Lesson 31

Explore Volume of Rectangular Prisms

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SWBAT discover the formula for the volume of a prism through problem solving

Big Idea

Students progress through a quick concrete->pictorial->abstract sequence of activities to understand area.


10 minutes

Partner Problem Solving

10 minutes

I will collect the unifix cubes before this section.  Now we are moving to the pictorial activity.  Students will be given a few minutes to answer the questions on the page.  As students are working, I will walk around to assess student work.  Problems 1 & 2 are essential for students understanding the generic formula for the volume of prisms, so I will initially focus my attention there.


Question 4 is an opportunity for students to develop a viable argument (MP3).  The bullet points are provided to help them construct their arguments.  Any number of answers may be appropriate, but they must be well constructed answers.  For example:  “I see that the number of cubes in each layer is equal to the product of the length and width of the prism.”  A well formed argument will use language precisely as well (MP6)!  Question C1 and C2 are so that students can see that rotations do not affect volume or surface area.  We will have a share out of findings before moving on to the next section.


Independent Problem Solving

10 minutes

Now I would like my students to work through some problems independently.  There are only 5 problems, so I expect everybody to make it to the extension questions.  Notice these are just a variation on the warmup acitivity.  The only difference here is that I only want unique combinations (not permutations).  I will most likely not allow any calculator use as the problems are pretty straight forward and questions 4-5 provide a good review of decimal multiplication and division.

Extension question B is a review of surface area.  It also allows students to develop MP1 and MP3.

Exit Ticket

5 minutes

The exit ticket has 2 simple application problems and a slightly more difficult 3 problem, where the volume is given but one dimension is missing.  It is very important that students show their work or explain their solution for problem #3.   Some may write an equation; others may use arithmetic only.   Either way is fine as long as they can justify the answer.