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This is a very elegant volume lesson, complete with worksheets

Subject:

Math  

Grade:

8  

Title – Volume
By – Stacey Karpowicz-Boring
Primary Subject – Math
Secondary Subjects – Math
Grade Level – 8

TEKS/TAKS Objectives:

      TEKS: 111.24 — Measurement 8.8 (B)

    TAKS Objective VIII: Measurement

Lesson Objective:

      A. Students will able to identify and use the following vocabulary words: Volume, prisms, cylinders, pyramids, and cones.

      B. Students will be able to find the volume of prisms, cylinders, pyramid, and cones.

      C. Students will be able to determine which volume formulas to use with the correct shape.

    D. Students will be able to solve problems using the volume formulas.

Anticipatory Set:

    Think of different objects that we see and/or use in every day life that has volume. What are these objects? Can you describe the shape that makes up the three dimensional object?

Input Procedures:

    The teacher will first ask the students “What is the definition of a prism?” followed by “What is the definition of a cylinder, pyramid, and cone?” After the class discusses these definitions the teacher will ask “What is Volume?”

Definitions Prism

      is a polyhedron that has parallel and congruent polygons, called bases, for two faces and parallelograms for all other faces.

Polyhedron

      is a figure bounded by plane surfaces.

Cylinder

      is a prism with circular bases.

Pyramid

      is a polyhedron that has a polygon as its base and sides that consist of triangles having a common vertex, called the apex.

Cone

      is a pyramid with a circular base.

Volume

      is the number of cubic units contained in its interior.

      The teacher will then explain by using a three dimensional diagram (on the board or overhead) what each side of the figure is and the shapes that make up the figure, so that the students will be able to understand the make up of the formula when it is presented.
    Then teacher will introduce the formulas.

Cube : V = a 3
Prism : V = Bh
Cylinder : V = Bh = [Pi] r 2 h
Pyramid : V= 1/3(Bh) = 1/3(1/2bh)(h)
Cone : V = 1/3 (Bh) = 1/3 [Pi] r 2 h
Note 1: B represents the area of the Base of a solid figure. Note 2: [Pi] represents the symbol for Pi

    The teacher will also demonstrate each formula and ask if there are any questions.

Checking for Understanding:

      The teacher will but problems on the board for each formula and instructs the students to work the problems. As the students are working the problems, the teacher will walk around the classroom and answer questions and help students on an individual bases.
    The teacher will also ask questions openly about volume and if time allows the teacher will have students come to the problem and work the problems to demonstrate their understanding of volume.

Guided Practice:

      The students the will work in their groups to complete the “Volume” worksheet.
    While the students are working on the worksheet, I will move around the classroom and answer any questions. During this time, I will also ask the class general questions about surface area to ensure that every on understands.

Independent Practice:

    The students will be given a worksheet called “Cones, Pyramids, and Spheres”. The students are required to show all work for credit.

Closure:

    The students will be asked to describe what was covered today in class. I will also ask the students how they fell about solving volume problems.

Assessment:

    The students will be given a Performance Assessment problem. This is worksheet “Volume Performance Assessment”. The student will be required to justify their answer to this problem.

Re-teach:

      The teacher will have students complete the web activities

        (

www.aaamath.com/B/g79_vox3.htm

        ) for the volume of a cube,


        (

www.aaamath.com/B/g79_vox6.htm

        ) for the volume of a Rectangular Prism,

        (

www.aaamath.com/B/g79_vox1.htm

        ) for the volume of a Triangular Prism,

        (

www.aaamath.com/B/g79_vox4.htm

        ) for the volume of a Cylinder,

        (

www.aaamath.com/B/g79_vox2.htm

        ) for the volume of a Cone, and

        (

www.aaamath.com/B/g79_vox5.htm

        ) for the volume of a Pyramid.

    Teacher should evaluate which activity the student should participate in to aid the learner in further their understanding in volume.

Enrichment/Extension:

    The students will be asked to write a problem over volume that relates to a real life situation.

Materials:


Volume Worksheet

Complete.

  1. A water tank has been purchased for the farm. It will be used to water cattle. It is an oval shaped metal container that is 2.6 feet tall. the area of the bottom of the tank is 9.3 square feet. If the cattle drink two hundred four cubic feet of water a day, how many times per day will the tank have to be filled?
  1. Mr. Bloop has a cylindrical water tank on his farm. It is nine feet long and 2 feet 2 inches in diameter. Water flows out a valve in the bottom of the tank at a rate of 3.1 cubic feet per minute. At that rate, how long will it take to empty the tank when the tank is full?
  1. An underground chamber has been discovered in an old mansion. The chamber is thought to have been used for storing ammunition. The dimensions of the chamber are 13 feet by 5 feet by 5 feet. An old ammunition crate was also found in the chamber and it had dimensions of 1 foot by 1 foot by 2 feet. What is the maximium nuber of ammunition boxes of that size that could be put in the underground chamber?
  1. If a cube with a 5-in. side length is sliced in half, what is the surface area of the two pieces?
  1. If you have five 5-in. by 5-in. aluminum cubes and superglue them together in a row, what is the surface area of the resulting shape made by the five cubes?
  1. A pillar from an ancient city was found buried in the ground. It had a cross-sectional shape of a sextagon (stop sign shape). If the length of the cross section is nineteen and one hundredth square meters, and the pillar was sixteen and four tenths meters tall, what was the total volume of stone contained by the pillar?



Volume Performance Assessment

Mrs. Sandly asked her students to create a cylinder to hold chocolate candies for a statistics problem using a standard piece of paper. (8.5 inches by 11 inches). Some of the students made cylinders that were 11 inches tall, and others created cylinders that were 8.5 inches tall. The students in Mrs. Sandly’s class began having a discussion regarding the amount of chocolate candies that each person could store. Oliver said that each cylinder would hold the same amount of chocolate candies, because all of them used the same size paper, but others disagreed. Who is correct? Justify your answer.


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