I'll start the lesson by showing an image of the composite solid block tree. I don't fully understand how this device is used, but I know that it is used for construction. I'll explain that it may be important for the manufacturers to know the exact surface area of each object. Perhaps the tool is coated with a special liquid and the manufacturers need to know how much liquid is used per square unit. I'll then ask students to think about how they could find the surface area of the device. As a prompt, I may ask them to consider the shapes that make up the tool. I'll ask them to discuss these ideas with their partners for about a minute. Students are trying to make sense of the problem to generate generate a way to solve it (MP1). I will walk around to listen in to the conversations. I'll try to pick up a few off-based comments and some that are more relevant. I'll want to present both so that students have a chance to critique the reasoning of their classmates (MP3). As we discuss answers, I'll try to make sure students bring up the fact that their are 5 large cylindrical holes - we would need to find the lateral surface area of the cylindrical holds. I'll make sure we discuss the rectangular faces as well and discuss in general how to calculate the surface area of the external surfaces. I like this image because it should generate a lot of discussion and help prepare students for the problems to come.
Now students will find the actual surface area of solids. Note that problem number 3 is meant to be a cylindrical hole. It is kind of difficult to tell based on the drawing. Based on the previous discussion, students should be very well prepared to solve the first 2 problems as they are the same shapes now with dimensions labeled.
The following day is an assessment, so I have included some review problems for students who finish early.
I have provided a scaffolded exit ticket to help me assess any breakdowns of understanding. In fact, the first two questions may be the most telling. If a student can't identify the total surfaces, there is probability a visualization issue.