The main purpose of this lesson is to make sure that students have a good understanding of the differences between surface area and volume. It may go well at the beginning of the a unit on surface area and volume; I taught this lesson after we already worked through the surface area sequence of the unit. In the opening part of the lesson, I want to quickly assess what students know about volume. I will ask: 1) How do we measure distance? 2) How do we measure area? 3) How do we measure volume? Most of my students will have no problem answering the first two questions. For question 1, it is okay if a student says "using a ruler or tape measure" or some such thing, but I will use that to lead them to describe the type of units used to measure distance. On question 3, I am listening for students who understand that volume measures space in 3 dimensions and/or that it is measured in cubic units. Being able to correctly describe the units belong with MP6. I will be very insistent that units are described accurately (i.e. feet, square feet, cubic feet, etc).
Each student will be given 10 cubes, though they will be working through the problem set with partners. Students are expected to solve the problems in the manner of the example: 1) build the model; 2) draw the 2D views; 3) find the surface area and volume; 4) Examine the relationship between the 2D views and the surface area. While students are working, I will walk around to help students who are struggling with the models. I will also be looking for proper labeling of units (MP6) and accurate 2D views. It is important to let the students know that there are no "holes" or missing cubes hidden from view. For example, in problem a there are only 3 visible cubes, but the top cube is sitting on stop of a hidden cube. It can be tricky to keep track of the faces when counting for surface area. I may let students who are getting frustrated to lightly mark each face using a wet erase marker.
Page 2 of the model, labeled "independent problem solving", has the extension problems. These will present a bit more of a challenge for students who make quick work out of the first 6 problems. I will give these students another 10 cubes to work with.
First, I will call on students to give answers to the volume and surface area of each problem. When there is disagreement, I will ask the students to build the model being discussed. I will then call on a student to explain what they think the correct answers are by using the model as an aid. This is an opportunity in the lesson for students to practice MP3. After we have agreed to all of the volume and surface area problems, I will ask the 2nd essential question. We should be able to now confirm the relationship between the 2D views and the surface area. I will also ask students if solids with the same volume have the same surface area. Again here is another chance to practice MP3. A student could quickly build their argument by using problems a & b (same volume/same surface area) and c & d (same volume/different surface area).
I will ask students to include the 2D views on the exit ticket in addition to finding the volume and surface area. This will allow me to diagnose any misconceptions and also assess their spatial reasoning. They may use the unfix cubes to help answer the questions.