Topic 12 Year 8 Mathematics
Mathematics | |||
Topic |
Circles and composite shapes |
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No of lessons | 8 | ||
When is it happening | Term 3 Year 8 | ||
What will students learn | Within this unit, students explore the connection between the circumference of a circle and its diameter and through this are introduced to pi as the constant linking the relationship between the two measures. When introducing the area of a circle, dynamic geometry software can be used to show how the area formula for a circle can derived by slicing a circle into sectors. We can decrease the width of these sectors, so they become infinitely small, and the area can be shown to be equivalent to the area of a rectangle where one side length is the radius and the other is half the circumference. Exposure to this proof is important as often this type of formula can seem like a trick and applied with little understanding of the meaning behind it. However, it is not important for them to remember the exact steps of the proof. The unit ends with opportunities for students to apply their understanding to geometric problems involving the area and circumference of a circle. | ||
Key Knowledge that students should know at the end of 'Topic' | This is the knowledge that students will meet for the first time in this topic | • Explore relationship between circumference and diameter/radius • Formula for circumference • Explore relationship between area and radius • Formula for area of a circle • Area and circumference of a semi-circle and other sectors • Area and perimeter of composite shapes involving sectors of circles | |
This is knowledge that students may have met before but will need to deepen their understanding | Area and perimeter of 2D shapes | ||
Key Skills that students should be able to demonstrate at the end of 'Topic' | This is the skills that students will meet for the first time in this topic | using a protractor | |
This is skills that students may have met before but will need to develop | Using a scientific calculator | ||
Key vocabulary that students should know and understand | Radius, diameter, circumference, Composite, Pi | ||
The Big Question | How do we find the circumference of a circle? | ||
Key questions that students should be able to answer at the end of the 'Topic' |
Can I name parts of the circle? | ||
How is pi linked to circles? | |||
Can I find lengths of parts of circles? | |||
Can I find the area of a circle in terms of pi? | |||
Can I find the area of a sector? | |||
Can I find the area of compound shapes involving circles? | |||
Can I find the area of compound shapes involving circles in terms of pi? |