amp 2012: week1 : part1
DESCRIPTION
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. . - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/1.jpg)
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.
*AMP 2012: Week1 : Part1
![Page 2: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/2.jpg)
*The Rules of Engagement:
*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
![Page 3: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/3.jpg)
*Define
SquareTriangleAngle
![Page 4: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/4.jpg)
*True or False?
A square is a rectangle.
![Page 5: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/5.jpg)
![Page 6: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/6.jpg)
*Quadrilaterals
![Page 7: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/7.jpg)
*Quadrilaterals
![Page 8: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/8.jpg)
*Quadrilaterals
![Page 9: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/9.jpg)
From http://www.healthreform.gov/reports/hiddencosts/index.html (6/3/2011)
![Page 10: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/10.jpg)
The Broomsticks
![Page 11: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/11.jpg)
The RED broomstick is three feet longThe YELLOW broomstick is four feet longThe GREEN broomstick is six feet long
The Broomsticks
![Page 12: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/12.jpg)
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 BurjThe Burj is _____________ percent the size of the Willis tower.The Willis tower is _____________ percent the size of the Burj.
![Page 13: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/13.jpg)
*Perimeter
What is “it”?
Is the perimeter a measurement?
…or is “it” something we can measure?
![Page 14: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/14.jpg)
*Perimeter
*Is perimeter a one-dimensional, two-dimensional, or three-dimensional thing?
*Does this room have a perimeter?
![Page 15: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/15.jpg)
![Page 16: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/16.jpg)
![Page 17: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/17.jpg)
From the AZ STD's (2008)
*Perimeter
*Perimeter: the sum of all lengths of a polygon.
*Discuss
![Page 18: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/18.jpg)
From the CCSS:
![Page 19: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/19.jpg)
What do we mean when we talk about “measurement”?
*Measurement
![Page 20: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/20.jpg)
•“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
![Page 21: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/21.jpg)
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
![Page 22: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/22.jpg)
![Page 23: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/23.jpg)
*Continuing to circles...
![Page 24: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/24.jpg)
*What is a circle?
![Page 25: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/25.jpg)
*What is circumference?
![Page 26: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/26.jpg)
From the AZ STD's (2008)
the total distance around a closed curve like a circle
*Circumference
![Page 27: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/27.jpg)
•So.... how do we measure circumference?
*Circumference
![Page 28: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/28.jpg)
*Tennis Balls
![Page 29: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/29.jpg)
The circumference is about how many times as large as the diameter?
The diameter is about how many times as large as the circumference?
![Page 30: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/30.jpg)
*Circumference
*If I double the RADIUS of a circle what happens to the circumference?
![Page 31: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/31.jpg)
•Using objects at your table measure the angle
*Angles
![Page 32: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/32.jpg)
•What attribute are we measuring when we measure angles?
*Angles
![Page 33: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/33.jpg)
![Page 34: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/34.jpg)
What is the length of “d”? You may choose the unit.
![Page 35: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/35.jpg)
What is the measure of the angle? You may choose the unit.
![Page 36: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/36.jpg)
Reflection
•How is measurement an application of multiplicative thinking?
•How does this apply to angles?
![Page 37: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/37.jpg)
*How many Rotations?
![Page 38: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/38.jpg)
Define: Area
![Page 39: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/39.jpg)
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
![Page 40: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/40.jpg)
![Page 41: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/41.jpg)
*What about the kite?
![Page 42: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/42.jpg)
![Page 43: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/43.jpg)
Area of whole square is 4r^2Area of red square is 2r^2
Area of circle is…
![Page 44: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/44.jpg)
Are of whole square is 4r^2Area of red square is 2r^2
Area of circle is…
![Page 45: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/45.jpg)
![Page 46: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/46.jpg)
![Page 47: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/47.jpg)
*Pizza
• $10 for 14” large• $12 for 16” x-large• Papa John's claim: 30%
more!
![Page 48: AMP 2012: Week1 : Part1](https://reader033.vdocuments.mx/reader033/viewer/2022061510/56815eee550346895dcdabbf/html5/thumbnails/48.jpg)
*Geometric Fractions