Warm Up 2/5 Draw and label the net of the triangular prism and then find the surface area 9 in. 8 in. 6 in. 11 in.

V OLUME How much can something hold?

S TANDARD AND E SSENTIAL Q UESTION MCC6.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. How can you find the volume of a solid figure by using formulas and unit cubes?

B RAINSTORM ! W HAT DO YOU REMEMBER ABOUT VOLUME ?

I MPORTANT T ERMS Volume : The amount of space occupied by an object. Prism: A polyhedron with two parallel and congruent faces, called bases, and all other faces that are parallelograms. Right rectangular prism: In a right prism, the lateral faces are each perpendicular to the bases. Volume of a Prism: The area of a base times the height. The number of cubic units to fill a prism.

H OW TO FIND VOLUME WITH U NIT C UBES Length Width Height Unit Cube * You can find volume by counting the number of unit cubes in a solid figure.

L EARN ZILLION V IDEO volume-of-a-rectangular-prism-by-filling-it-with- unit-cubes

H OW CAN YOU FIND THE VOLUME OF A SOLID ? 1. Find the area of the base of the solid figure and multiply it by the height. 2. Find the volume by multiplying length times width times height. V = B h V = lwh

Warm Up 2/21 A cereal company is trying to decide which box would be the cheapest to make. 6 in. 4 in. 9 in. 3 in. 4 in. 1. What is the surface area of each box? 2. Which would be the cheapest to make and why? Box ABox B

S TANDARD AND E SSENTIAL Q UESTION MCC6.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. What is the process for finding volume of figures with fractional edge lengths?

L ET ’ S R EVIEW How do you calculate volume? Length Width Height THINK FAST!!! What is the volume of the rectangular prism?

F RACTIONAL E DGE L ENGTHS  First change all mixed numbers into improper fractions!  Then just multiply your length, width, and height together to find the volume. Example! 7 3 / 5 in. 14 in. 5 in. V = 532 in 3

V OLUME OF A CUBE Volume of a cube = s 3 1 / 5 cm. 1 / 2 in. 1 / 8 ft. V = 1 / 125 cm 3 V = 1 / 512 in 3 V = 1 / 8 in 3

F RACTIONAL EDGE LENGTHS PRACTICE V = 470 mm 3 5 mm / 4 mm. 8 mm. V = 882 cm / 5 cm. 15 cm. 6 cm.

Stacy has a rectangular flower box with a height of 9 inches, a width of 8 inches, and a length of 10 ½ inches. If the flower box is currently only 1 / 3 full with soil, how much soil is in the flower box? Stacy’s flower box is filled with 252 in 3 of soil.

Warm Up 2/6 Rachel has a rectangular swimming pool with a height of 8 feet, a width of 6 feet, and a length of 12 ½ feet. If the pool is currently only 1 / 3 full with water, how much water is in the pool? Rachel’s pool has 200 ft 3 of water.

S TANDARD AND E SSENTIAL Q UESTION MCC6.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. How can you combine multiple processes for finding volume?

L ET ’ S R EVIEW 1 / 5 in. V = 1 / 125 in 3 Calculate the volume of the following figures with fractional edge lengths In a cube you multiply the side length together 3 times to get the volume of the cube! ns/198-find-the-volume-of- a-fractional-rectangular- prism-using-unit-cubes

C OMBINING FRACTIONAL EDGE LENGTHS AND COUNTING UNIT CUBES ! 1) Calculate the volume of one unit cube 1 / 4 cm. Volume of one unit cube = 1 / 64 cm 3 Method #1

2) Count the total number of unit cubes in the figure Total 160 cubes

3) Multiply the number of unit cubes by the volume of one unit cube to get the total volume / 64 cm 3 Total Volume= 2.5 or 2 ½ cm 3

M ETHOD 2! 1) Find the lengths of the sides using the fractional measurement 1 / 4 cm. 2 ½ cm 1 cm

2) Use the volume formula! (Multiply length times width times height) 2 ½ cm 1 cm = Total Volume= 2.5 or 2 ½ cm 3 Discussion Question Why did we get the same volume using both methods?

V OLUME S PEED R OUND 5 mm. 10 mm. 8 mm. 4 in. 12 in. 2 in. 3 cm. 6 ft mm 3 27 cm 3 96 in ft 3