Arc Length and Sectors of a Circle: Probing Questions
Whether you are looking for a question to stimulate discussion in lesson, or a challenge at the end of a homework, then hopefully you will find these useful.
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Convince Me That... keyboard_arrow_up
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I use Convince Me That questions lots in my lessons and homeworks. Providing students with a statement and challenging them to come up with as many different ways of convincing you as possible can lead to some fascinating discussions. The different ways of seeing the same thing can also help improve the depth of students’ understanding. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!
The formula can be used to find the area of a sector of a circle with angle size and radius r
If you know the arc length and sector angle, you can work out the radius
If you know the perimeter of a sector and the radius, you can work out the sector angle
It is possible to find a sector whose area and arc length are numerically the same
VI3 Treatment keyboard_arrow_up
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We devised VI3 Treatment as a versatile way of giving students meaningful follow-up work at once we have marked their homework. The idea is that students are challenged to come up with 3 things with certain constraints. These are ideal to use as an extension for students who have got everything correct, and also as further purposeful practise for students who have got a particular question wrong. Use the ideas below and adapt them accordingly, using different numbers where appropriate. Either mark them yourself or better still, get other students to do it. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!
Find three different angles and radii that give you a sector with an area of
Find three different angles and radii that
give you a sector with an arc length (or perimeter if you are
feeling nasty!) of
For a radius of 6cm, find 3 angle sizes that give you integer values (in terms of pi) for the sector area and the arc length