While working on our first chapter, we learned about three-dimensional figures, their surface area and their volume. The students were asked to solve problems involving measurements. To solve problems of this type, one needs to apply tools like, computing measurements using formulas, decomposing compound shapes into simpler ones, and using right triangles and their properties to solve real-world problems. To assess how well students master those skills, I gave them three glasses shown in the picture.
They were asked to calculate the volume of each bowl. The bowl of Glass 2 has a cylindrical top and a hemispherical base. A convenient way to calculate the volume is to divide it in
to these two figures. The second problem was how to calculate the height of the liquid in Glass 2 when it is half full. This question requires deep understanding.
At the beginning of the lesson, students worked individually to solve the problems. Next, students worked in small groups on the same task, to produce better collective solutions than those they produced individually. Throughout their work they justified and explained their decisions to each other.
I provided the students solution to the Glasses task, written by other students (not from our class). They were asked to criticize the other student’s responses and to correct errors in those solutions.
In a whole-class discussion, students discussed their own solutions, and explained how to correct the common misconceptions.