The Arizona Mathematics Partnership: Saturday 3: Geometry Ted Coe, January 31, 2015 cc-by-sa 4.0 unported unless otherwise noted

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

Define Square Triangle Angle

Quadrilaterals

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

Perimeter What is “it”? Is the perimeter a measurement? …or is “it” something we can measure?

What do we mean when we talk about “measurement”? Measurement

Using objects at your table measure the angle Angles

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

Warm-up: Geometric Fractions

See: A. Bogomolny, Pythagorean Theorem and its many proofs from Interactive Mathematics Miscellany and Puzzles Accessed 12 September

Is this a proof?

a b Area of whole (red) square = b a OR c This means that: a a b b c c c

Indiana (1896) House Bill 296, Section 2: “…that the ratio of the diameter and circumference is as five-fourths to four;” What is the mathematical value they are proposing for Pi? From

 Find the dimensions of the rectangle  Find the area of the rectangle  Find a rectangle somewhere in the room similar to the shaded triangle

 When we say two figures are similar we mean… Answer on your own. Share.

What is a scale factor? Teaching Geometry According to the Common Core Standards, H. Wu Revised: April 15, Grade 7 notes, p.49:

Working with similar figures “Similar means same shape different size.” “All rectangles are the same shape. They are all rectangles!” “Therefore all rectangles are similar.”

CCSS: Grade 2 (p.17)

CCSS: Grade 7 (p.46)

From the Progressions ime.math.arizona.edu/progressions

CCSS: Grade 8 (p.56)

Teaching Geometry According in Grade 8 and High School According to the Common Core Standards, H. Wu Revised: October 16, 2013, p.45

CCSS: Grade 8 (p.54)

From the progressions documents Source: p.5http://commoncoretools.me/wp-content/uploads/2013/07/ccss_progression_functions_2013_07_02.pdf

CCSS: HS Geometry (p.74)

CCSS: Grade 8 (p.56)

CCSS: HS Geometry (p.77)

Pythagorean Theorem?