INVESTIGATIVE
LESSON PLAN ON VOLUMES AND SURFACE AREAS
Name: Adil
Benhayoun
Title of lesson: Surface
Area and Volumes
Length of lesson: 50 mins
Source of the lesson:
The source is a Investigation 5 of the “Filling and Wrapping” book of the Connected Mathematics textbook series.
TEKS addressed:
7.04.(A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling
7.04.(B) graph data to demonstrate relationships in familiar concepts such as
conversions, perimeter, area, circumference, volume, and scaling
7.06.(C) use properties to classify solids, including pyramids, cones, prisms, and cylinders
7.08.(B) make a net (two-dimensional model) of the surface area of a solid
7.09. The student is expected to estimate measurements and solve application problems involving length (including perimeter and circumference), area, and volume
The students should know the definition of a prism and a cylinder. The students should be able to differentiate between the notion of volume and surface area. They should be able to calculate surface area and volume of any prism or cylinder.
Tape, rulers.
None in particular.
V.
Supplementary materials, handouts.
A set of pre-assessment handouts.
Several pre-cut shapes that can be made into either prisms or cylinders.
A set of post-assessment handouts.
Teacher Does Student Does (hopefully)
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Engage: Off in the Bahamas you are with plenty of wonderful free time. But you are only there because of a great mind that you have that can figure out exactly how much water is needed to fill up any swimming pool, no matter what the size. And so some one asks you how much water is needed for their pool that is 100 ft. long, 60 ft. wide, and 15 ft. deep. What would you say? What about if he asks how much paint is needed to paint the walls of the pool? These are simple surface area and volume questions, and after today you should be able to answer them all. |
The students pay attention to the problem presented. They try to answer it to the best of their abilities. |
Evaluate: The level of attentiveness and engagement of the students will be this measure.
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Explore: A pre-assessment worksheet will be given. Once that is done, hand every student 2 different shapes that can be made into prisms and cylinders. The students will be asked to calculate the total area of the unfolded shapes by using a ruler to calculate the lengths and write down the values of the different surfaces. Then they will be asked to fold the shapes into a three dimensional shape and tape the edges together. The students will be asked for how much paper would be needed to ‘wrap up’ the object that they made and how much water would be needed to fill it up. They will also be asked what the surface area and volume of the objects are (which is the same question asked using the terms) |
The students will work individually on the pre-assessment worksheet. Then, students will form groups of two, each with one prism and a cylinder (unfolded when it is given to them). The students will calculate the area of each shape by summing the area of each piece. They will thus find the surface area. If the students cannot find this value, they will remain curious until the explanation is given. Students may have difficulty applying the same concept to the cylinder. The volume will be a bit difficult for most. Some who know the process would get the answer, and other would not. The volume of the cylinder should be as difficult as the surface area. |
Evaluate: The students need not get the right answers. Their evaluation is based on how they are thinking about the surface area and the volume. The students should be considering the whole internal space for volume while only the external for the surface area. Students will be thinking and intrigued about why did I ask them to write down the values of the different surfaces they measured.
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Explain: Define the prism for the students – an object with congruent (identical) top and bottom and rectangular faces, and explain why the cylinder is not prism. Define what surface area is and why it is the amount needed to wrap-up the prism or cylinder. Explain how it is calculated, and show that the surface area is a 2-dimensional value (i.e. units-squared). Show the basic technique for calculating surface area for all the shapes given to them. Then to calculate the surface area of a cylinder, It takes 3 steps, and not one to calculate the surface area of a cylinder; first, to calculate the area of the top and the bottom of the cylinder, which is 2 * pi * r2, and then to calculate the area of the curved surface, which is 2 * pi * r * h, which is the circumference of the top/bottom circle * the height of the cylinder; then add the area of the bottom/top surface to the curved surface to get total surface area of a cylinder. Due
to the complexity of calculating the surface area of a cylinder, I will ask
students the following questions. What is the name of the curved area of a cylinder? Right answer: rectangle What is the length of that rectangle in terms of the radius of the top/bottom circle? Right answer: l = 2 * pi * r What is the width of that rectangle in terms of the height h of the cylinder? Right answer: w = h Then what is the surface
of that rectangle? Finally, what is the
surface area of the cylinder?
Ask each student to use this knowledge to get the surface area for all objects if they did not get it earlier, or check it again if they did get it. Then define what volume is and why it is the amount needed to fill-up the object. Explain how it is calculated, and show that it is a 3-dimensional value, unlike surface area. Show the basic technique for calculating this for all the shapes they have. Ask each student to use this knowledge to get the volume for the objects if they did not get it earlier, or check it again if they did get it. |
Students will attentively listen to the explanations, and ask questions about anything they don’t understand in regard to volumes and surface areas. Students will listen to the questions being asked and try to correctly answer them. Based on what is learned, the students to either calculate the values or check their previous values of the surface areas of the objects. This will again be done within the group. Then the students will do the same for the volume of the objects. |
Evaluate: All students should now have the correct method for calculating surface area and volume of any prism or cylinder. After my thorough explanation of how to calculate the surface area of a cylinder, I expect that all students will correctly answer all questions that I asked during the explanation phase.
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Extend / Elaborate: The students will be asked
which cereal box would be buy, given four different cereal boxes with
different surface areas and volumes. They will be asked which one can hold
most advertisements on it. The students will also
be asked which canned food would they buy, given four different cylinders. Explain to the students
why sometimes maximum surface area is needed and minimum volume, such as to
make boxes seem bigger or rooms look larger. And sometimes least surface area
is needed and maximum volume, when material is scarce and most room is
needed. Explain maximum volume is for a cube while maximum surface area is
for a long object. |
Students will calculate the volume of the cereal boxes and choose the one with most volume. Then they will do the same with surface area. The same process will be done for the volume and surface area of cylinders (cans). The students will ask questions as to why a cube is optimal for volume. This will be explained by having the students calculate volumes of three shapes with different volumes but same surface area, one of them being a cube. |
Evaluate: The students will be given another worksheet, very similar to the pre-assessment worksheet. This will be the students’ final evaluation. It will cover surface areas and volumes of prisms and cylinders. Question 4 will slightly be modified, they will be asked to use the values of the different surfaces they measured during the engagement part in order to check their work, they will also be asked to write all the steps and the formulas they used (no cheating allowed in using values already measured with the ruler, show me the work!!!!).