AMP 2012-2013: Saturday #3

AMP 2012-2013: Saturday #3

Ted Coe, Scottsdale Community College, 2012. 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.

The Rules of Engagement

• Speak meaningfully• Exhibit intellectual integrity • Strive to make sense • Respect the learning process of your colleagues

• Marilyn Carlson, Arizona State University

The Plot...

The Broomsticks

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

The Broomsticks

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

•Using objects at your table measure the angle

Angles

Define: Area

Area of whole square is 4r^2Area of red square is 2r^2

Area of circle is…

𝑎2+𝑏2=𝑐2

Image from wikipedia. cc-sa

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

Speaking of areas…

• Is “Area” a measure?

• Or is it an attribute to be measured?

Find the dimensions of the rectangle

Find the area of the rectangle

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

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.”

Two figures are similar if…

Scale Factors23

What is a scale factor?

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

CCSS: Grade 2 (p.17)

CCSS: Grade 7 (p.46)

CCSS: Grade 7 (p.46)

CCSS: Grade 8 (p.52)

CCSS: Grade 8 (p.54)

CCSS: Grade 8 (p.56)

CCSS: HS Geometry (p.74)

CCSS: HS Geometry (p.74)

CCSS: HS Geometry (p.74)

CCSS: Grade 8 (p.56)

CCSS: HS Geometry (p.77)

• Pythagorean Theorem?

Everything is better in 3D!

Volume

• What is volume?

• What do students find challenging about understanding volume?