practice exam: corrections modeling fractions (on board) continue circles new topic: similarity

Practice exam: correctionsModeling fractions (on board)

Continue CIRCLES

New topic: SIMILARITY

Agenda for today

An obstacle”A measure of effort or participation during

class”Stressful (they put pressure on you)”(usually) too long”Full of confusing questions (wording is

confusing)”Just another piece of paper”No problem (if everything has been

covered and it’s not too long)”

"Tests are…

Kid Cudi – Super BooGodsmack – ToucheHillbilly NinjaInvisible String – Stopping Cars

Tunes

To find a part (arc, L)of the circumference:

Circles (continued)

To find the area ofa sector:

Circles (continued)

Find the arc spanned by the Pacific Crest Trail

Clues:17o of latitudeEarth’s diameter:

12,742 km

http://upload.wikimedia.org/wikipedia/commons/0/02/Pacific_crest_trail_route_overview.png

Circles (continued)

Find area of whole, area of a sector

Find circumference, arc length

Find radius, diameter

Apply vocabulary

FIRST, SECOND, THIRD PROBLEM SETS(from the Day Five Assignment)

Circles TASKS

http://www.youtube.com/watch?v=HEheh1BH34Q&feature=related

http://www.youtube.com/watch?v=OuC8hOC_wO0

When you see a really accurate drawing, it is a shape

similar to the original

EXAMPLES ON BOARD

Topic: Similar polygons

Discussion questionsBeef or chicken?Is there a consistent relationship between

area and its perimeter (for each polygon)?When do I call it a fraction and when a

ratio?What does proportion mean?What is the difference between a ratio and

a percent?

Similar polygons (cont'd)

If two polygons are similar…

They have the same angle sizes in the same order

ANDThey have corresponding sides whose ratios are equal

FOURTH PROBLEM SET

Similar polygons (continued)

Scale drawings have a scale that shows the ratio of the scale drawing to the real size

What is the width of the real version of this house?

Similar polygons (cont'd)

Lighthouse – how tall is the real thing if the scale of this model is 1:1200?

Elephant – how tall is the real thing if the scale of this model is 1:120?

Car – come up with the scale based on the actual length of Dodge’s 2005 Charger: 200 inches

Ship’s cannon – come up with the scale based on an actual barrel length of 5 feet

Beaver – If the actual length of Castor canadensis is 2 feet from snout to tip of tail and model length is 2 inches, what is the scale?

Quarters – when the case is open, what is the ratio of area of paper to area of quarters?

Eyeballs – if real human eyes are 1 inch in diameter, what is the scale of the chocolate eyeball model?

Green plastic design tool – draw (and furnish) a room and label the scale factor

Bicycle map – based on the map’s scale, what is the closest that the Willamette River gets to Rocky Butte (as the paper airplane flies)

More…

Triangles are similar if they…

Have the same angle sizes in the same order (AA)

Have corresponding sides whose ratios are equal (SSS)

Have two corresponding sides with the same angle between them (SAS)

Similar polygons (con't)

Draw similar polygons

Create a scale drawing

Determine whether two polygons are similar or not

FIFTH & SIXTH PROBLEM SETS

Similar polygonsTASKS

What is the relationship between the size of individual triangles’ interior angles and the sides across from them?

Discussion question