# Better Questions

Week 3 of the 2016 Blogging Initiative!

The blogging prompt this week is about questioning. There were many different prompts and I decided on the following:

You’re planning a lesson and you try to come up with super good question to ask to get kids to think about something. What is that question? Why did you phrase it the way you did? Why do you think it will prompt discussion/thinking?

This week my S3 class have been looking calculating arc length and area of a sector of a circle. The class have previous knowledge about circumference and area of a circle.

My introductory question was:

A slice of pizza is cut from an 12 inch pizza. The angle at the centre is 25°.

What is the area of pizza eaten?

What is the length of the crust around the slice of pizza?

This led to a discussion about what fraction of the pizza was eaten and how we could use the area and circumference of a whole circle to solve the problem.

The class made a note about how to calculate the arc length and sector area. My options at this point were to give out an exercise on calculating arc length and sector area – but I know that this will quickly get repetitive for the class. So I decided to go for writing three questions on the board – one easy, one medium and one hard. Here they are:

1. Calculate the arc length and area of a sector with radius 15cm and centre angle 145°.
2. Design a sector which has an area of 100cm².
3. Design a sector which has the same area and arc length. How many different solutions are there and why?

I like this structure of questioning as it allows all the pupils to work at their own pace, doesn’t give too much repetitive practice and moves pupils onto problem solving quickly.

At first, some pupils didn’t understand how to tackle question 2 – I pointed them to the Problem Solving strategies on my wall – Guess and Check. I was really pleased with the strategies then used – adjusting radius and/or angle depending on the answer.

Not all of the class got to question 3 by the end of the lesson. But, those who did came up with some good responses.

Some tried Guess and Check again until they came up with the answer of 2. Another pupil realised that the angle didn’t matter and that the square of the radius had to be the same as the diameter – so 2 was the only option. One group decided that zero was a valid answer – some debate if a sector with radius zero would actually exist!

## 3 thoughts on “Better Questions”

1. Yes, I heard of the idea of an “Anticipatory Set,” a introductory question that motivates the students to start thinking. I’m glad that your Anticipatory Set question worked well!

I’ve tutored students in the past, and when they reached this lesson, I motivated them by bringing them an actual pizza slice and make them calculate the area before I let them eat it!

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2. I also appreciate the structure of the questioning you used. I never thought of doing something like that when I was teaching middle school, but it’s clearly a good way to differentiate and get your students to explore and practice the same related material with increasing difficulty. Thanks for sharing!

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3. Cool way to bring together math and food–students always love that!

One practice for students that I’ve seen some teachers work on around the #MTBoS is getting students to as the good questions that you posed. I wonder what would happen if you showed students the picture above and/or showed yourself eating a pizza and asked them what questions they could come up with. You might be pleasantly surprised by their questions! Of course, then you’d have to be willing to tackle whatever comes your way.

I also really like the third challenge–I like how you made it more difficult, yet kept it to the topic at hand.

Thanks for sharing!

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