In the Do Now, students solve word problems involving concepts from the previous lessons. They work independently to answer the questions. After about 5 minutes, we go over their answers. I use this Do Now as a formative assessment. If students still have difficulty solving problems involving volume, I take some extra time during the Mini-Lesson to review the methods for finding the volume of various solids.
During the activity, students solve more complex problems involving volume. In order to prepare for the activity, we practice a problem together:
The dimensions of a brick, in inches, are 2 in by 4 in by 8 in. How many such bricks are needed to have a total volume of exactly 1 cubic foot?
Before we solve the problem, we discuss the information needed. I give the students two minutes to talk to the person next to them (MP1). Pairs then share their thoughts with the class. My students will know we need to find the volume of the brick, but they sometimes have difficulty formulating a plan for how to use this information. They don't immediately recognize that the units are different. Although it is possible to convert the inches to feet, it is much easier to convert feet to inches for this problem. We work together to solve the problem (MP4). Then, I assign groups for the activity.
For today's Problem Solving Activity, I have the students work in groups of 3 to solve more complex word problems involving volume (G.GMD.3, G.GMG.3). I give each group a sheet of paper with one problem to answer and present to the class.
Students are required to solve the problem, draw a diagram, show all work, and explain their solution using complete sentences. Group roles are as follow:
After about 12 minutes, we gather as a whole class and the students begin their presentations. Since there are only three problems, there will be multiple presentations of the problems. As part of the summary to the lesson, students will be comparing the different methods for solving the same problem. While the students present, the other students in the class record the results on a paper in their notebook. I have each group present before we discuss the validity of the solutions. Since they've seen multiple presentations of the same problem, the students in the class are able to decide which, if any or all, problems are correct. We discuss any misconceptions students may have had and how to correct any mistakes.
At the end of the lesson, the students complete an Exit Ticket, which asks them to compare their methods with those of other the other groups that answered their question. After about 3 minutes, we have a brief whole class discussion about how the solutions varied. This discussion of methods for solving problems prepares students for the next unit on geometric modeling.