Transcript Day2

Math Institute
Geometry and Measurement
August 17, 2004
Exploring Triangles (naming by angle and by side)
Measuring Angles in Polygons
Informal Proof: Sum of the Angles in Polygons
Quadrilaterals
Quad Nets
Pinpointing Properties
Perimeter and Area
Bumper-Cars (constant area)
Wreck Tangles (constant perimeter)
Can a triangle be made with three sides of any
length?
a
b
c
6
8
20
20
12
10
6
18
6
8
12
18
12
14
10
20
8
8
14
8
16
6
8
6
6
12
18
Yes or No
Draw a conclusion about the lengths
of the sides of a triangle.
Angles in Polygons
Developing an Informal Proof for
the Sum of Interior Angles of Polygons
Use the geoboards to make different polygons.
Divide the polygon into triangles. Measure the
angles. Find a pattern.
Number of Sides
3
4
5
6
7
8
9
10
Number of Triangles
Sum of Interior
Angles
What can you say about the number of sides of a
polygon and the sum of its interior angles?
Perimeter and Area
Is it possible for two shapes to have the same
area but different perimeters? Explain your
answer by using words and drawings.
Is it possible for two shapes to have the same
perimeter but different areas? Explain your
answer by using words and drawings.
Can you figure out a perimeter if you know its
area? Why or why not?
Designing Bumper-Car Rides
Each tile represents one square meter. A bumper
car ride design that consists of only one square
meter would require 4 meters of bumper rail to
surround it.
How many meters of railing are needed for this
floor plan?
Begin a table for recording data.
Number of Tiles
1
2
Number of Rails
4
?
Designing Bumper-Car Rides
Begin a table for recording data.
Number of Tiles
1
2
3
4
5
Number of Rails
4
?
Designing Bumper-Car Rides
Design a bumper-car floor plan with an area of 24
square meters and a perimeter of 22 meters.
Design a bumper-car floor plan with an area of 24
square meters and many rail sections.
What is the floor plan with the most rails? With the
fewest number of rails?
Wreck-Tangles
How do areas of rectangles with equal perimeters
compare?
Complete this activity using the push pins, 30 cm
string loop, cardboard and worksheet.
Conclusion: