Download Assignment 1 Lesson Plan - Overview EDU 506

Jenni Harmon
Mathematics: Geometry
North Rose Wolcott High School
Circles: Inscribed Angles
Mathematical Task: After this lesson students should know the definition of inscribed
angles and intercepted arcs. They should know and be able to apply the inscribed angle
theorem. They should also know and be able to apply the inscribed angle corollary which
says that if inscribed angles of a circle intercept the same arc then they are congruent.
Students should also know and be able to apply the theorem that says an inscribed angle
subtends a semicircle if and only if the angle is a right angle. Students should know and
be able to apply the theorem that says if a quadrilateral is inscribed in a circle then its
opposite angles are supplementary.
Grade Level, Approximate Number of Students, Types of Students: This lesson will
be taught to two geometry classes. There are about 20 students in each class. The
students are all high school students from grades 9th – 12th.
Materials and Sources:
 Smartboard
 Geometers sketchpad
 Textbook: Holt Geometry
 Resource Book: Holt Geometry
 Rulers
 Pencils
 Vocabulary Worksheet
 In Class Practice Worksheet
 Homework: Worksheet (“Inscribed Angles”)
Duration: 75 minutes
NYS Mathematics Performance Indicator(s):
Content Strand:
 G.G.27 Write a proof arguing from a given hypothesis to a given conclusion
 G.G.51 Investigate, justify, and apply theorems about the arcs determined by the
rays of angles formed by two lines intersecting a circle
Process Strand:
 G.PS.1 Use a variety of problem solving strategies to understand new
mathematical content
 G.PS.2 Observe and explain patterns to formulate generalizations and conjectures
 G.CM.5 Communicate logical arguments clearly, showing why a result makes
sense and why the reasoning is valid
 G.CN.4 Understand how concepts, procedures, and mathematical results in one
area of mathematics can be used to solve problems in other areas of mathematics
Performance Objectives:
 Students should know the definition of inscribed angles and intercepted arcs
 Students should know and be able to apply the inscribed angle theorem

Students should know and be able to apply the inscribed angle corollary which
says that if inscribed angles of a circle intercept the same arc then they are
congruent.
 Students should know and be able to apply the theorem that says an inscribed
angle subtends a semicircle if and only if the angle is a right angle.
 Students should know and be able to apply the theorem that says if a quadrilateral
is inscribed in a circle then its opposite angles are supplementary.
Part of Lesson
Teacher and Student Actions Mathematical Questions.
These can repeat for
different parts of the lesson
if appropriate. Include both
lower order and higher
order questions for each
lesson.
Launch/Anticipatory
The lesson will start with a
What different types of
Set/Before
State prior knowledge
brief review of the previous
angles is there that are
needed, then explain how lesson on sector area and arc
related to circles?
you will access prior
length. The teacher will use
knowledge and draw the this time to go over any
students into this
questions on the previous
particular lesson.
class’s homework.
Also explain how you
will launch the
“problem” the students
will solve during the
explore. Some problems
need more extensive
launches than others.
Explore/During
Describe what the teacher
will do and how the
students will be engaged
in the lesson/activity.
Students will also be asked to
identify as many different
types of angles they can in
relation to circles.
The teacher will hand out the
vocabulary/theorems/examples
worksheet. The teacher will
go over the first two
vocabulary definitions of
inscribed angles and
intercepted arcs while showing
the students examples on the
given diagrams.
The teacher will then go over
the inscribed angle theorem.
The students will then be
asked to apply this theorem to
example one.
Does the angle measure
change if one side of an
inscribed angle passes
through the center of the
circle? Why or why not?
Do you think the inscribed
angle corollary applies to
angles that are not inscribed
in a circle? Why or why
not?
Then the teacher will go over
the inscribed angle corollary
which says that if inscribed
angles of a circle intercept the
same arc then they are
congruent. Students will then
be asked to apply this
corollary to examples two.
The teacher will then go over
the inscribed angle and
semicircle theorem and have
the students apply that
theorem to example three.
The last theorem that the
teacher will go over is the
inscribed quadrilateral
theorem. This theorem will
correlate with example four.
The teacher will then hand out
the in class practice worksheet
which requires the students to
apply all of the theorems
learned in class. The teacher
will have the students work on
this practice as pairs while
he/she walks around asking
any questions and making sure
the students are on task. The
teacher will go over each of
the problems as a class before
the students move on to a new
problem.
Summary/Closure/After The lesson will be summarized
Describe how you will
by going over each of the in
summarize the lesson.
class practice problems. These
This is a most important
will give students practice
part of a problem solving apply all of the theorems and
lesson where the students corollaries learned in the
share their strategies.
lesson.
The teacher should
facilitate the discussion
and the students should
be actively engaged.
When given a diagram of a
circle with an inscribed
angle, how do you know if
the inscribed angle subtends
a semicircle?
Can you assume any
relationship between the
adjacent angles of an
inscribed quadrilateral?
Why or why not?
How can you check if the
four angle measurements of
a quadrilateral are
reasonable answers?
Assessment
Clearly describe how the
teacher will know if the
students met the
objective. Assessment
should be embedded
within the activities. The
assessment may include a
separate independent
component.
Modifications for
Advanced Learners
Modifications for two
types of disabilitiesstate the name of the
disability here. You
may include a
modification for ELL.
Students will be assessed by
how well they do on the
examples and in class practice
problems and how well they
participate. The teacher will be
walking around the room
checking the students’
progress. The students will
also be assessed on how well
they do on the homework.
There are several more
challenging problems on the
homework that all of the
students will be required to
try. The homework will not
be graded for accuracy.
Students who have trouble
seeing or hearing will be given
a copy of the notes. The notes
will also be placed on the
Smartboard so they are easier
to see and read.
For ELL students, they will be
given a copy of the notes in
both the English language and
their native language. They
will be asked to follow along
so that they are hearing the
notes in English but can read
them in their native language.
This will help them make a
better connection between
their language and the English
language.