The Do Now problem is an assessment of students' understanding of finding the surface area of a polyhedron. The Do Now problem has multiple steps. Students may have difficulty with and should be mindful of the following key pieces of information when working out their answer.
- there are 4 units in the building
- the floor and ceilings will not be painted
Students will have 5 minutes to work on the problem independently and then they will discuss their work with their group.
The B&B Painting Co. is bidding on a job to paint the inside of an apartment building that has 4 units. Each unit is an efficiency apartment in the shape of a rectangular solid with a length of 20 feet and a width of 30 feet. The ceilings are 9 feet tall. Assuming that they do not have to paint the floor or ceiling, how many square feet of wall space is there that needs to be painted?
For this activity, students will develop the formula for finding the volume of a rectangular prism. Each group of students will receive a container of unit cubes (blocks). Each student will have five minutes to create their own rectangular prism. After five minutes students will be directed to count the cubes to find the length, width and height of their polyhedron. I will then ask them to deconstruct their polyhedron and count how many cubes they used in total to construct it. I will explain to students that the total count of cubes is the volume of the rectangular prism and I will give them a formal definition of volume.
Volume - The number of cubic units needed to FILL a 3-D Figure (layering)
Rather than count the total number of cubes needed to assemble a polyhedron, is there a way we can use the length, width, and height of the polyhedron to arrive at the same answer?
Students will have a few minutes to discuss the question with their group. I will encourage them to use their rectangular prisms and its' dimensions to find the relationship.
Many students will calculate that the product of the length, width, and height will give them the volume of the polyhedron. I will encourage them to test their theory on each of the groups' polyhedron. When students have confirmed that the relationship is true for all rectangular prisms, I will give them the formula for volume of a rectangular prism.
V= lwh, where l = length, w = width, h = height
Each student will receive a Volume of Rectangular Prisms worksheet. Students will have 10 minutes to complete the worksheet independently. Problems 1 and 2 are a straightforward use of the formula. Students may have difficulty with problems 3, 4, and 5.
Problem 3 requires students to understand that the dimensions of only one cube is given. To find the length, they need to multiply 3/8 by 5. To find the width, they need to multiply 3/8 by 2. To find the height, they need to multiply 3/8 by 3.
Problem 4 requires students to use the algorithm for multiplying decimals correctly.
Problem 5 requires students to use the algorithm for multiplying fractions correctly.
After 10 minutes, students will discuss their strategy and work with their group. Students should agree on their answers, but if they disagree, students will discuss their steps. Through discussion, students should be able to find where and why their answers are different.
If there are any unanswered questions, we will discuss them as a class. It is important for students to know that although the formula for volume of rectangular prism is relatively easy, the problem may not be.
To assess students' understanding of the volume of rectangular prism, students will complete an exit ticket. Although the focus of the exit ticket is volume, students should understand that a problem may not directly ask for volume.
Homework assignments are usually given by math skill level. The exit tickets will be used to determine future homework assignments for students.
A fish tank measures 17.2 m by 18 m by 42.1 m. How much water can be used to fill the tank?