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Dark Poison

Activity Plan, Math 2

Surface Area and Volume

                                    

Lesson Summary:

In this activity, students will compare the relationship between surface area and volume of geometric shapes.  The students will use two rectangles with the same surface area to make two different sized cylindrical tubes.  They will evaluate the volume each tube holds.
           
Subject: Math: Numbers and Operations, Geometry, Measurement

 

Grade Level:

  • Target Grade:  8
  • Upper Bound: 8
  • Lower Bound: 6

 

Time Required: One class period

 

Materials:

  • Construction paper
  • Scissors
  • Sugar [The reason sugar is being used as the filler is to relate this lesson back to the Dark Poison Science 1 PowerPoint slides that discuss sugar cane], or a less messy filler, such as pinto beans, M&Mís, jellybeans, etc.
  • Tape
  • Trays for each group
  • Dark Poison Science 1 PowerPoint
  • Surface Area Worksheet


Lesson Plan:

        Divide the students into groups of two.  Each group should collect the materials for the activity. 

        The students will cut the construction paper in half.  The students will roll the first half of paper into the largest cylinder possible and connect it using tape.  This tube (without a top or bottom) should be short and fat.  By rolling the other half of the construction paper, the students should create a taller slimmer cylinder, once again without a top or bottom. 

        The students will make a hypothesis about whether or not the cylinders with the same surface area will have the same volume and record it on their Surface Area and Volume Worksheet.

        Have the students place the skinnier cylinder inside the larger one and fill the skinny cylinder with the filler on top of the tray. 

        Once the cylinder is filled, the students will slowly remove the skinny cylinder by carefully pulling it up and out, allowing the sugar to fill the thick cylinder.  The students will observe the differences in volumes of the two cylinders.  Have the students discuss the reason for the difference in volume.

        Then have them compare their results with their hypotheses.  It is important to recognize/discuss that although the two cylinders have the same surface area, they have different volumes.  The thicker cylinder has a larger radius.  It gives the larger base area (п r2) and thus generates a larger volume (height ◊ base area). After the experiment, the students should finish completing the worksheet.

 

Background & Concepts for Teachers: 

        It is important that the students understand that the base area is the area of the circular top/bottom bases of each cylinder.

 

            Vocabulary / Definitions:

        Base area of circular top/bottom of cylinders: п r2

        Surface area: 2-dimensional exposed area of any shape

        Volume: Height * base area

 

Lesson Extensions:

  • The students may discuss ways in which items can be produced in order to save on cost-related expenses.  For example, bring in the three different sizes of canned green beans (small, medium, and large).  Have the students measure the surface area and volume of all three cans.  For each can, (small medium, and large) the students should generate the measurements of a can with a different (smaller) surface area but that holds the same amount of green beans (same volume).  By fabricating this can with less surface area but the same volume, production costs can be decreased.      

 

References

  • http://www.math.niu.edu/courses/402/zollman/rolling.rect.pdf

 

TEKS:

8.2 (A) Select and use appropriate operations to solve problems

8.2 (B) Add and subtract rational numbers

8.4 Patterns, relationships and algebraic thinking

8.7 (B) Use geometric concepts to solve problems

8.8 (A) Find surface area and volume

8.8 (B) Use formulas to solve problems with volume

8.14 (A) Identify and apply math to everyday experiences

8.14 (B) Use problem-solving models

 

Science:

8.2 (A) Plan and implement investigative procedures

8.2 (B) Collect data by observing and measuring

8.2 (C) Organize, analyze, evaluate, make inferences, and predict trends

8.3 Use critical thinking and scientific problem solving

 

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