Transcript The Arizona Mathematics Partnership: Saturday 1: Geometry Ted Coe, September 2014 cc-by-sa 3.0 unported unless otherwise noted.

The Arizona Mathematics
Partnership:
Saturday 1: Geometry
Ted Coe, September 2014
cc-by-sa 3.0 unported unless otherwise noted
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
The Foot
Square
Triangle
Angle
Define
Quadrilaterals
Quadrilaterals
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
What is “it”?
Is the perimeter a measurement?
…or is “it” something we can measure?
Perimeter
Is perimeter a one-dimensional, twodimensional, or three-dimensional
thing?
Does this room have a perimeter?
Perimeter
Progressions
Progressions:
http://ime.math.arizona.edu/progressions/
http://commoncoretools.files.wordpress.com/2012/07/ccss_progression_gm_k5
_2012_07_21.pdf p.16.
From the CCSS, Grade 3:
What do we mean when we talk about
“measurement”?
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
•So.... how do we measure circumference?
Circumference
Tennis Balls
Circumference
If I double the RADIUS of a circle what
happens to the circumference?
The circumference is three and a bit times as large as the diameter.
http://tedcoe.com/math/circumference
•What is an angle?
Angles
•Using objects at your table measure the angle
Angles
CCSS, Grade 4, p.31
How many Rotations?
How many Rotations?
s
Measure the length of s. Choose your unit of measure carefully.
Measure the angle. Choose your unit carefully.
Define: Area
Area: Grade 3 CCSS
What about the kite?
Area of whole
square is 4r^2
Area of red square
is 2r^2
Area of circle is…
http://geogebratube.org/material/show/id/279
http://geogebratube.org/student/m279 (cc-by-sa)