Lesson 32

Find the Volume of Prisms Using a Formula

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Objective

SWBAT find the volume of prisms using a formula

Big Idea

Move from the concrete to the abstract. Students turn the modeling of a prism's volume into an algebraic formula.

Hook

5 minutes

Teacher Model

10 minutes

I will ask students to recall the two things that we considered in a previous activity for volume.  I expect to hear answers that say we first found the number of unit cubes that would fit on the base and then we found out how many layers of unit cubes were used.  We will then (again) refer to the formula.  Example 1 is similar to what we have already done.  Before we do example 2, I will ask students if the volume can be found by multiplying 5.5 * 4 * 2.  It is a triangular prism so the answer is no, but students who have been taught l * w * h will sometimes apply this blindly to any prism. I ask the question to provide an opportunity for students to quickly put MP3 to use.  A thoughtful response may include an explanation that the base shape is a triangle and only 0.5 * 5.5 * 2 unit cubes would fit on the base; and, we would use 4 layers. 

 

As students use the generic equation to solve the problems today they are practicing MP4.

 

I will expect students to write out solutions in a manner similar to how I present.  This helps me assess how students are doing. 

Guided Practice

10 minutes

Students will now answer 6 guided practice problems.  They should refer to their notes and their neighbors as a resource.  This allows me to spend time checking in on how students are doing.  During these direct instruction lessons, I focus my check for understandings on students who I know generally struggle with math topics because I don’t usually have enough time to thoroughly check in with everyone.  When I see that they are doing well, I know the majority are doing well. 

 

I love GP5 (pentagonal prism) because, while I think it may be the easiest, it will cause the most confusion.  The area of the base is given.  GP6 is just another chance to make sure students distinguish surface area and volume (MP6).  We will quickly go over the solutions to GP1 – GP6.

Independent Practice

15 minutes

Students will work on the independent practice without the help of their partners.  I will pull aside students that I’ve already identified are not ready for the independent practice.  The problems (as they should) mirror the work already done.  Problem 6 provides an opportunity for students to practice MP3 as they critique an error in work.

 

Most students should make it to the extension.  Problem number 9 requires some proportional reasoning.  Problem number 10 is a test in a student’s ability to be able to use MP1.

 

Solutions will be discussed as necessary.

Exit Ticket

5 minutes

The exit ticket has 3 questions.  The first two are pretty straight forward.  Problem number 3 may cause problems for some students only because I have provided an image of a heptagonal prism.  However, it will let me know if students understand how to find the volume of any prism.