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The Arizona Mathematics Partnership: Saturday 1: GeometryTed Coe, September 2014

cc-by-sa 3.0 unported unless otherwise noted1THE Rules of Engagement

Speak meaningfully what you say should carry meaning; Exhibit intellectual integrity base your conjectures on a logical foundation; dont pretend to understand when you dont; 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 Foot

DefineSquareTriangleAngleQuadrilaterals

Quadrilaterals

From http://www.healthreform.gov/reports/hiddencosts/index.html (6/3/2011)

The RED broomstick is three feet longThe YELLOW broomstick is four feet longThe GREEN broomstick is six feet long

The Broomsticks08/13/09908/13/09910

Source: http://tedcoe.com/math/wp-content/uploads/2013/10/broomsticks-for-nctm.doc

11

Source: http://tedcoe.com/math/wp-content/uploads/2013/10/broomsticks-for-nctm.doc

12Source: http://tedcoe.com/math/wp-content/uploads/2013/10/broomsticks-for-nctm.doc

08/13/091308/13/0913PerimeterWhat is it?

Is the perimeter a measurement?

or is it something we can measure?

08/13/091408/13/091408/13/0914PerimeterIs perimeter a one-dimensional, two-dimensional, or three-dimensional thing?

Does this room have a perimeter?

08/13/091508/13/0915ProgressionsProgressions: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?Measurement08/13/0918How about this?Determine the attribute you want to measureFind something else with the same attribute. Use it as the measuring unit.Compare the two: multiplicatively.Measurement08/13/091908/13/0919

So.... how do we measure circumference?Circumference2108/13/0921Tennis Balls

CircumferenceIf 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/circumference25What is an angle?Angles2608/13/0926Using objects at your table measure the angleAngles2708/13/0927

CCSS, Grade 4, p.31

How many Rotations?How many Rotations?

Measure the length of s. Choose your unit of measure carefully.Measure the angle. Choose your unit carefully.sDefine: Area34Area: Grade 3 CCSS

36What about the kite?

08/13/094008/13/0940

Area of whole square is 4r^2Area of red square is 2r^2Area of circle is08/13/094108/13/0941

http://geogebratube.org/student/m279 (cc-by-sa)

http://geogebratube.org/material/show/id/279