Negative into positive with a paper aeroplane

Inferior models

Irritated by paper aeroplanes being thrown in your classroom? It happens to all of us during out teaching career at one time or another, some ‘character’, usually a boy, has learnt how to make a paper aeroplane and uses your class to demonstrate his new found skill. I am always amazed at the poor level of construction of these missiles; they are usually just successive folds along a central axis, a demonstration of symmetry. My dad taught me a far more intricate and aesthetically pleasing method but I’m not sure if it flew as far as the, in my opinion, inferior models.

What is a decimal?

A difficult question

Fractions to decimals

What is a decimal? Can you answer in one sentence? If there was a pause for thought good, because it is a really difficult question to answer, we are so used to decimals we forget what they are. If you did struggle imagine pupils’ confusion when you start to talk about decimal fractions or changing fractions into decimals.

We have all at one time or another thought ‘decimals should be easy to understand’. After all no matter where we are in the world money is based upon the decimal system, which child has not experienced that? Yet if you ask a student what is the value of 7 in 0.12379 the answers given will probably be not what you want.

Comparing fractions (part 2)



Comparing fractions - how many segments?

How do you compare fractions with different denominators? Comparing fractions is a nightmare for pupils and teachers. This is a very difficult subject to teach and probably an even worse topic to learn. Put this on an examination paper and you will separate the wheat from the chaff, and mostly it will be chaff. How can we be more successful and not have to teach it year after year to the same pupils.

Fractions – is that pizza for me (slice 2)?

What fraction of the pizza am I getting?

 Who has not had problems teaching or learning fractions?  It is a painful experience for educator and learner. Despite our best intentions we do not always succeed. How can we make it easier? (if you have not done so have a look at my previous post Fractions - is that pizza for me (slice 1)?

  

Comparing fractions (part 1)

Comparing fractions (part 1)

Comparing fractions

How do you compare fractions? Who has not struggled with learning or teaching comparing fractions? Ask a child (or even an adult) which is bigger 3/4 or 5/7 and you’ll be met with a blank stare and a shrug of the shoulders, lets be honest it is difficult.

Why do people have such difficulty with fractions and even more so comparing them?  Perhaps they do not comprehend that a fraction is just part of a whole and have not had enough practical experience beyond 1/2, 1/4, etc. They need to involve themselves in dealing uncommon fractions such as 5/7, 4/9 and so on.

Below is how I tackle this problem, there is no rushing this activity and it could take several lessons to achieve good results but it is worth it. Once established it will provide a firm foundation for further work.

Fractions – is that pizza for me (slice 1)?



Another fraction of a pizza

Have you ever wanted to improve the pupils learning and your teaching of fractions? I have and I have probably taught fractions the same way as everyone else, but I still had children who did not fully understand what a fraction is, just like everyone else. How many metaphorical pizzas have been used each day during Maths lessons up and down the land? Yet our pupils have the same misconceptions year after year, despite using their favourite food. What is the problem? What was I doing wrong? What is to be done?

 

The problem

If you give a diagram like the one below and ask the question what fraction is shaded? What fraction is unshaded? How many children would give the answers 2/8 and 6/8, probably most, but can they make the leap to ¼ and ¾? They find this really difficult and need lot of questioning and prompting to see the equivalence.

 

 

Another issue is when you ask a student to share 4 chocolate bars between say 5 friends and ask how much do they each get. It takes some time before a 12 year old for example realises it is 4/5. (Perhaps I am being a bit optimistic there.)

 

As the pupil get older they are introduced to ratio. Do they ever see the link between a ratio of 2:3 and the fractions 2/5 and 3/5?