Teaching Surds

My introduction to surds this year was by setting a problem to my class:

Calculate the exact value of the length of each missing side:

Initially the class knew exactly where to start. Pythagoras. Great. The problem arose when calculating the length of the hypotenuse of the red triangle. The class wanted a calculator. This led to a discussion about exact values and accuracy.

Then I set the class the challenge of drawing the Spiral of Theodorus and to calculate the hypotenuse of each triangle and also to calculate the area of each triangle.

Interestingly, the most challenging part for my class seemed to be drawing accurate right angled triangles rather than working with surds.

Some other activities I gave the class to complete were:

• Which one doesn’t belong?

• Tripod Surds

This resource can be found at Resourceaholic:Surds

• Show that the statement is true

This resource can be found at Resourceaholic:Surds

My class loved the resource above. It was so useful for the pupils to see the result they were aiming for. This allowed for self checking and knowing if an error had been made. There were lots of discussion and far less asking me for help – which would have happened if I had only set the questions.