Choose three numbers and ...

Ever felt that sinking feeling as you are about to tackle fractions again? You can imagine what the pupils think, well you probably knoe when they say ‘We’ve done this.’ Or ‘Not again’. Here is an idea tht will give a different slant to the fearsome task of teaching factions.

 

Step 1

Ask for 3 numbers between 2 and 9 inclusive. Write them on the board. Now ask the pupils in pairs to make as many different fractions as they can in 2/3 minutes. At the end of the allotted time collect the results on the board, the chances are they’ve forgotten to repeat the numbers with same numerator as denominator. Add any they have missed.

 

Step 2

Again in pairs or groups ask them to put the fractions into groups that appear the same. Collect the results, hopefully you will get top heavy fractions, equivalent fractions and ‘normal’ fractions. Ask them how they could be displayed in a table. Again some paired or group work.

 

Step 3

Now demonstrate that probably the most effective way of showing the results is in a table like that below. So for example if the numbers chosen were 2, 3 and 7 the table would look like this.

 

 

Step 3

You can now start to ask questions such as what is special about the diagonal with the entries 2/2, 3/3, 7/7? What do they equal? What other numbers can equal these?

 

What is different about 3/2, 7/2, 7/3? What are these type of fractions called? Hw can we change them?

 

I am sure you get the idea, the variations are endless and where you go depends on the class, their prior learning and what you want to achieve. This can also be extended to 4 numbers or where ever you want.

 

This idea was taken from the book ‘Starting points’ by Banwell, Saunders and Tahta published in 1972. A vision of how maths education could have gone. It would be interesting to compare it to today’s practice in classrooms throughout the world.

If anyone has used the ideas that I have given you over these last few blogs how did it go? Were they successful? How did you improve them? (I'm sure you can). Please leave a comment.