Virginia - Mathematics Standards of Learning (2009): 6.10d Virginia - Mathematics Standards of Learning (2016): 5.8.a, 5.8.b,

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1 1 Lesson Plan Volume of a Rectangular Prism Age group: 5 t h Grade, 6t h Grade Virginia - Mathematics Standards of Learning (2009): 6.10d Virginia - Mathematics Standards of Learning (2016): 5.8.a, 5.8.b, 5.9.b Fairfax County Public Schools Program of Studies: 6.10.d.1, 6.10.d.2 Online resources: Lo o ki ng T hro ugh a P ri sm Opening Teacher present s Students pract ice Math Pract ice Closing M at h Obj ect ives E xpe ri e nc e a visual model for detering volume P rac t i c e the volume formula Learn to use cubic units when finding volume De vel o p spatial sense Ope ni ng 5

2 2 What is the definition of volume? Volume is the amount of space inside a three-dimensional figure. Display the following rect angul ar pri sm: Let s say this prism can fit 6 unit cubes across, 5 cubes deep, and 2 cubes high. How many cubes are needed to fill the prism? We need 60 unit cubes to fill the prism. How did you get this answer? I multiplied 6 by 5 by 2. I multiplied the width, the length, and the height of the prism. Display the following rectangle: If we were to find this rectangle s perimeter, what units would we use? The units are centimeters. If we were to find this rectangle s area, what units would we use? The units are square centimeters. Display the prism again:

3 3 So what units should we use for volume? Why? We should use cubic centimeters because we are measuring a three-dimensional space. We are asking how many unit cubes fit inside that space. T e ac he r prese nt s M at h game : Lo o ki ng T hro ugh a P ri sm - Vo l ume o f P ri sm: M e t ri c Uni t s 12 Present Matific s episode Lo o ki ng T hro ugh a P ri sm - Vo l ume o f P ri sm: M e t ri c Uni t s to the class, using the projector. The goal of the episode is to calculate the volume of a rectangular prism and give the answer in cubic centimeters. Example : Please read the question that the episode is asking. It is asking, What is the volume of the prism? What units are we using for the answer?

4 4 The answer is in cubic centimeters. Let s fill the prism in the episode with unit cubes. Let s start by putting in the cubes one at a time. Move one cube into the prism. Ask a student to come to the front to continue moving cubes into the prism. Once the prism is full, ask: what is the volume of the prism? Click on the to enter the students answer. If the answer is correct, the episode will proceed to the next question. If the answer is incorrect, the question will wiggle and the episode will display cubes stacked along the length, width, and height of the prism. The episode will present a total of six questions. You have the choice of filling up the prism one cube at a time, clicking on to completely fill the prism all at once, or just filling in the length, width, and height of the prism.

5 5 St ude nt s prac t i c e M at h game : Lo o ki ng T hro ugh a P ri sm - Vo l ume o f P ri sm: M e t ri c Uni t s 12 Have the students play Lo o ki ng T hro ugh a P ri sm - Vo l ume o f P ri sm: M e t ri c Uni t s on their personal devices. Circulate, answering questions as necessary. M at h P rac t i c e : Vo l ume o f a R e c t angul ar P ri sm Wo rkshe e t 15 Let s consider rectangular prisms whose volume is 20 cubic centimeters. What could the dimensions of the prism be? Display the answer to this problem: These are all of the rectangular prisms with a volume of 20 cubic centimeters (with whole number dimensions) that exist. Any other rectangular prism that you could find will be one of these four, just rotated or turned in some way. Display the following prisms:

6 6 These two prisms are identical. Display the following problem: Your task today is to find all the rectangular prisms (with whole number dimensions) with volume: cubic centimeters cubic centimeters cubic centimeters cubic centimeters Have the students work in groups of four. Circulate, answering questions as necessary. Review solutions. Discuss any questions the students may have.

7 7 How do you know when you have found all of the rectangular prisms that exist? A possible response: We look at the factors of the number. For example, 32 has 6 factors, 1, 2, 4, 8, 16, and 32. We see how we can set them up in triples to multiply to 32. We started with 1 times 1 times 32. Then we kept the first factor (1) but increased the second factor to 2, the next larger factor of 32. So now we have 1 times 2, and we know that the third factor must be 16 to get a product of 32. Then we keep the first factor (1) and again change the second factor to the next larger possibility, which is 4. So we get 1 times 4 times 8. When we try this again, we end up with 1 times 8 times 4, which we already have. So now we know that we have all the options that start with 1. So now we change the first factor to 2 and repeat the process. We continue systematically until we have found all possible dimensions.

8 8 Cl o si ng 3 Hand out a small piece of paper. On it, ask the students to solve the following three problems independently. 1. Find the volume of a rectangular prism that is 3 cm by 5 cm by 8 cm. 2. Find the volume of a rectangular prism that is 4 cm by 4 cm by 9 cm. 3. State a possible set of dimensions for a rectangular prism that has volume 24 cubic centimeters. When the students are done working, collect papers, to review later.