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# Cones & Cylinders Math Lab

Summary: Integrate Harry Potter themes into some great geometry lessons. Designed for 6th Grade

TEACHER NOTES AND SUPPLIES
Supplies: notebook paper and examples of cones, cylinders, and nets

Supplies: chart paper, measuring tape, calculator, drawing paper, scissors, and straight-edge
Notes: Review mean, median, mode
Discuss what a prototype is
Discuss perspective (top, bottom, side)

Supplies: cans of fruit, vegetables, soda, etc. paper towel rolls,
Notes: Discuss “appropriateness”
3-D
Perspective (top, bottom, side)
Radius, diameter, circumference, lateral surface area

Supplies: paper plates, scissors, compass, protractor, calculator, tape, scales & weights, rice, and graph paper
Notes: Discuss how to find the exact middle of the paper plate.
Review how to draw angles
Review converting fractions to decimals to percents
Review x and y-axis
Review what are appropriate intervals
Review volume

Supplies: notebook paper

Supplies: notebook paper and worksheets from previous tasks
Notes: Review the parts of a friendly letter

CONES & CYLINDERS MATH LAB

You have been employed by Cook’s Chapeau & Cloak Shoppe on Diagon Alley to create prototypes for the next school year at Hogwarts. Mr. Ollivander is getting ready to retire and he has asked that you take over the store and business.
You will have several tasks to complete. You will need to create a “net” for a witch or wizard’s hat (cone), a net for a child’s size wand (cylinder), and to determine what is the best cost efficient size for a student’s cauldron.
We will gather data for hat sizes together in class, but you will need to record all of the data on your report form.

On a piece of notebook paper, write whatever “pops” into your head about CONES and CYLINDERS. Think about where you see them, how they are used, etc. Make sure to consider each shape as if it were rotated, translated, or reflected.

After you have completed your list, create a working definition of a “net”. Discuss your definition with the others at your table to see if you need to make any revisions. When you are satisfied with the definition, discuss where and why “nets” are used in a real world setting.

TASK TWO: HATS AND HAT SIZES
You will need to record your classmate’s head size (circumference in cm) from the chart paper. Next, take the raw data and organize it in order from least to greatest or greatest to least. After your have organized the data, determine what the mean, median, and mode is for the class.
Why would these statistics be needed to determine a prototype? Would you consider the mean, the median, or the mode? Why?

Birthday party hats, New Year’s Eve party hats and snow cone cups are cones without bases. DRAW the cone in three different perspectives (top, bottom, and side). If we cut a party hat and lay it flat, what shape would it be? Use a straight cut line on the cone from bottom to top. The cut that you are making will represent the slant height. The point at the top is called the apex.
Open it up and lay it flat. What do you observe? LABEL the slant height of the cone.
CALCULATE what the area of the base would be if it existed.

Labels from a soup can or a paper towel roll are cylinders without bases. Your task is to work backwards and create a “net” for a wand. Brainstorm what would be an
appropriate length and circumference for the wand so it can be easily held and still remain lightweight. Once you have created your 3-D prototype, draw the wand in three different perspectives (top, bottom, and side views). Next, open the wand and lay it flat. What shapes make up a cylinder? On your wand model, LABEL the radius and diameter of the bases. What is the circumference for each circle base? COMPUTE the lateral surface area for the wand. Explain the relationship of the circular bases to the lateral surface. Does it make a difference where the circle shapes are located on the net?

For this experiment you will need paper plates, scissors, a compass and a protractor to make various sizes of “cauldron” prototypes. The cauldron will be an inverted cone. After you have created the cones, you will be doing some calculating and measuring.
Take a paper plate and find the exact middle. What are some strategies or techniques that might be used to accomplish this task?
Draw a radius line from the midpoint to the edge of the plate. Use your protractor and draw the angle on the paper plate. Cut out the angle and save both pieces. Carefully tape one of the pie pieces on the cut lines to make a cone. Do NOT overlap edges when you are taping. This will cause a measurement error later. Tape the cone on both sides for support.
After you have made the cones, stop and complete the table.

ANGLE In degrees FRACTION OF THE CIRCLE DECIMAL FORM PERCENT FORM ANGLE In degrees FRACTION OF THE CIRCLE DECIMAL FORM PERCENT FORM
30 330
45 315
60 300
90 270
120 240
135 225
150 210
180 180
225 135
270 90

What was the circumference for the paper plate before you did any cutting?
Which cone was the most difficult to construct? Why?

MEASUREMENT
Once you are sure your cones will support weight, get a scale and gram stackers. Fill each cone with rice and record the weight in grams.

GRAPHING
A. The fraction of the circle will be the TITLE for the x-axis (horizontal). Be sure the scale is correct. Hint! Look at the denominators.
B. The volume will be the TITLE for the y-axis (vertical).
C. Should you connect the dot plots? Why or why not?
D. Make three observations based on the results of the graph.
E. In your opinion, which “cauldron” would be the most cost efficient to mass- produce for the students at Hogwarts?