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AMP 2012: Week1 : Part1. Ted Coe, Scottsdale Community College, 2012. Some materials were also created or refined as part of the development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project. .
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AMP 2012: Week1 : Part1 Ted Coe, Scottsdale Community College, 2012. Some materials were also created or refined as part of the development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project.
Speak meaningfully — what you say should carry meaning; • Exhibit intellectual integrity — base your conjectures on a logical foundation; don’t pretend to understand when you don’t; • Strive to make sense — persist in making sense of problems and your colleagues’ thinking. • Respect the learning process of your colleagues — allow them the opportunity to think, reflect and construct. When assisting your colleagues, pose questions to better understand their constructed meanings. We ask that you refrain from simply telling your colleagues how to do a particular task. • Marilyn Carlson, Arizona State University The Rules of Engagement:
Square Triangle Angle Define
A square is a rectangle. True or False?
From http://www.healthreform.gov/reports/hiddencosts/index.html (6/3/2011)
The Broomsticks The RED broomstick is three feet long The YELLOW broomstick is four feet long The GREEN broomstick is six feet long
The Willis tower (formerly the Sears tower) is 1730 feet high. The Burj Khalifa (formerly Burj Dubai) is 2717 feet high. The Burj is ______________ times as large as the Willis tower. The Willis tower is _____________times as large as the Burj The Burj is _____________ percent the size of the Willis tower. The Willis tower is _____________ percent the size of the Burj.
What is “it”? Is the perimeter a measurement? …or is “it” something we can measure? Perimeter
Is perimeter a one-dimensional, two-dimensional, or three-dimensional thing? • Does this room have a perimeter? Perimeter
From the AZ STD's (2008) • Perimeter: the sum of all lengths of a polygon. • Discuss Perimeter
What do we mean when we talk about “measurement”? Measurement
“Technically, a measurement is a number that indicates a comparison between the attribute of an object being measured and the same attribute of a given unit of measure.” • Van de Walle (2001) • But what does he mean by “comparison”? Measurement
How about this? • Determine the attribute you want to measure • Find something else with the same attribute. Use it as the measuring unit. • Compare the two: multiplicatively. Measurement
From the AZ STD's (2008) the total distance around a closed curve like a circle Circumference
So.... how do we measure circumference? Circumference
The circumference is about how many times as large as the diameter? • The diameter is about how many times as large as the circumference?
If I double the RADIUS of a circle what happens to the circumference? Circumference
What attribute are we measuring when we measure angles? Angles
Reflection • How is measurement an application of multiplicative thinking? • How does this apply to angles?
Area has been defined* as the following: • “a two dimensional space measured by the number of non-overlapping unit squares or parts of unit squares that can fit into the space” • Discuss... • *State of Arizona 2008 Standards Glossary
Area of whole square is 4r^2 Area of red square is 2r^2 Area of circle is…
Are of whole square is 4r^2 Area of red square is 2r^2 Area of circle is…
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