Procedures

Vocabulary: volume, base, and height

Aim: How can we determine the volume of package (box)?

Mini Lesson:(10-15 minutes)

1.  Make two different rectangular prisms (without bases) by folding two 8.5 in. by 11 in. sheets of paper into equal fourths: using the longest side and one using the short side.  Tape the edges to form the prism

2.  Make a layer of unit cubes to cover the base of each rectangular prison.
            a.  How tall is a single layer of the cubes?
            b.  How many cubes cover each basis?

3.  For each prism, how many cubes are needed to make two layers?  Three layers?  For layers?  Make a table to record your data.

4. a How tall is each rectangular prism (in centimeters)?

5. How many cubes would fill each prism?

6. Exploer the virtual manipulative for volume.

How High? – Try your hand at the classic Piagetian conservation of volume test
http://nlvm.usu.edu/en/nav/category_g_3_t_4.html

 

Example # 1
            1. Explain to the student that the area of the base of polyhedron is shown by the letter B.  The length of the base of the polygon is shown by b.
           
            2.  Using the overhead transparency and using the following measurements below have the students complete the following steps as follows.
           
            3.  Give the students of following scenario:
                        a net a delivery service to live as a package with dimensions 12 in. by 7 in. by 30 in. What is the volume of the package?

            4.  First, draw the prism and label the dimensions.

            5.  Now explain to the students to find the area of the rectangle  based, B

            6.                                 B = 12 x 30 = 360
                                               
                                                V = B x h
                                               
                                                V = 360 x 7

                                                V = 2520 in 3
           
                                                The volume is 2520 in 3

Example # 2

            1.  Explain to students to find a higher rectangular prism with the volume of  72 cm 3 and base dimensions 6 cm 3 by 3 cm.

            2.  First, find area of  the rectangular base, b
                       
                        B = 6 x 3 = 18 cm 3

            3.  Then use the volume formula to solve.

                                                V = B x h

                                                72 = 18 x h

                                                4 = h

                                                The prism  has a height of 4 cm.

Practice: Complete the Examples:
         

                        B = 9.8 cm x 5.0 cm                             B = 6.5 in x 6.5 in
                       
                        H = 4.2 cm                                           h =  6.5 in

 

                        V = ___________                          V = ___________

 

 

Homework: sketch each figure, find its volume.

            a) A box of granola cereal that measures 23 cm by 8 cm by 35 cm.

            b) A fly-casting testing pool in the park that is 30 ft. wide, 40 ft., and 5 ft. deep.

Test Prep: A cube-shaped storage container measures 1.5 ft. on each side.  What is the volume of 6 containers.