until you think they, or you, have had enough.

• This is fun and it enables you to see who is secure in their knowledge of the 3 times table, or whatever table you chose; it is an almost instant assessment tool.

## Variations

• Of course you can use other multiplication tables, but sticking to our three times table you could start to use 2 X 3, 4 X 3, 6 X 5, 2 X 7, etc. see if they can work out which are in the chosen multiplication table.

## Order of teaching

I think there is a distinct order in which times tables should be taught, namely 10, 5, 2, 4, 9, 6, 3, 8 and 7. Experience has shown that these are the most difficult in ascending order.

This excellent book by Steve Chinn, 'What to do if you can't learn your multiplication tables', discusses the problems and strategies for learning the multiplication tables. He is an expert on learing difficulties, especially dyslexia and dyscalculia, who shares his knowledge through a series of books focused on Mathematics.

## The class that didn't need me

Ever had a great moment when you know things have gone well?

How about a class being self starting working on a topic or idea that you have kicked off in a lesson before and they carry on without you?

Sounds almost impossible doesn't it but it happened to me. This idea is simple and it works.

Many of you will already know this activity a numeracy game at its best, but for those that don’t it is great fun. One day I was late for a class , the school was built on two sites and it took at least 3 to 4 minutes to get from one site to another.

By the time I had arrived in my class the pupils had organised the starter for themselves and were playing snowballs. How many lessons would that happen in?

Want an instant resource book for starters? This book is full of ideas that are easy to implement and will provide you with starters that you can use straight away.

An excellent book that will get any lesson off to a flying start Letts Red Hot Starters - Maths (Letts 101 Red Hot Starters)

## The game

The game starts when you select two pupils from the class. Stand them back to back  at the front telling them they are going to have a duel. There are no guns allowed but they can use snowballs.

They have to cup their hands in front of them into which you place an imaginary snowball. Instruct them that you are going to count to three and at each number they have to take one pace away from each other. On the count of three they stop back to back at 6 paces apart.

You ask a question for example ‘how many sides does a pentagon have?’ or ‘what is 4 x 9?’ My favourite re the multiplication tables as this is  fun way to practise them.

When one of our duellist has the answer they turn around and say the answer out loud, if right they throw the snowball at their opponent, if incorrect the initiative goes to their rival who has to give an answer.

If correct they can throw the snowball at the other person. The loser sits down and another challenger is selected. If they are both wrong they both sit down. This great fun and has endless variations.

## After the snow has melted

There is no better way for  child to become comfortable with the tools of numeracy than if they are playing and having fun.

It sometimes difficult to stop the non-combatants from whispering the answer to one another or getting excited that they know the answer.

After doing this activity the atmosphere in the classroom is very positive. The children often ask if they can start, or end, a lesson with snowballs.

I have adapted this game to include division, addition, subtraction, fraction of quantities etc. there seems to be no limit.

The more activities you can find like this to add to your teaching portfolio the better for everyone especially if they are fun.

I was amazed that the starters book can even be purchased for 1p from Amazon. Click on one of the links to buy the book.

Letts Red Hot Starters - Maths (Letts 101 Red Hot Starters)

More resources for your classroom click on resources

For general books on how to move your teaching to outstanding click on general teaching books

Books to feed your mind click mind food