standard_description: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
problem_activity: Problem 1
The data table below shows the weight of a typical male greyhound, a breed of dog, during the first 28 months of his life. Graph the corresponding points, then connect the points in the order they are given to form a line graph.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:30%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Age (in months)"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Weight (in pounds)"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "30"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "8"}, {"_attributes": {"style": "text-align:center"}, "_value": "55"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "12"}, {"_attributes": {"style": "text-align:center"}, "_value": "66"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "16"}, {"_attributes": {"style": "text-align:center"}, "_value": "69"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "20"}, {"_attributes": {"style": "text-align:center"}, "_value": "72"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "24"}, {"_attributes": {"style": "text-align:center"}, "_value": "72"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "28"}, {"_attributes": {"style": "text-align:center"}, "_value": "72"}]}]}]}]}
What do you notice? What do you wonder?
Problem 2
Using the information about a typical male greyhound’s weight from Anchor Task #1, answer the following questions.
How much does a typical male greyhound weigh when he is born?
What does the coordinate pair (12, 66) mean in the context of this graph?
How much weight does the typical male greyhound gain in the first 4 months of his life? How do you know? What about between 4 months and 8 months? How do you know?
How long does it take the typical male greyhound to grow from 55 to 72 pounds?
Challenge: When does the typical male greyhound gain weight the fastest? How do you know? What about the slowest?
Problem 3
Using the information about the typical male greyhound’s weight from Anchor Task #1, answer the following questions.
How heavy do you think a typical male greyhound gets? How do you know from the graph?
At what age do male greyhounds reach their full weight? Why?
How heavy do you think a typical female greyhound gets? Why?


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