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)?

  

The problem

I, along with my colleagues throughout the years, have struggled to teach fractions, perhaps we had not analysed and explained the many forms that a fraction can take. Despite the amount of pizzas we have used and drawn on the board to explain fractions there is still a struggle to going beyone this is simple idea.

As Steve Chinn says in his excellent book What to Do When Your Can't Do Fractions, Decimals and Percentages 'Fractions often cause great anxiety in people.' Lets try to reduce this anxiety.

Beyond the pepperoni

Perhaps we need to move on and use other types of 'whole' or see them in a different light. Being explicit about the different forms and sharing it with the students will pay rich dividends and make everyone's life easier. 

Assessment

Perhaps we had not assessed our pupils level of understnding and a more careful assessment of their learning needed to be undertaken. a very useful booklet to read is the one below on assessment for learning.

MATHS INSIDE THE BLACK BOX

A solution

Fractions are parts of a whole. In the last blog, ‘Fractions – is that pizza for me (slice1)?’ we looked at ways of categorising those wholes. Just to refresh your memories the four types of whole are discrete, continuous, definite and indefinite. Children must work with all four representations to be able to perform comfortably with fractions. Below are some strategies, although by no stretch of the imagination exhaustive, that may help a busy teacher to help overcome the problem with understanding fractions and reduce the need to cover the topic year after year.

Teaching strategies

There are a number of ways in which we can develop children’s deeper understanding of what a fraction is and the relationship between the part and the whole. The article ‘Teaching fractions with understanding: part-whole concept’, which is available on the nrich website, that inspired this blog suggests that we encourage children to ‘… reason out the consequences of different actions.’ What does this mean? An example could be telling the children that you have ten one pound coins that you wish to share between four people, how much should each get? Here a discussion should ensue about the nature of a pound coin and its divisibility. This exercise would of course be for younger pupils but I am sure we can think of similar age appropriate problems.

The next strategy is particularly powerful. We are used to presenting children with diagrams like the one below.



We then pose the age old questions, ‘What fraction is shaded?’ ‘What fraction of the shape is unshaded?’ Students happily count the shaded squares and put that answer over the totally number of squares and as a bonus for the teacher, if they are lucky, will cancel down. But it can be taken a step further, this will really oenable you to probe and assess their understanding of the key fraction relationship. Give them some questions where the shape has not been comfortably divided into equal portions, such as the one below.

			k

Now ask the questions, ‘What fraction is shaded?’ ‘What fraction of the shape is unshaded?’ ’ ‘What fraction of the shape is the rectangle marked K?’ This last question is so important as it really does test their understanding of shape. The answers should prove a very useful assessment tool and be the starting point for a very profitable discussion.

The way forward

Thee are by no means exhaustive examples, but many further ideas can be generated from these starting points. One obvious issue to tackled is what happens when we have improper fractions?  The way forward is to do as many examples like those above to develop pupils understanding of fractions as being part of  a whole plus we need to analyse the different 'flavours' that fractions can take.

What problems have you had with teaching fractoons? What solutions have you found o this age old problem? Whay not write a comment. You can follow me on twitter @croftsr1.