What do you do on the last day of class?

I needed to spend some time talking with students about their grades. So they worked on a task while I met with individual students. Which means I wasn’t able to orchestrate as productive of a mathematical discussion as I would have liked.

We started with the pictures, absent of any explanation or measurements. What question could we explore?

What is the circumference of the circles? 1

What is the volume of the cylinder? 1

are circles equal? 1

are the 2 circles the same size

what are their radii 1

are the areas of the two circles equal 1

are the bases the same size 1

are the bases the same size? 1

could the one of the bases of the cylinder have the same diameter as the other?

dilation 1

does the highlighted line have any significance to the cylinder 1

does this shape qualify for a cylider 1

is it a cylinder or 2d lines and circles resembling a bike chain? 1

is it a cylinder or gears 1

is it a cylinder 1

is it a cylinder?

is it 2 similar circles with a sring around them? 1

is it a cylinder? 1

what are the wheels connected by the belt being used for? 1

what is the length of the darker line? 1

what is the length of the line around the wheels? 1

what is the radius of both circes? 1

what is the relationship between the lines and the circles 1

what is the volume of the cylinder 1

what is the volume of the figure? 1

whether its a cylinder or a dialation 1

why are the circles not touching 1

Does is help to know that these are two wheels and a belt?

Does looking at a picture of some gears help to make sense of the picture?

I asked the question again.

What information do you need to determine the length of the belt?

Teams worked together to make a list of measurements.

Then they started working.

I checked in every few minutes in the midst of meeting with students about grades. I knew some of the misconceptions that students would have because we did this task last year.

Students had the opportunity to **look for and make use of structure**.

Is the quadrilateral a rectangle?

Many students were calculating as if it were.

Someone convinced us that the quadrilateral is only a trapezoid.

Students corrected calculations and made more progress.

I checked in again.

Is the part of the belt highlighted in green a semicircle?

Many students were calculating as if it were.

Someone convinced us that the arc is greater than a semicircle.

It wasn’t the ideal way to have class and discuss student work. But for the last day of class, it wasn’t bad.

And now the journey continues to a new school year …

Howard Phillips

August 9, 2014 at 7:00 pm

More questions:

Do the wheels go the same way round or the opposite?

What about the gears?

If we turn the little wheel, what does the big wheel do?

Who’s got a bicycle? And what’s that got to do with it.

I do think that a bit of prodding is necessary to help the kids to open their eyes and minds fully.

I do admire what you are doing.

jwilson828

August 10, 2014 at 7:30 pm

Thank you for the suggestions … there are so many possibilities with a diagram like this!