What is This Thing Called Volume?

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SWBAT use and understand the formula for the volume of right rectangular prisms.

Big Idea

Fill ‘er up! Understanding the formula for volume and how it is used to figure out how much a figure can hold.

Curriculum Reinforcer

10 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.


10 minutes

To open up this lesson on volume, I will provide each group of students will 36 cubes. Each group will build a rectangular prism using those cubes. Using the rectangular prism that they have built, the students will answer the following questions:

  • What is the length of your figure?
  • What is the width of your figure?
  • What is the height of your figure?
  • What is the surface area of your figure?
  • How much desk area does your figure cover?
  • Tell me three ways that you can find the volume of this figure


In completing this activity, students could end up with a variety of different rectangular prisms. For example, a students could end up with a prism that is 4 units wide, 3 units long, and 3 units in height… or they could have a prism that is 6 units wide, 2 units long, and 3 units tall. These are just two of the possible examples.

Using the prism that they created, I will then have my students write down what they observe about the prism that they created. They should be telling me things like; how many units are in one layer and how many layers there are.

The reason for this activity is for the purpose of laying the foundation for understanding and conceptualizing the formula for area and how it can be the same for all prisms with congruent bases.

Instruction & Teacher Modeling

10 minutes

In today’s lesson, I will be placing an emphasis on the difference between area an volume. While doing this, I will stress to my students that they need to pay close attention to the units when dealing with area and volume. At this point, I have already taught my students that area deals with square units. Now, I want to ensure that my students know that volume deals with cubic units. To stress this point, I tell my students that we find the area of 2-dimensional figures… 2-D… to the second power or squared (a square is 2-dimensional). I then tell them that we find the volume of 3-dimensional figures… 3-D… to the third power or cubed (a cube is 3-dimensional).

During this lesson, I will also show them how we are take the area of shape and multiplying that area by how tall that shape is. While doing this, I will show them how V=lwh and V=Bh are the same by showing them how the lw portion in V=lwh is the area of the base of the shape which is the B in V=Bh.

Today is all about getting a deep understanding of the formula for volume and understanding the differences between area and volume.



Try It Out

5 minutes

For the guided practice portion of this lesson, the students will practice finding volume of one right rectangular prism using the formula V=Bh by ensuring to show how B stands for the area of the base of the prism. They will do this step by step with me as I explain the process. 

Then, I will have my students find the volume of another right rectangular prism on their own. They will have to show what portion of the formula represents, "B" and demonstrate how volume is taking the area of the polygon that is the base shape of a prism and multiplying that area by how tall that prism is.


Independent Exploration

20 minutes

To explore this concept of finding the volume of right rectangular prisms using the formula for volume, I will have my students complete 8 problems where they are exploring the concept of volume of right rectangular prisms. Then, they will have one problem where they will be provided with the rectangular prism but no measurements. They will have to come up with their own measurements for the rectangular prism and write a word problem that could be solved using their rectangular prism and its measurements. And then, they will need to solve their word problem. Last, students will have to write a brief essay about how volume can be applied to a real-world situation.

During this time, I want my students to demonstrate that they have mastered the concept of volume of rectangular prisms. In order to demonstrate their mastery of this concept, my students will need to be able to present their work, articulating the steps to solving problems with volume, what the formula means, and how volume is applicable to real life. 


Closing Summary

15 minutes

We will check the answers to the problems that the students completed during the independent practice. To do this, I will have one student, for each of the first 6 problems, to come to the board and complete their assigned problem on the board. After they have completed their problems, I will then allow discussion to commence concerning the validity of the solutions of each problem. The students will either agree or disagree with the presented solutions. And, they will need to be able to articulate why they agree or disagree. 

After going over the first 8 problems, I will then choose one student to present their answer to number 9, which required that they create and solve their own word problem. Next, I will choose another student to present their answer to number 10, which requires the students to be able to articulate how volume is applicable to the real world.

During this time, observing students should be ready to contribute to what is being presented by either adding to what is being stated, providing critique, and/or asking questions.