When I read the second challenge for the 2016 Blogging Initiative, my instant reaction was “I love fractions”.
My twitter name is @fractionfanatic and all my pupils at school know I love fractions. But why do I love fractions?
The main reason is that they are accurate and far easier to work with than decimals.
Here are some examples:
- when solving equations, an answer of x = 4/3 is far more accurate than x = 1.3, which is what I see often written in jotters. When I see this written down I pull a face and put a sad face beside it in the jotter. It makes me so sad to see expressions like 2/3 expressed as 0.7.
- substitution – for example, when finding stationary points if the x-coordinate turns out to x = 1/3, it is far easier to calculate the y-coordinate without a calculator especially when the equation may be a cubic or quartic.
- similarity – finding the area or volume scale factor – if pupils write the length scale factor x = 5/7 as x = 0.7, this will add a huge error when squaring or cubing to find area or volume scale factor.
- when solving trigonometric equations in radians, many pupils try to solve in degrees then convert the final answers into radians. But, which is easier? π + π/4 = 5π/4 or 180 + 45 = 225 then converting 225° back to radians. Especially if the equation ends up with 6 solutions.
I think that the one thing that my pupils remember about me is my obsession with writing answers in fractions.
The above examples are more about using fractions within other problems.
One of my favourite fraction activities is “Peaches Today” – taken from NRich.
It is all about calculating fractions of a quantity but has 4 different stages which allows all pupils to access it.
I also love teaching pupils about Egyptian Fractions even though they are not part of the curriculum.
To finish off: