Planning tool

Students:

• identify and name the parts of a circle, including circumference, diameter and radius
• understand the significance and meaning of the symbol π as the ratio between the circumference and diameter of a circle
• revise that π is an irrational number and that a decimal or fraction is only an approximation of its exact value
• revise and use the relationships between the radius, diameter and circumference
• use a formula to find the area of a circle or sector
• know the units of measurement for the area of a circle
• apply the formulas for the area and circumference of a circle to solve practical problems.

Students may:

• confuse radius and diameter. Be explicit about using correct vocabulary. Have a list of common terms displayed to assist students.
• confuse the formulas for circumference and area.
• not appreciate that π is a number.
• use the wrong measurement. Support students to identify the diameter and radius of each circle and which measurement is required to solve problems.
• confuse square numbers – students often multiply by two instead of multiplying the number by itself.
• have difficulty in leaving answers in terms of π, preferring rounded decimals. Note: suggesting students always use 3.14 to represent π may lead students to think that π = 3.14.
• see π as a variable and substitute 3.14 for that variable.
• have difficulty in relating circumference to the distance around a circle. Make explicit that circumference is another word for perimeter.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning to identify the features of a circle such as circumference, area, radius and diameter.
• We are learning to apply the formula to solve the circumference of a circle.
• We will understand irrational numbers, including π.

Why are we learning about this?

If you can build understanding and knowledge of the correct formula for measuring circles and how to approach the same problem in different ways, you can choose the best method to apply to circle problems whether they are from your textbook, worksheets or circular problems in the world around you.

What to do

1. Find a spare piece of grid paper at home, or ask your teacher to provide you with some. If you have different kinds of grid paper that vary in size of the squares, then all the better.
2. Use a compass to draw a circle with a diameter of 10 cm. If you don't have a compass, see if you can find a circular object to draw around on your grid paper, but make sure you measure the radius of the circle. 
3. Using the grid paper and a ruler, figure out how many grids exist in 1 cm².
4. Count the number of 1 cm² squares there are in your circle.
5. You might need to estimate the squares that border the edge of the circle by adding up part-squares to approximately 1 cm².
6. Using another sheet of paper, calculate by hand the area of your triangle using the area formula for a circle. Remember your radius will either be 10 cm or it might be something else if you used an object to draw your circle. Use cm² for the units. 
7. Compare your calculated results with your grid approach. How close are you? Can you get closer? What if you used larger or smaller squares in your grid approach? What result do you get if you used mm²?

Success criteria

I can:

• apply the correct formula for the area of a circle
• understand and utilise π 
• identify and name parts of a circle
• use different approaches to solve problems.