As students enter the room, they will have a seat, take out their Problem of the Day (POD) sheet and begin to work on the question on the SMARTboard. The POD allows students to use MP 3 continually based on the discussions we have about the problem each day.
To start the class, our POD is designed to generate thinking from the students about their understanding of ratios and the ratios that exist between the surface area and volume of figures. I want them to recognize the distinct difference between the two measurements and to know how to apply each measurement during problem solving.
What is the connection between the surface area of a figure and the volume of the same figure? Are you able to predict the volume if you know the surface area of a figure? How?
Students will work in small groups of 3 to continue exploring surface area and volume. Using linking cubes or centimeter cubes, groups will start by making four cubes that range in edge length from one to four. Students will fill in the dimensions, surface area and volume of all four cubes. They will also record the information for a cube with edge length 5 and with an edge length of 6. Next, students will find the ratio of surface area to volume for each cube and identify the one with the highest ratio and the lowest ratio. On a piece of grid paper, I want students to graph the edge length vs. the surface area to volume ratio. Within each group, students will discuss the relationships they see on their graph. What happens between the relationship between surface area and volume as the size of the cube increases? Would this relationship be the same if the object were a prism instead of a cube? What would happen if only one dimension was increased rather than all three?
Students will investigate using a prism. Groups can choose what size to make the prism. The dimensions, volume, and surface area will be recorded on the Cover and Fill sheet. Students will increase the height of the prism by one cube then find the new surface area and volume. Students will increase the height of the prism five more times and find the new surface area and volume. They will record the surface area to volume on the lab sheet. Students will create a second graph that compares the height to the surface area to volume ratio.
Students will summarize their learning from this activity by writing a paragraph that represents their conclusions. We will share paragraphs with the whole class to compare and discuss findings.
To close the lesson today I want students to think about the relationship between the surface area of a figure and the volume of that figure. The activity today required them to write the relationship between surface area and volume as a ratio and to use that ratio as a factor in a graph. Do they understand what that means? How do they determine that ratio? What does that ratio mean and can they explain it?
Describe the relationship between the surface area and volume of a figure. What does the surface area to volume ratio represent?