Wednesday, 5 June 2013

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.

Step 1


Ensure that pupils know what shading 5/7ths is. This may sound simplistic but think about your experience, the pupils can shade a grid like that below where they colour in 5 out of the 7 squares.




Now give them grid like that below and it begins to fall apart, shade 5/7ths and the chance are only 5 will be shaded.






 




Step 2


This is the vital step, it may sound simplistic but this is where the misconception occurs, the students do not realise that 5/7 means you shade 5 out of every 7. Draw a grid like the one below and tell them you want to shade 4/5, ask how many squares should be shaded?






The chances are you will get the answer 4, if you get 8 you ask why? There will be a significant group of the class that will not expect or understand why it is 8. It is better tat one of the group explains why it is 8. Emphasise that 4/5 means you shade 4 out of every 5 squares. If needed do further examples.


Step 3


Now hand out  worksheet with unshaded grids on with associated fractions for them to colour. The next step is to hand out a worksheet with rectangles, notice they do not have any grid lines drawn on them, they’re blank.





Choose just one fraction such as 3/4, The task now is to divide the grid into ¾ in as many ways as you can. This will be more challenging than you think but it really does expose whether the pupils understand the concept of a fraction or not. I like to, after they have attempted this to collect their results by drawing blank grids on the board and asking them how they divided the grid.


Fractions are very difficult for most pupils and it takes a lot work to make the concept concrete and the pupils completely comfortable with the idea. Once they are comfortable with this exercise it is a short step to finding a fraction of a quantity such as what is 4/5 of £20? Only when the idea is solid within their minds can you progress to comparing fractions. Any attempt to go further without this concept fully established will result in failure. I will write more on comparing frctions in my next post.
Comparing fractions (part 2)

Steve Chin writes about mathematics and dyslexia. In essence teaching children who are dyslexic is no different to teaching those who are not, it is just good teching using a multisensory approach. I would recommend looking at his books such as the one below.

What to Do When Your Can't Do Fractions, Decimals and Percentages
 
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