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Two Wheels and a Belt

09 Aug

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?

Screen Shot 2014-07-30 at 6.44.35 PM

Screen Shot 2014-08-09 at 5.39.14 PM

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?

2014-05-14 09.02.45

I asked the question again.

Screen Shot 2014-08-09 at 5.41.42 PM

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

Teams worked together to make a list of measurements.

Screen Shot 2014-08-09 at 5.53.20 PM

Screen Shot 2014-08-09 at 5.52.28 PM Screen Shot 2014-08-09 at 5.52.07 PM

Screen Shot 2014-08-09 at 5.52.54 PM

Screen Shot 2014-08-09 at 5.53.09 PM

Then they started working.

Screen Shot 2014-05-14 at 9.48.19 AM

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?

Screen Shot 2014-05-14 at 9.48.35 AM

Many students were calculating as if it were.

Someone convinced us that the quadrilateral is only a trapezoid.

Screen Shot 2014-05-14 at 9.49.27 AM

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.

Screen Shot 2014-05-14 at 10.00.37 AM

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 …

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2 responses to “Two Wheels and a Belt

  1. 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.

     
  2. jwilson828

    August 10, 2014 at 7:30 pm

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

     

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