Area, equations and that frog again

Those of you who read my post about how to use a frog to solve equations might want to use this before that lesson. It can also be used independently before starting to find the areas of complex shapes. It is deceptively simple, but powerful.

 

All you need to do I draw two lines and on one put its length, say 10cm, and on the other x cm and 8cm. Explain that the two lines are the same length. Two frogs have a jumping competition, they agree to jump over the same course of 10 cm. The first jumps the full 10 cm. Fred the frog jumps but only a distance of  x cm but then covers the rest of the course, which is 8 cm. How far is x cm?

As you know this is really x + 8 = 10. Depending on the level of pupils you can continue with further examples, make the link to algebra or move on.

 

The next step (or jump if you are a frog) is to draw similar lines  such as one which is 10 cm and the other which is x cm, x cm and 3 cm or whatever appeals to you. Again you can use the story of the two frogs one jumping the full 10 cm the other Fred covering x, cm then x cm then 3 cm. Emphasise that both x cm are the exactly  the same distance. Then ask how far is x cm?

 

Of course the pupils are solving 2x + 3 = 10. You can judge how far to take this idea it really does depend on the class or pupil. Use in its simplest form before doing complex shapes as pupils often fail to grasp how to find a missing dimension.

 

If you are wondering about previous mentions of Fred the frog see my previous post ‘solving equations with a frog’.

 

 

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.