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.

Stand up/Sit down - times tables practice

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.

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Please feel free to leave a comment, I would really appreciate it.

An algebra starter - money in my pocket

Algebra starter - just for a change

Want to revise basic algebra with your class? Want a quick starter that doesn't involve equipment, not even a worksheet?  This is a starter activity for you.

Use of algebra

 This activity is fantastic for starting algebra or revising basic concepts. You need to have some coins in your pocket or purse, preferably of a low denomination. Tell the class, as you jangle the coins (that you have out of sight) that you have some money but you don’t know how much. Ask them what shall we call the amount? A variety of answers will be offered, many quiet amusing, such as ‘cash’ ‘wonga’, ‘dosh’ or whatever the current vogue word is for money. Once you have arrived at a consensus for the change that you have in your pocket guide them to some algebra by saying that you will use one of their chosen words but you'll only use the first letter. Establish that the unknown amount of money in your pocket is m for example if you are using the word money.

The generous Maths teacher

Now in a fit of generosity, well all Maths teachers are kind, caring warm and generous, give someone in the class 1p. Ask how much you have in your pocket now. Again the answers will be very revealing, as they struggle with algebra, their understanding of the concept of an unknown and how it is represented, eventually the discussion should led to m – 1. Retrieve your 1p and now ask them how much now do you have in your pocket? Hopefully they will get to m.

The generous Government

Next explain that the Government has awarded all teachers a bonus of 5p which has just magically arrived in your pocket. I did have m how much do I have now in my pocket? n will be a popular response, this really does demonstrate their misunderstanding and misconceptions about algebra. That is why this exercise is so important. In a short time you should get to m + 5. Now ask how much you have if you give away 3p reminding them that you now have m + 5. Again the responses will be very illuminating, highlighting understanding, or not as the case may be. Keep asking questions of this nature. It is often useful to record your answers on the board. Vary the questions depending upon the responses.

Further work

This oral question and answer session is very good for highlighting misconceptions or building understanding. Further question could be ‘I have m in my pocket what do you have in yours?’ If they say m you say ‘so if we put our money together what do we both have? Or if they say c what do we both have? If I lose 2p what do I have? After I have lost 2p I double my money what do we have now? The variations are endless.

For another esy starer why no see Stand up/Sit down.

 

I suggest that you repeat this exercise at regular intervals just to keep the class on the ball. we all know how knowledge slips way if it is not used.  Repeating this activity will give your class a head start when it comes to basic algebra.

 

An excellent book for mathematical starters is 101 red hot starters.

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

 

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Snowballs in the classroom

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

Just looking for a good read click good read

Solving equations

When planning to teach a class how to solve equations I would normally follow the steps outlined in my previous blogs which are

1. Solving equations, a staring activity

2. Solving equations with a frog.

The class should now have all the skills and knowledge to be able to solve equations. I reintroduce the frog story but this time I show them we cn write it as 3x +1 = 16. It is important to now make it clear what your objective is, to find x. Link it back to your diagram by asking 'what did you do first when trying to find how far Fred jumps?' Hopefully they will repond subtract 1, which you now show them.



Once again link back to the Fred the frog story, reminding them about the three jumps covering 15 metres and ask 'so how long was one jump?' To which they should answer 5. 'How do you know?' This leads on to division by 3. You then show them usual notation used with the arrows by the side.

I am confident that hould you follow the three stages I have outlined in thee blogs your success rate in teaching solving equtions will soar. Don't forget to use a different colour for the arrows and operations as this help pupils to distinguish what is happening to the equations form the equation itself.