Created by: Mercedes Hutchens Adapted by: Lisa Collins, Ed.S. Volume Created by: Mercedes Hutchens Adapted by: Lisa Collins, Ed.S.

CCSS 5.MD.3 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

CCSS 5.MD.4 4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

CCSS 5.MD.5 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Volume Volume is a multiple meaning word. Turn the volume down on the TV, please! What is the volume of that box?

In Math, volume is the amount of space a 3D object occupies. Huh?

Let’s review some vocabulary! This will help us understand volume.

Measure to find the size

There are many different kinds of units. inches feet meters centimeters yards millimeters miles

Linear Unit 1 unit When you first learn to measure, you measure in a straight line. This is a linear unit. Line ar

When you measure the area of an object, you use square units.

Area is the measurement of a 2D (flat) shape. A = L x W A = B x H A = ½ B x H

Surface Area Surface area is the area on the outside of box. Think of it as the wrapping paper. A=LxW To find the surface area, find the area of each square and add them all up.

Volume If surface area is the wrapping on the outside of the box, volume is what is inside the box.

Volume V = L x W x H height length width Volume = Length x Width x Height V = L x W x H

Cubic Unit 1 unit 1 unit 1 unit 1 cubic unit 1 unit 3

Length: How long is it? Width: How wide is it? Height: How tall is it? Length X Width X Height Length: How long is it? Width: How wide is it? Height: How tall is it?

Let’s find the volume Basically, we are finding out how many cubes will fit into the 3D object.

Let’s find the volume V = L x W x H V = 1 x 3 x 1 V = 3 units 3 height 1 unit 3 units length width Volume = Length x Width x Height V = L x W x H V = 1 x 3 x 1 V = 3 units 3

1 unit 1 unit 3 units What if I can’t tell which is the length or which is the width or which is the height?

The shape has the same volume even when it spins. 1 unit 3 units

As long as you multiply the three numbers, you’ll find the volume. Oh! It doesn’t really matter which is the length, width, or height. 1x3x1=3 3x1x1=3 1x1x3=3 I like it when it is hard to make a mistake! 1 unit 3 units

What is the volume? V = L x W x H V = 3 x 2 x 1 = 6 cubic units 1 unit

Most things aren’t see through. Good. My eyes are getting confused.

Sometimes we won’t see the cubes. 2 units 1 units 4 units V = L x W x H V = 4 x 1 x 2 = 8 cubic units

Your Turn

Find the volume. V = L x W x H V = 4 x 1 x 1 = 4 cubic units 1 unit

Find the volume. V = L x W x H V = 5 x 1 x 2 = 10 cubic inches

Find the volume. V = L x W x H V = 2 x 1 x 2 = 4 cubic inches 2 inches

Find the volume. Oh! I remember learning about exponents! An exponent of three is called cubed. Now I see why! V = L x W x H V = 2 x 2 x 2 2 inches V = 2 3 V = 8 cubic inches 2 inch 2 inches V =8 in. 3

Volume Wrap-Up Volume is a term for measures of the ”size” of three-dimensional regions. Volume typically refers to the amount of space that an object takes up. Volume is measured with units such as cubic inches or cubic centimeters-units that are based on linear measures Two types of units can be used to measure volume: solid units and containers.

Wonderful Job!

Check out this website http://www.mathsisfun.com/definitions/volume.html You can play with volume.

Volume by Mercedes Hutchens Surfing to Success Find my products: http://www.teacherspayteachers.com/Store/Mercedes-Hutchens Find my blog: http://surfingtosuccess.blogspot.com © 2013 Mercedes Hutchens Surfing to Success All Rights Reserved by the Author/ Designer Single Classroom Use Only

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