Discovering Volume (Part 2)

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SWBAT find the volume of various rectangular prisms using the volume formula and cubes.

Big Idea

Students build a conceptual understanding of volume by using cubes to support their thinking.


5 minutes

As a warm-up for today's lesson, students work in groups to build more rectangular prisms.  They roll 2 dice, multiply the numbers and find a volume.  Using this volume, they create as many rectangular prisms as they can.


Some groups of students struggled with building a prism when given a set volume.  They were ok with making a flat rectangle ex: 15 x 2 x 1 to make a prism with a volume of 30.  When prompted to make these prisms "taller" without changing the volume, some students struggled.  They debated with in their groups because some students wanted to take more cubes to add a second row, and others recognized that this would change the total number of cubes.  I found it interesting to allow students to struggle with these mathematical arguments and to listen to their discussion.  If needed, I stepped in to adjust their thinking by adding 3 rows high and asking if they could make a prism that had 30 cubes and was 3 inches high.



10 minutes

I use a video as a bridge between the lesson and the warm-up section because it is helpful for students to learn using a variety of modalities. This video is an example of the type of videos I use to enhance my instruction.

Also, learning from a variety of resource types helps students develop the ability to think flexibly about a concept. 

Guided Practice

15 minutes

For the guided practice portion of today's lesson, I work with students to consider the size of different cubic units.  What cubic unit would be an appropriate choice for measuring the volume of our salmon tank? A swimming pool?  

I want the students to understand that cubic units, like all units of measurement, are different sizes and the most appropriate unit should be used.

I show an image of an empty pool, an empty fish tank, and an empty tissue box.  We talk about these rectangular prism "containers" that can hold various things (water, tissues, etc).  The space within these containers is the volume.  

This discussion lends itself to talking about liquid capacity too. We talk briefly about the various ways to measure volume, but I keep the class focused on determining the most appropriate unit of measurement for the volume of each prism.

Before students move on to solving more solving more problems, students participate in another "rectangular prism" Vocabulary review.  Constantly reviewing these terms helps students build them into their daily language. 

As with yesterday, I encourage students to ask questions and lead the discussion.  As students learn more about volume their questions become more interesting, complex, and engaging.  It is important to allow students to have opportunities to express their curiosity.  In the reflection for this section I share some of the student's questions from the lesson.

Independent Practice

20 minutes

Students continue to solve problems involving the volume of various rectangular prisms.  A conceptual understanding is developed through building prisms to match pictures.  

After groups have had a change to work with the fifth problem (the base of the rectangle is give, rather then the 3 dimensions) , I regroup the students to discuss this example.  This is an example of demonstrating the importance of having the math and the model match.  Because this example shows the area of the base, not the dimensions of the base, this problem is more challenging for the students to make sense of what the model is showing.

I ask the students to lead the discussion about number five.  I hope they will discuss the following challenges.  If they do not, I encourage them to do discuss:

• The base is 16 square yards.  It can be shown as 16 x 1, 4 x4, or 2 x 8.  When building the model, it should match the image.

• 16 square yards and 16 squared.  What is the difference between these two?

• When we build prisms, we just use cubic units.  The picture says that it is 2 yds high, but not 2 cubic yards high.  This is because they are measuring the side of the cubes.  

Group Share

5 minutes

Students create the dimensions of a rectangular prism, then use that to determine the volume.   Then, they answer the two questions that are posted on the board.

• What is volume?

• How is it measured? 

I ask students to create the dimensions themselves so they can make the numbers appropriate for their own level.  Students who are advanced are motivated to challenge themselves by using larger numbers, and those who rely on drawing or building will choose numbers that are more reasonable for this approach.  Prompting is used to help all students make the best choice from themselves. 

Group share will allow students to see that images are helpful, but the labeled dimensions are essential.