12 Jul Complete Middle Grade Mathematics Discussion
Question Description
THIS DISCUSSION HAS 3 PARTS:
Discussion Post_July 2:
Activity 1: Surface Area Formulas
Choose one cylinder and it’s corresponding cone (same base and height)
Use the Nets to come up with a formula for the surface area of these two 3D shapes. (FYI: the “net” of a 3D shape is when it is opened and unfolded to create a flat shape. The flat shape is called a “net”. The “net” is what I provided for you on June 27)
Can you generalize these formulas for any cylinder? And any cone?
For the discussion post, write your derived formula for the surface area of a cylinder and a cone. How did you find this?
Activity 2: Surface Area Video
Watch the video titled “Surface Area of Cylinders.”
In this video, students are discussing the surface area of a cylinder.
For the discussion post, answer the following questions:
What teacher moves helped the students in the video generate the formula for the surface area of a circle-based cylinder?
How would you want to respond to the student’s last question in the video?
Activity 3: Surface Area of a Sphere (“Orange” You Glad?)
You are going to use an orange to investigate the surface area of a sphere.Before you begin, make sure you know the definition of surface area, radius, and circumference.
Materials:
Orange
Knife
Paper plate
Instructions
Squeeze and roll one orange around making it as spherical as possible.
Cut the orange into two equal halves (hemispheres) to reveal a great circle of the orange.
Lay the orange face down on a paper plate and trace it.
PREDICT how many great circles can be covered with the pieces of your orange peel.___________
Trace several more great circles onto the plate.
Tear off pieces of the orange peel, each about 1 square inch (or slightly smaller) in size.
Place pieces in one of the circles. Fill the circle as much as possible without overlapping the pieces.
Continue filling circles until you are out of orange peel.
Use your results to answer the following questions in complete sentences.
Write a (general) mathematical expression that tells the amount of area you covered on a single circle.Be sure to define your variables.______________________________
How many circles did you cover in all? ______ Based on this result, write a mathematical expression that tells the surface area of your orange (sphere). _________________
For the discussion post, write your derived formula for the surface area of a sphere. How did you find this?
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