MATH 414 Grossmont College Circles and Angles Lesson Activity Paper

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In this assignment, you will do what all teachers do: look at the content you need to teach and come up with a lesson or an assessment (real-life application, not a test) for that content.1) Select the course/grade level that you think you’d like to teach and look at the Common Core State Standards for Mathematics which can be found here (Links to an external site.). Select one or more standards. (If you pick more than one, make sure they go together well.)2) Find or design a lesson to teach the standard(s) in an inquiry way (where students discover the rule on their own). You do not have to create this from scratch! Teachers borrow from whatever they can find on the internet along with creating their own. If you choose to use or adapt someone else’s work, just be sure to cite the source/give them credit.3) Your work will likely take one side or two sides of a page (no more!!). Be sure to include the standard that you are focused on so that I can see how well the activity/assessment relates to it

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CIRCLES AND ANGLES (CCSS. MATH. CONTENT. HSG. C.A. 2)
Write the coordinates of the points from the figure below:
A = ________________
B = ________________
C = ________________
Find the missing side of the triangle and calculate the area of the circle.
Write the coordinates of the points from the
figure below:
A = ________________
B = ________________
C = ________________
Find the missing side of the triangle and calculate
the area of the circle.
What are the differences between the two graphs above?
What are the similarities between the two graphs above?
What do the words “inscribe” and “circumscribe” mean?
Classwork: Follow the instructions. Calculate the values of the missing angles, segment, or sides.
For the figure at the left, point B is the center of the circle.
Given the information about the lengths below, find the length of ̅̅̅̅
BF.
1. EC = 12, AB = 14
2. EC = 33, AB = 19
3. FD = 3, EF = 8
4. EF = 7, FD = 4
For every value of the adjacent and opposite leg, calculate the diameter
and area of the circle.
1. YZ = 4, 𝑋𝑌 = 6
2. YZ = 10, 𝑋𝑌 = 24
3. YZ = 8, 𝑋𝑌 = 15
4. YZ = 56, 𝑋𝑌 = 33
Calculate the measurement of the arcs.
1. If angle 1 is equal to 50° and angle 2 is equal to 30°, find the lengths of
arcs AB and DC.
2. Find the lengths of arcs AD and BC.
3. Find the circumference of the circle.
CIRCLES AND SECTORS (CCSS. MATH. CONTENT. HSG. C.B. 5)
If ̅̅̅̅
OH has a length of 6 units, find the length of the following:
̅̅̅̅ = ________________
FH
̅̅̅̅
GH = ________________
̅̅̅̅
FO = ________________
̅̅̅̅
OG = ________________
Find the area of the sector formed by triangle FOH.
Find the area of circle O.
If ̅̅̅̅
AO has a length of 6 in and the area of the shaded sector is 12𝜋 in2 ,
find the length of the following:
̅̅̅̅
OC = ________________
Minor arc AC = ________________
Major arc AC = ________________
Find the measurement of the minor angle AOC.
Convert the angle from degrees to radian.
What are the differences between the two graphs above?
What are the similarities between the two graphs above?
What do the words “sector” and “radian measure” mean?
Classwork: Follow the instructions. Calculate the values of the missing angles, segment, or sides.
For the figure at the left, point E is the center of the circle.
Given the information about the lengths below, find the length of minor
arc GH.
1. GE = 6
2. GE = 13
3. HE = 10
4. HE = 3
If the triangle inscribed in a circle has a diameter of 15 cm, find the
measurement of the following:
1. ̅̅̅̅
𝑌𝑂 = ________________
2. ̅̅̅̅
𝑌𝑍 = ________________
̅̅̅̅ = ________________
3. 𝑋𝑌
4. ̅̅̅̅
𝑋𝑍 = ________________
5. The area of the circle = ________________
5. The area of the sector created by triangle XOY = ________________
6. The area of the sector created by triangle YOZ = ________________
A
The angle ABC is inscribed in circle B. The radius of the circle is r and has
an angle of θ. The length of the arc is L.
B
C
Find the area of the circular sector using the information provided.
In this assignment, you will do what all teachers do: look at the content you need to
teach and come up with a lesson or an assessment (real-life application, not a test) for
that content.
1) Select the course/grade level that you think you’d like to teach and look at the
Common Core State Standards for Mathematics which can be found here (Links to an
external site.). Select one or more standards. (If you pick more than one, make sure
they go together well.)
2) Find or design a lesson to teach the standard(s) in an inquiry way (where students
discover the rule on their own). You do not have to create this from scratch! Teachers
borrow from whatever they can find on the internet along with creating their own. If you
choose to use or adapt someone else’s work, just be sure to cite the source/give them
credit.
3) Your work will likely take one side or two sides of a page (no more!!). Be sure to
include the standard that you are focused on so that I can see how well the
activity/assessment relates to it

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