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.