# Complete Middle Grade Mathematics Discussion

I’m studying and need help with a Mathematics question to help me learn.

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.

• 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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