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
Shade in the grids to represent the following fractions:
{"table": [{"_attributes": {"class": ["table"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "a.", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${30\\over 100}$$"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "b.", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${3 \\over100}$$"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "c.", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${{1\\over3}\\over 100}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png", "style": "height:207px; width:184px"}}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png", "style": "height:207px; width:184px"}}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png", "style": "height:207px; width:184px"}}]}]}]}]}]}
Problem 2
Fill in the chart below to represent equivalent fractions, decimals, and percentages.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:Fixed; width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Fraction"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Decimal"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Percent"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{4}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "0.5"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "20%"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{3}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "0.05"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{3}{8}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "1.3"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{2}$$"}], "_value": "%"}]}]}]}]}
Problem 3
Use mental math to answer the questions below.
a.
What is 50% of 20?
What is 25% of 48?
What is 10% of 125?
What is 5% of 50?
b.
6 is 50% of what number?
10 is 25% of what number?
9 is 10% of what number?
c.
21 is what percent of 210?
450 is what percent of 900?
20 is what percent of 80?
30 is what percent of 20?


aligns: no