# Measuring the Volume of Solid Figures

#### 1 Hook

Begin by telling the class that today we are going to learn how to measure volume. Tell students that the word volume is a homophone and it has more than one definition. Tell students that we all know that one definition of volume is how loud something is. See if there is anyone in the class who knows that mathematical definition of volume. Record all responses that are offered, without validating if any of these defintions are correct.

Tell the class that they will watch a short Brain Pop video titled "Volume of Prisms" found at http://www.brainpop.com/math/geometryandmeasurement/volumeofprisms/ that explains what volume is. Their job is to see if they can restate what volume is in their own words at the end of the video and then review the definitions given by the class to see if any of the definitions, or parts of definitions, given by the class is correct.

When the video is finished, ask students to review what they learned from the video and record their responses. What did you learn about what volume? What objects can you find the volume of? What are methods for measuring volume? Anything else that you think is important to remember?

Make a list of the learning goals for today’s lesson, making sure to highlight whichever of the learning goals the students already identified.

1. Volume means the space inside of a 3-dimensional object, which we will be measuring in cubic units. (Define cubic units, specifying that any unit of measurement can create a cubic unit, ex. cubic centimeters, cubic inches, etc.)

2. Volume can be measured in 2 ways - 1) by counting how many cubic units occupy the prism or 2) by using a formula

3. There are 2 formulas for volume, V=l*w*h or V=B*h

#### 2 Direct Instruction

- Model for students how to find the volume of a few rectangular prisms with simple dimensions. Depending on your resources, you can draw simple prisms, labeling the length, width, and height, or you can use centimeter cubes to build a rectangular prism. A combination of the two is probably best, so that students who are tactile learners can actually see how the cubic units come together to form a rectangular prism.
- The first couple of examples should be simple examples with smaller dimensions, making it easier for students to simply visualize and count the cubic units inside the prism. Some examples are 2*2*2 or 1*2*3. With each example, you should first model how to measure volume using the formula l*w*h and then show b*h. This allows students to see you model both formulas.
- The following couple of examples should contain increasingly larger dimensions that would be too tedious for students to count in individual cubic units and even too tedious for you to build. This will force students to realize that using either of the formulas makes calculating volume more efficient. Some examples are 2*4*5, 3*5*5, etc. Continue to first model how to measure volume using the formula l*w*h and then show b*h. By this time, students have had ample models of how to find volume using both formulas, making it easier for them to do it on their own.

2. Draw or use the centimeter cubes to build a simple irregular solid by making some rows wider than other and some columns higher than others. Model that irregular solids require you to count indvidual cubic units, or use a combination of multiplication and addition (to find the volume more efficiently).

#### 3 Guided Practice

- Provide 3 simple problems for students to solve. The first problem should be to find the volume of an irregular solid figure and the others should be finding the volume of rectangular prisms. Students can use centimeter cubes to create the prism themselves if necessary. Require the students to draw and label their own diagram of the figures you presented and to show which their answer using one of the formulas.
- Walk around as students solve problems to record difficulties that students are having and to offer quick assistance to students. Review with the class the general difficulties that you noticed as you walk around and allow a couple of students to share their solutions with the class. Address any questions before assigning their indepdendent work.

#### 4 Independent Practice

Tell students that they will now have an opportunity to practice measuring volume on their own through Khan Academy. If your students are unfamiliar with Khan Academy, explain that Khan Academy is an amazing website that provides instructional videos on many different math topics, followed by short quizzes to assess how much understanding they have with that particular math skill. The quizzes are not part of their grade and are meant solely to give them an opportunity to practice, get immediate feedback about their answer, get hints for how to solve a problem, and provide them additional support through the tutorial video that they can review if they get confused about how to solve any of the problems. Tell them it’s like having their own teacher, right there with them if they need help solving the problems on their own.

First students should complete the “Volume with Unit Cubes 1” skill quiz, found at http://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-volume/e/volume_with_unit_cubes, which follows the video “Measuring Volume with Unit Cubes”. Students do not have to watch the video to complete the quiz, although the video is linked to the quiz as a reference if students need it. The quiz contains 5 questions for students to complete, which show a combination of labeled rectangular prisms and irregular solids, which will require students to count individual cubic units or utilize multiplication and addition to solve. Tell students that they should note problems that are particularly challenging or confusing to them, even after the supports of the hints and the video.

Once finished with that, students should complete the quiz “Volume 1”, found at http://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-volume/e/volume_1 ,which follows the video “Volume of a Rectangular Prism and Box examples”. Again, students do not have to watch the video to complete the quiz. These 5 questions focus solely on finding the area of rectangular prisms. These problems increase in difficulty, as some questions will give the volume and one or two dimensions and ask students to figure the remaining dimension.

#### 5 Wrap-Up

Ask the students to share questions with the class that were challenging for them and ask their classmates who were more successful with those questions, to share their strategies for solving them.

Provide an exit slip for the students to assess their understanding of the 3 learning goals established at the beginning of the lesson. Students need to answer the following 3 questions:

- When we find the volume of a 3-dimensional object, what are we measuring? (cubic units)
- What are two strategies for finding the volume of an object?( Counting how many cubic units occupy the prism or by using the formula for volume.)
- What are the two formulas for volume? (V=l*w*h or V=B*h)