Transcript Day 2 August 17, 2004

Elementary Mathematics
Institute
August 18, 2004
Two Dimensional Shapes:
Triangles and Quadrilaterals
Day 2 Agenda
 Exploring Triangles (naming triangles 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
Can a triangle be made with three sides of any
length?
a
b
c
Yes or No
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
no
yes
no
yes
yes
no
yes
yes
no
Draw a conclusion about the lengths
of the sides of a triangle.
In a triangle the sum of the length of the two
shorter sides must be greater than the
length of the third side.
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
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
Number of Triangles
Sum of Interior
Angles
3
1
180
4
2
360
5
3
540
6
4
720
7
5
900
8
6
1080
9
7
1260
10
8
What can you say about the number of sides of
a polygon and the sum of its interior angles?
What can you say about the number of sides of a
polygon and the sum of its interior angles?
The sum of all the angles in a polygon is equal to the
number of sides minus two times 180 degrees.
S = (n-2)(180)
S=sum of angles in a polygon; n=number of angles
This works because we know that the sum of all the
angles in any triangle equals 180° and we found out when
we drew them that there are two less triangles than the
number of sides in the polygon.
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: