AMP 2013-2014: Saturday #2

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 ●Habits of thinking

http://www.youtube.com/watch?v=ZffZvSH285c

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

The Broomsticks

PerimeterWhat is “it”?

Is the perimeter a measurement?

…or is “it” something we can measure?

Perimeter 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”?

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

Area: Grade 3 CCSS

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”.

Warm-up: Geometric Fractions

Geometric Fractions

How many Rotations?

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”.

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

http://www.cut-the-knot.org/pythagoras/

Find the dimensions of the rectangle

Find the area of the rectangle

Find the dimensions of the rectangle

Find the area of the rectangle

Find a rectangle somewhere in the room similar to the shaded triangle

Or not…

http://goldenratiomyth.weebly.com/

What do you mean when you say two figures are similar ?

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.”

What is a scale factor?

Teaching Geometry According to the Common Core Standards, H. Wu Revised: April 15, 2012. Grade 7 notes, p.49: