Ted Coe, Scottsdale Community College, 2012. Some materials were also created or refined as part of the development of the “Math 5: Geometry” curriculum.

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Presentation transcript:

Ted Coe, Scottsdale Community College, 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 Plot...

Square Triangle Angle

The Broomsticks

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

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.

* Is perimeter a one- dimensional, two-dimensional, or three-dimensional thing? * Does this room have a perimeter?

What do we mean when we talk about “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.

The circumference is about how many times as large as the diameter? The diameter is about how many times as large as the circumference?

Using objects at your table measure the angle

What is the length of “d”? You may choose the unit.

Define: Area

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…

$10 for 14” large $12 for 16” x-large Papa John's claim: 30% more!

 Cut out a right triangle from a 3x5 card – try to make sure that one leg is noticeably larger than the other.  What strategies could you use to create this? ab c

Lay down your triangle on construction paper. Draw squares off each of the three sides. Estimate the areas of these squares.

X Y Z Draw the following parallel and perpendicular lines: X: Along the right side of the hypotenuse’s square Y: Perpendicular to line “X” passing through the corner of the opposite square Z: Perpendicular to line “Y” passing through the intersection of the square and line “Y”.

 If the Pythagorean Theorem is true AND  If you have constructed and cut correctly THEN  You should be able to show that the sum of the area of the smaller squares equals the area of the larger square.

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