We used the Mathematics Assessment Project formative assessment lesson on Calculating Volumes of Compound Objects. MAP also has a Glasses task that includes student work.
Students calculate the volume of liquid that the glasses can hold, and then determine the height of the liquid in Glass 3 when it is half full.
Minutes before I gave students their handout with the glasses, I decided to cover up all of the measurements on the glasses and ask the students what information would be sufficient for calculating the volume.
(I’ve been learning from reading Dan Meyer’s blog about being less helpful.)
radius height 1
height and radious 1
circumfrence, height 1
Height and radius of the cylinder and the volume of the solid holding up the cylinder 1
surface area uf cup part
radius of cup part
height of cup part 1
dimensions, shape 1
area of circle and height 1
Just the radius and the height, but either if the volume is given. 1
height and base 1
radius of circle, height of glass 1
height, radius 1
radius and height of the cylinder 1
height of cylinder and radius 1
radius of base, height of cylinder 1
diameter, hieght, to get volume. 1
height and radius of the cylinder 1
Every thing you need to know for volume of a cylinder 1
height of cylinder, height of hfmishpere, and radius 1
height of the straight side and radius 1
radius and height of the cylinder 2
radius and straight side length 1
radius height 1
Radius and height 1
Asking what information students needed gave a different spin to mindless calculations with volume formulas, even for volumes of compound objects.
Once students had the needed information, they calculated. I sent a Quick Poll with all four questions at once so that students could work at their own rate without feeling the pressure of a timed poll.
I monitored student responses as they came in, talking directly with teams who needed to revise their work.
Until we got to the question about the glass being half full.
From the student responses, it seemed that the glass was half empty instead.
What do you do when no one has the correct response?
There are times that I have given the correct response and asked students to determine how to get it. I’m not sure how effective giving a decimal approximation of the correct height would have been here. Instead, we looked at the picture. Can you draw where the height will be when the glass is half full? What do you see?
Similar triangles are often elusive for my geometry students. We need more practice.
And so the journey continues, trying to find a balance between giving too much information and too little information …
Easing the Hurry Syndrome 
Andrew
July 29, 2014 at 7:18 am
Is this a regular high school geometry course? My calculus students had trouble finding height of half a glass like that without estimating. They struggled to model it in a way that led them to an exact answer.
jwilson828
July 29, 2014 at 9:05 pm
I thought about having students estimate afterwards. I am having to retrain myself to provide students opportunities for estimating. I’ll definitely have them estimate first next year. Had I asked them to estimate first, they might have realized that many of their responses were not reasonable and eventually gotten to an exact answer. Some, but not all, of the students are 9th grade geometry students.