Lesson 15 Circle functions

# Episode 2

Reasoning Resources
Whole class and small group work
Handling the circumference and area together, with a variable radius.

The difference between the linear and the quadratic functions is explored in both tables and graphs and can be bridged with TM13: Chocolate box which deals with ideas similar to perimeter and the area of a square of variable length of side.
Ask the pupils: What happens to the area of the circle when the radius changes? How does that compare to what happens to the circumference?

Give out Worksheets 2 and 3. You may wish to demonstrate the circumference and area calculations and fill in the first few values in the table as a class. Then leave pupils to complete the rest of the table in pairs.

Help pupils in drawing and joining points on the graph. Prod pupils to describe the differences between the two graphs, and encourage them to estimate mentally areas and circumferences of some circles with easy measurements.
Whole class sharing/discussion
Episode 1 deals with inverse processes, whereby the radius of a circle is generated from its area. This can be utilised in finding the circumference, thus connecting all the elements of the circle. Start after most or half the pupils have drawn the two graphs. Draw the graphs yourself or ask pupils to do so on the board.

There are several relationships and issues that can be explored with the two graphs. Follow the issues that crop up in the particular class.
Whole class reflection
Conduct a discussion on mentally estimating diameters and areas of circles with easy numbers, from the graph and using the inverse operations.