Solving equations with a frog




Fred, ready to solve an equation

 

 Solving equations with a frog

Solving equation can be a slow and painful experience for many pupils and teachers. It just seems to be a complete mystery for far too many kids despite our best efforts that is why I have found using Fred the Frog such a powerful tool, you don’t even have to teach them about equations.

I start by telling them they are going to solve an equation butt I’m not going to tell them how to do it because they already know. This causes quite a few puzzled looks. Here is the story.

‘Fred the frog is resting on his Lilly pad not having had breakfast and feeling quite hungry when he spotted a bug in the distance his favourite food.’

 I then draw a picture of Fred and the bug. As you can see no special artistic skills are needed for this.



‘Fred jumps a distance we don’t know how far. Let’s give it a letter, what letter would you like?’

‘d’ says our enthusiastic pupil. I then draw d on the diagram like this.



I then say, ‘Fred jumps again and being an exceptional frog he jumps exactly the same distance again’. Further drawing now takes place.

 ‘Surprise, surprise he jumps the same distance again.’ More drawing takes place.

Finally he does one more jump but this time we know it is exactly one metre and Fred has breakfast  he eats the bug. Yet more drawing.





I then explain that Fred is truly exceptional, not only can he jump the same distance he can also read. ‘He looks up from his breakfast and sees a sign which says he is 16 metres from where he started.

Now ask ‘How far is one jump?’ Very quickly you will get the answer 5 metres. Now the killer question to ask ‘how do you know?’ Pupils will tell you to take 1 off the 16 so you are the last d that make 15 . Because there are 3 ds them you divide 15 by 3 to get 5. Its now up to you how you develop this. You can tell more Fed the frog stories with different numbers or you can go straight into ‘you’ve just solved 3d + 1 = 16’ and show them what they have done using traditional algebra.  I taught one girl who loved Fred so much she solved all her equations using this technique, never progressed to conventional notation and passed all her maths exams. You can also extend it to solving simultaneous equations, but that’s another story.