Type
of Class: Honors Geometry
Related VA SOL: G.10
Time
Frame: 90minute
block period
Objectives:
·
Students will investigate the
lengths of chords, tangents and secants and their relationships.
·
Students will be able to find the
area of a sector.
·
Students will be able to find the
length of an arc.
·
Students will investigate
applications of architecture, art, and construction using the properties of
chords, tangents, and secants.
Materials:
·
Geometer’s Sketchpad 4.0
·
lengthseg.gsp
·
Large pizza with 14 inch diameter
·
Small pizza with 10 inch diameter
·
Worksheet
Procedures:
1.
Explore the segment lengths on worksheet
#3.
Length of Chords and
Secants:
Lengths of Tangents and Secants:
2.
Give algebraic examples using the theorems above. For instance:
3.
Teacher will bring in two whole pizzas. The small pizza will have a
diameter of 10 inches and the large pizza will have a diameter of 14 inches.
Students will find the area of a sector. (Hint: Area of slice = 1/8 * area of
pizza)
Area of a Sector:
If x represents the measure of the arc of a sector and r is the
radius of the circle, then
Area of the sector = x/360
* π r ^{2}
4.
Give examples using the formula of the area of a sector. For instance:
5.
Students will find the length of arc.
Length of an Arc: If x represents the measure of an arc and r is the radius
of the circle, then
Length of the arc = x/360 * 2 π r.
6.
Give examples using the formula of the length of an arc. For instance:
Find the length of the minor
arc EF.
7.
Students will work on the last two real world application problems on the
worksheet.
Assessment:
Students should be tested on the conjectures or
theorems that they made during the lab and pizza activities. For further
assessment, let students explore and find the relationship between the four
theorems and prove why they are true. Create more handson activities on finding the area of a sector or an arc length.
Suggestions/Comments (if applicable):
The lesson can be used in other levels of
Geometry. Give more algebra problems like the one above so that students will
have more practice. Instead of a pizza activity, you can have three or four
students bake cakes of different sizes.
