G.2 - Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
warm-up
Find the Volume of the following rectangular prisms:
1) Length = 8 inches Width = 5 inches Height =10 inches
2) Length = ½ inch Width = 2 ¼ inches Height = ¾ inch
3) Length = 5.6 cm Width = 2.4 cm Width = 5.3 cm
4) Find the new volume of the prism in example #1, if you used ½ inch cubes to measure each side.
1) Length = 8 inches Width = 5 inches Height =10 inches
2) Length = ½ inch Width = 2 ¼ inches Height = ¾ inch
3) Length = 5.6 cm Width = 2.4 cm Width = 5.3 cm
4) Find the new volume of the prism in example #1, if you used ½ inch cubes to measure each side.
Find the volume of these rectangular prisms. Be careful of the fractional edges!
mini lesson - independent work/share out/discussion
Directions: You and a partner will need to agree on one problem to complete in 3-5 minutes. When time is called, share your solution and work with him/her and discuss how you solved the problem.
1) A right rectangular prism has edges of 1 1/4 ”, 1” and 1 1/2”. How many cubes with side lengths of 1/4 would be needed to fill the prism? What is the volume of the prism?
2) Banana Bread: Leo's recipe for banana bread won't fit in his favorite pan. The batter fills the 8.5 inch by 11 inch by 1.75 inch pan to the very top, but when it bakes it spills over the side. He has another pan that is 9 inches by 9 inches by 3 inches, and from past experience he thinks he needs about an inch between the top of the batter and the rim of the pan. Should he use this pan?
1) A right rectangular prism has edges of 1 1/4 ”, 1” and 1 1/2”. How many cubes with side lengths of 1/4 would be needed to fill the prism? What is the volume of the prism?
2) Banana Bread: Leo's recipe for banana bread won't fit in his favorite pan. The batter fills the 8.5 inch by 11 inch by 1.75 inch pan to the very top, but when it bakes it spills over the side. He has another pan that is 9 inches by 9 inches by 3 inches, and from past experience he thinks he needs about an inch between the top of the batter and the rim of the pan. Should he use this pan?
team challenge
Directions: See how far your table can get with these four problems in 10-15 minutes. We will come together when time is called to discuss our answers.