Design Your Own Office Building
Connie Sargent and Ryan Kimbro
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Application of Surface Area and Volume
AUTHOR: Connie Sargent
TITLE OF THE LESSON: Introduction to Surface Areas and Volumes
DATE OF LESSON: TBD
LENGTH OF LESSON: 45 minutes
NAME OF COURSE: Geometry
SOURCE OF THE LESSON: Myself
TEKS ADDRESSED: §111.34. Geometry; G.8.D.
CONCEPT STATEMENT: Surfaces areas and volumes of polygons.
PERFORMANCE OBJECTIVES: Define and calculate the formulas for surface area and volume for rectangular prisms and cylinders.
RESOURCES: Worksheet with surface areas and volumes
SAFETY CONSIDERATIONS: N/A
SUPLEMENTARY MATERIALS, HANDOUTS: Worksheet
Engagement |
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Time: 10-15 min |
What the Teacher Will Do |
Probing Questions |
Student Responses Potential Misconceptions |
Begin by writing the “box of sand present” questions on the board. Have the students work on it by themselves for 3-5 minutes and then pair share for another 3-5 minutes to come up with the best solution. Have students volunteer their solutions and write them on the board. |
If I was wrapping a rectangular present, create an equation I could use to find out exactly how much wrapping paper I need.
If this box I was wrapping was filled with sand, create an equation I could use to find out exactly how much sand was in the box.
What shape would allow the largest amount of sand but would use the least amount of wrapping paper? |
Might be scared by the terms “create an equation.”
Might have trouble coming up with ratios for the volume vs. surface area problem, especially since this is a hypothetical situation and there are no numbers involved.
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Exploration |
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Time: 15 min |
What the Teacher Will Do |
Probing Questions |
Student Responses Potential Misconceptions |
Have students get into their project groups and discuss the various possible shapes for their building. |
Come up with three different possible shapes of your building and calculate the surface area and volume of each of them. |
May have trouble coming up with the equations for the shapes they come up with.
May have trouble coming up with shapes for their building other than squares or rectangles. |
Explanation |
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Time: 7 min |
What the Teacher Will Do |
Probing Questions |
Student Responses Potential Misconceptions |
Have students get into their project groups and discuss the various possible shapes for their building. |
Come up with three different possible shapes of your building and calculate the surface area and volume of each of them. |
May have trouble coming up with the equations for the shapes they come up with.
May have trouble coming up with shapes for their building other than squares or rectangles. |
Elaboration |
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Time: 7 min |
What the Teacher Will Do |
Probing Questions |
Student Responses Potential Misconceptions |
Have each student individually come up with a shape for their building that maximizes the volume but minimizes the surface area. |
What shape would you make your building to maximize the volume but minimize the surface area of your building? Show your work. |
. Could try to make this more complicated than it is. |
Evaluation |
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Time: 5 min |
What the Teacher Will Do |
Probing Questions |
Student Responses Potential Misconceptions |
Have students turn in a sketch of their building with the maximized surface area and volume with the appropriate calculations. |
Create a sketch of your building that maximizes the surface area and volume. Make sure to label everything correctly and show your work. |
They might get confused as to how to come up with the volume of their entire building since it will most likely be more than just one specific shape. |