Exploring Volume

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Objective

SWBAT find the volume of rectangular prisms using centimeter cubes.

Big Idea

Modeling volume with centimeter cubes deepens understanding of the formula for finding volume.

Do NOW

25 minutes

For the do now, I’ve decided to play a game.  I’m going to review with the students the naming protocols for prisms and pyramids.  Students need to know what solid they are looking at to determine how to find it’s volume.  This activity will help set them up for today’s learning.  Students will be working in groups.  Each student needs their own white board and marker.  The activity will be a Numbered Heads Together  structure.  The difference will be that when the students are done using their team time, and they have shown me their answer, we will be playing basketball for an extra point.  If you don’t have a nerf basketball set available, garbage can basketball works well too. During this activity, I keep score of correct answers and the students can shoot for the extra shot to gain more points.  This part of NHT is for fun and can be eliminated without loss of learning.

NHT supports:

SMP1: Sense-making, students use their knowledge of 3-D vocabulary to make sense of the shape.

SMP3: Arguing, students prove that their answers are correct

SMP5: Tools, students use nets and vocabulary to help them classify the solid.

Tools:  Exploring volume power point

Exploring Volume

30 minutes

For this part of the lesson you will need centimeter cubes or something similar.  The students will be creating rectangular prisms given certain side lengths.  Once the students have the prism built, explain to them that the volume of a rectangular prism is defined by how many cubic units can fit inside of it.  Have the students count the number of cubes used to create their prism. If you can find a couple of students who built their prisms differently, it would be a good idea to point this out.  Ask the students if the volumes of their prisms are different?  You can even ask each student what they found the volume to be.  Students should see that it really doesn’t matter which way the structure is built, you will still get the same volume using those side lengths.  Have students create another rectangular prism using different side lengths.  Have them compare structures and volumes with a partner.

The next example has them building a cube.  Students may struggle setting up the cube given there is only one side length.  Ask students what they know about a cube?  Students should know that all sides of a cube are the same.  Students should create their cube and find its volume.

Finally, students will be creating their own rectangular prism.  They will need to explain the side lengths and volume. Allow students time to share their rectangular prisms with the group or they can share with partners.

Using centimeter cubes supports SMP 5 and understanding the numbers to mean length, width, and height supports SMP2.

Tools:  Exploring volume notes and power point, centimeter cubes

Indendent Practice - Exploring Volume

20 minutes

The students will be creating 10 more rectangular prisms or cubes and determining their volume.  Students should write down the side lengths and find the volume.  Some students may begin to see that if you multiply the side lengths together, you will find the volume.  Our goal is to get them to see this. If students start multiplying their side lengths together, be sure to have them create the prism to prove their solution is correct.  Also, be sure that students are using the label u³ with their solution.  Labeling our solutions supports SMP6: precision.

Upon completion, I want the students to write the relationship between the side lengths and volume.  Students should be able to notice that if you multiply the side lengths together, you get the volume. You can also ask the students to come up with a formula where V = volume and l,w,h stand for length, width, and height. (SMP 7 and 8).

Closure

10 minutes

This problem will give me a good idea of those that understand how to find the volume of a cube. It is an illustrative math problem. The problem asks them to find the volume of 2 different cubes, without building the structure.  The purpose of this problem is to get students to verbalize the relationship among the side lengths.

a.)    A single layer would be 3 x 3 = 9 and then there are 3 layers up so 9 x 3 = 27 u³.  Some students may say, you can multiply 3 x 3 x 3 = 27u³

b.)    A single layer would be 6 x 6 = 36 cm ³ and then there are 6 layers up, so 36 x 6 = 216cm³.  Some students may say, you can multiply 6 x 6 x 6 = 216cm³

Tools:  Closure problem