amp 2013-2014: saturday #2
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AMP 2013-2014: Saturday #2. Ted Coe, Grand Canyon University, 2013. 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. . My Summary. Ways of doing Ways of thinking - PowerPoint PPT PresentationTRANSCRIPT
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AMP 2013-2014: Saturday #2
Ted Coe, Grand Canyon University, 2013. 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.
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My Summary
●Ways of doing●Ways of thinking ●Habits of thinking
http://www.youtube.com/watch?v=ZffZvSH285c
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The RED broomstick is three feet longThe YELLOW broomstick is four feet longThe GREEN broomstick is six feet long
The Broomsticks
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PerimeterWhat is “it”?
Is the perimeter a measurement?
…or is “it” something we can measure?
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Perimeter Is perimeter a one-dimensional, two-dimensional, or three-dimensional thing?
Does this room have a perimeter?
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What do we mean when we talk about “measurement”?
Measurement
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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
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Area: Grade 3 CCSS
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X
Y
ZDraw 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”.
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Warm-up: Geometric Fractions
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Geometric Fractions
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How many Rotations?
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X
Y
ZDraw 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”.
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Area of blue square =
a
b
Area of whole (red) square =
(𝑎+𝑏)(𝑎+𝑏)b
a
Area of one green triangle =
OR
c
This means that:
𝑎2+𝑎𝑏+𝑎𝑏+𝑏2=2𝑎𝑏+𝑐2
𝑎2+2𝑎𝑏+𝑏2=2𝑎𝑏+𝑐2
𝑎2+𝑏2=𝑐2
a
a
b
b
cc
c
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http://www.cut-the-knot.org/pythagoras/
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Find the dimensions of the rectangle
Find the area of the rectangle
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Find the dimensions of the rectangle
Find the area of the rectangle
Find a rectangle somewhere in the room similar to the shaded triangle
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What do you mean when you say two figures are similar ?
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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.”
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What is a scale factor?
Teaching Geometry According to the Common Core Standards, H. Wu Revised: April 15, 2012. Grade 7 notes, p.49: