GEOMETRY CONTENT ACADEMY
Circles
SOL G.11, G.12
January 29, 2015
REPORTING CATEGORY: POLYGONS, CIRCLES, AND
THREE-DIMENSIONAL FIGURES
2011-12
2012-13
2013-14
PACING
CURRICULUM FRAMEWORK – G.11
HENRICO CURRICULUM GUIDE
http://teachers.henrico.k12.va.us/math/Teacher/Downloads/CurriculumGuides/GeomCurriculumGuide.pdf
2014 SPBQ DATA – G.11
PERFORMANCE ANALYSIS COMPARISON
SOL G.11
2012
The student will use angles, arcs, chords, tangents, and secants to
a) investigate, verify, and apply properties of circles;
b) solve real-world problems involving properties of circles; and
c) find arc lengths and areas of sectors in circles.
2013
Finding Arc Lengths and Areas of Sectors
The student will use angles, arcs, chords, tangents, and secants to
a) investigate, verify, and apply properties of circles;
b) solve real-world problems involving properties of circles; and
c) find arc lengths and areas of sectors in circles.
2014
Finding Arc Lengths and Measures of Chords, Tangents, and Secants
The student will use angles, arcs, chords, tangents, and secants to
a) investigate, verify, and apply properties of circles;
b) solve real-world problems involving properties of circles; and
c) find arc lengths and areas of sectors in circles.
2012 - SUGGESTED PRACTICE FOR SOL G.11
Students need additional practice using a measure of one part of the circle to find
measures of other parts of the circle.
Given: Circle M with secants AB and AC
m ∠ A = 30°
If the length of arc BC is 3 cm, what is the circumference of the circle?
18 cm
Common Errors? Misconceptions?
2012 - SUGGESTED PRACTICE FOR SOL G.11
Find arc lengths and areas of sectors in circles.
Bob divides his circular garden into 10 congruent sectors to plant different types of flowers.
The circumference of Bob’s garden is 50.5 feet. What is the area of one sector of Bob’s
garden?
1.
2.
3.
4.
Draw a figure.
Find diameter or radius.
Find the area.
Find the area of one sector.
Approximately 20.3 sq ft
Common Errors? Misconceptions?
2013 - SUGGESTED PRACTICE FOR SOL G.11
Students need additional practice finding the area of a sector or arc length when given the
radius or diameter and a central angle of a circle.
Find the area of the shaded sector of Circle Q.
33.5 cm²
Find the length of arc AB.
8.4 cm
Common Errors? Misconceptions?
2014 - SUGGESTED PRACTICE FOR SOL G.11
Students need additional practice solving real-world problems involving chords.
This figure represents a design for a stained glass window.
The window is divided by chords MN and ST.
1. What is the value of x?
9
2. What is the length of ST ?
(9 – 4) + 8
13
Common Errors? Misconceptions?
2014 - SUGGESTED PRACTICE FOR SOL G.11
Students need additional practice solving real-world problems using properties of circles.
Circle M represents a circular race track. The radius of this race track is 120 feet. Juan will
start at point A and run in a clockwise direction to point B. Angle AMB measures 55°.
Which is closest to the number of feet Juan will run from point A to point B?
A. 55 ft
B. 58 ft
Circumference of the circle
𝟓𝟓
C. 115 ft
𝟕𝟓𝟒 ≈ 𝟏𝟏𝟓. 𝟐 ft
754 ft
𝟑𝟔𝟎
D. 120 ft
Common Errors? Misconceptions?
CURRICULUM FRAMEWORK – G.12
HENRICO CURRICULUM GUIDE
http://teachers.henrico.k12.va.us/math/Teacher/Downloads/CurriculumGuides/GeomCurriculumGuide.pdf
2014 SPBQ DATA – G.12
PERFORMANCE ANALYSIS COMPARISON
SOL G.12
2012
Students need additional practice using the equation of a circle to identify the radius, diameter, center, and/or a point on the circle.
The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle.
• the coordinates of the center;
• the length of a radius;
• coordinate endpoints of a radius;
• the length of a diameter;
• coordinate endpoints of a diameter;
• the coordinates of a point on the circle; and/or
• the equation of a circle.
2013
The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle.
