For today's Warm Up, I have posed a question I adapted from an Illuminations lesson,Popcorn Cylinders, where students must determine which of two cylinders will have the greatest volume when using the same sized paper to create them. Before students tackle this problem, I do a quick survey by asking, "Who thinks that these two cylinders will have the same volume? Who thinks the taller cylinder will have the greater volume? Who thinks the shorter one will?" I record the numbers on the smartboard and then ask, "How can we find out?" I encourage the students to calculate the volume for each cylinder.
Once the timer sounds, I seek a volunteer to give me their calculations. After confirming with the rest of the class, I ask, "Which of the measurements had the greatest affect on the volume of the cylinder, the height or the radius?" I again ask for a student to volunteer their thinking. If the student suggests the height, I ask them to explain their thinking. I then ask if anyone thinks it is the radius and ask her to explain her thinking.
If students struggle to understand the concept, I create a quick table in which I compare four cylinders: r= 2 and h=5, r = 3 and h =5, r= 2 and h= 6, and r = 3 and h= 6. I ask for the volume of each to show the increase of the volume if the radius is increased versus the change in volume if the height is increased.
My goal with this Warm Up is to get students thinking about the formula pieces and how each affects the final volume. This concept will come into play again during today's Work Time.
Before launching today's lesson, I provide the students with the Learning Objective. Because we will be working with both cylinders and rectangular prisms, I share an example of a rectangular prism and remind students of the volume formula for it.
Today's lesson is a task taken from Illuminations called Cubed Cans. In the lesson introduction, students are 'hired' by Food Containers Corporation to design a new container for various food items. The lesson requires students to calculate the volume of a given can of food and then investigate until they find the dimensions of cube or rectangular prism that has the same volume. I intentionally give all students the same size can for this activity so that they work collaboratively across the class groups as the investigate. We record the measurements and dimensions on the SmartBoard so that Work Time can be focused on completing the table and answering the follow-up questions.
For Work Time, students work independently with a calculator to determine the measurements of rectangular prisms that will equal that of the cylinder that we calculated in the lesson introduction.
Some students may struggle with getting starting on the assignment, so I assist them with one prism by asking them to select a length and a width. I then ask how they will find the height of the rectangular prism so that the volume totals the same as their cylinder. Once we complete one together, I encourage them to find the dimensions of other rectangular prisms that have the same volume, but different dimensions, for less surface area.
Once the Work Time timer sounds, we move to Consensus Building so that students have an opportunity to share and justify their work and come to consensus as a class. During Work Time, I have intentionally selected students to respond during this time so that we can move more quickly to consensus. Once students have decided that cylinders use less material for the same volume, I ask them to "turn and talk" to their assigned partner to explain this concept in their own words.
On the subsequent lesson, I will ask students to recall this information in application.