Students should have experiences that require them to determine any of the following from given information:
• the coordinates of a point on the circle;
2014
The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle.
Students should have experiences that require them to determine any of the following from given information:
• the coordinates of a point on the circle; and/or
• the equation of a circle.
2012 - SUGGESTED PRACTICE FOR SOL G.12
Students need additional practice using the equation of a circle to identify the radius,
diameter, center, and/or a point on the circle.
The coordinates of the center of a circle are (-2, 6). This circle has a diameter of 10 units.
a) What is the equation of the circle?
(𝒙 + 𝟐)𝟐 + (𝒚 − 𝟔)𝟐 = 𝟐𝟓
b) Give the integral coordinates of two points that lie on the circle.
Possible points: (-2, 1), (-2, 11), (-7, 6), (3, 6)
Common Errors? Misconceptions?
2012 - SUGGESTED PRACTICE FOR SOL G.12
Students need additional practice using the equation of a circle to identify the radius,
diameter, center, and/or a point on the circle.
The equation of a circle is (x - 3)² + (y + 4)² = 16.
a) What are the coordinates of the center of the circle?
(3, -4)
b) What is the radius of the circle?
4
c)
What is the diameter of the circle?
8
d) Give the integral coordinates of two points that lie on the circle.
Possible points: (-1,-4) (7,-4) (3,-8) (3,0)
Common Errors? Misconceptions?
2013 - SUGGESTED PRACTICE FOR SOL G.12
Students need additional practice identifying the coordinates of points that lie on a circle
when given sufficient information to write the equation of the circle.
A circle has a center at (-1, 4) and a diameter of 20.
Select each pair of coordinates that represent a point on this circle.
(-7, -4)
(11, 20)
(19, 16)
(5, 12)
(-9, -2)
(-1, 4)
Common Errors? Misconceptions?
2014 - SUGGESTED PRACTICE FOR SOL G.12
Students need additional practice determining the equation of a circle when several steps
are necessary.
Write the equation of a circle, in standard form, that has a diameter with endpoints at (-4, 3)
and (0, -5).
First, find the midpoint of the
diameter which is the center of
the circle.
Next, find the length of the
radius using the center and one
of the points on the circle.
Common Errors? Misconceptions?
2014 - SUGGESTED PRACTICE FOR SOL G.12
Students need additional practice determining points that lie on a circle when given the
equation or enough information to find the equation.
Which of these points lie on the circle represented by this equation?
Select each pair of coordinates that represent a point on this circle.
(-4, 3)
(-6, 3)
(4, -3)
(4, 7)
(10, 5)
Common Errors? Misconceptions?
FORMULAS
Examine the Pacing Guide
again.
What formulas do students
need to know related to Circles
(SOL G.11 and G.12)?
What formulas are provided
on the formula sheet related to
Circles?
INSTRUCTIONAL RESOURCES
HCPS Math Website – G.11
http://teachers.henrico.k12.va.us/math/HCPSgeo/G-11.html
Instructional Highlights:
1. G.11a – VDOE Enhanced Scope and Sequence - VDOE ESS Activity Sheet 1: Problem Solving with Circles (pdf)
2. G.11a - JMU Pivotal Items - JMU Pivotal Question: Properties of Circles (doc)
3. G.11c – VDOE Enhanced Scope and Sequence - VDOE ESS Activity Sheet 2: Cake Problem (pdf)
4. G.11c – JMU Pivotal Items – JMU Pivotal Question: Arc Lengths (doc)
INSTRUCTIONAL RESOURCES
HCPS Math Website – G.12
http://teachers.henrico.k12.va.us/math/HCPSgeo/G-12.html
Instructional Highlights:
1. VDOE Enhanced Scope and Sequence - VDOE ESS Lesson: Circles in the Coordinate Plane - Polygons and
Circles (PDF)
2. JMU Pivotal Question: Circles (doc)
3. Explore Learning Circles
4. TI-84 Plus C Silver Edition Guidebook - Texas Instruments (pdf)
5. TI-84 Instructions for Graphing Circles Algebraically - Video
RESOURCES
1. ExamView Banks
2. NextLesson.org
Teaching Strategies
Student Engagement?
Activities?
Listen to audio and misconceptions…