Download 12b Geometry BM3

Lesson Design
Subject Area:
Geometry
Grade Level:
9 – 12
Benchmark Period
BM 3
Duration of Lesson: 2 days
Standard(s): Find and use measures of sides and interior and exterior angles of polygons to classify figures and
solve problems (12b)
Learning Objective:
Using theorems about the interior and exterior angles of convex polygons to solve problems.
Use Polygon Interior Angles Theorem and Polygon Exterior Angles Theorem.
Big Ideas involved in the lesson:
Using angle relationships in polygons, using properties of parallelogram, and classifying quadrilaterals by their
properties.
As a result of this lesson students will:
Know:
Vocabulary:
Diagonal, interior and exterior angles, polygon, vertices, consectutive and non-consecutive vertices,
convex, concave, parallelogram, rhombus, rectangle, square, trapezoid, kite, congruent, and opposite
angles.
Understand:
Polygon Interior Angles Theorem
Interior Angles of a Quadrilateral
Polygon Exterior Angles Theorem
Classifying polygons
Be Able To Do:
Solve problems and classify polygons using measures of sides and interior and exterior angles.
Assessments:
Formative: Observation, quiz,
CFU Questions:
What will be evidence of student ABWA
1. What is the sum of the measure
knowledge, understanding &
of the interior angles of a convex
ability?
Summative: CST & Benchmark
pentagon and hexagon? According
Given a regular n-gon, draw
(DWA)
to the pattern, what is the measure
diagonals, classify the triangles
of the interior angles of a convex
by their sides and angles, and
heptagon?
find the measure of the interior
and exterior angles.
Lesson Plan
Anticipatory Set:
T. creates set of index cards with the following figures on them (10). Have
a. T. focuses students
students work in groups of four. Each group is given a whiteboard and
b. T. states objectives
separates into polygons and non-polygons. Ask students to sort figures into
c. T. establishes purpose of
polygons or non-polygons and explain their grouping of the figures.
the lesson
d. T. activates prior knowledge
Together as a whole class, write the definition of a polygon.
Polygon: It is formed by three or more segments called sides, such that no
two sides with a common endpoint are collinear. Each side intersects exactly
two other sides, one at each endpoint.
1
Geometry 12b Lesson Plan
Lesson Design
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
7.
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide exs.
 Model
b. Check for Understanding
 Pose key questions
 Ask students to explain
concepts, definitions,
attributes in their own words
 Have students
discriminate between
examples and nonexamples
 Encourage students
generate their own
examples
 Use participation
8.
9.
10.
11.
12.
T. States:
You have already learned that the name of a polygon depends on the number
of sides in the polygon. You also already learned to find the sum of the
measures of the interior angles of quadrilaterals by dividing quadrilateral into
triangles. You will use the triangle method to find the sum of the measures of
the interior angles of any convex polygon with n-sides, called n-gon.
Investigate Angle Sums in Polygons (Investigate AngleSum.doc)
CFU: What is the sum of the measure of the interior angles of a convex
pentagon and hexagon? According to the pattern, what is the measure of the
interior angles of a convex heptagon?
T. states: Polygon Interior Angles Theorem – The sum of the measures of
the interior angles of a convex n-gon is (n-2)180°.
The measure of each interior angle of a regular polygon is
(n  2) 180
n
T. models how to solve problem 11 step-by-step along w/students at the same
time. Have students work in pairs, and complete problems 12 – 13.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
T. states: Polygon Exterior Angles Theorem – The sum of the measures of
the exterior angles of a convex polygon, one at each vertex, is 360°.
360
The measure of each exterior angle of a regular polygon is
.
n
T. models how to solve problem 11 step-by-step along w/students at the same
time. Have students work in pairs, and complete problems 12 – 16.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
2
Geometry 12b Lesson Plan
Lesson Design
Guided Practice:
a. Initiate practice activities
under direct teacher
supervision – T. works
problem step-by-step along
w/students at the same time
b. Elicit overt responses from
students that demonstrate
behavior in objectives
c. T. slowly releases student to
do more work on their own
(semi-independent)
d. Check for understanding
that students were correct at
each step
e. Provide specific knowledge
of results
f. Provide close monitoring
What opportunities will students
have to read, write, listen &
speak about mathematics?
Closure:
a. Students prove that they
know how to do the work
b. T. verifies that students can
describe the what and why
of the work
c. Have each student perform
behavior
Independent Practice:
a. Have students continue to
practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
Resources: materials needed
to complete the lesson
T. makes an overhead of the following problems. Have students complete
problems 12 – 16.
3
Geometry 12b Lesson Plan
QuickTime™ and a
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Students will be answering questions, writing notes and problems, describing
the process to the teacher and their peers, and reading problems.
Explain in words how to find the measure of each interior angle and each
exterior angle in a regular polygon.
Explain how to find the sum of the measures of the interior angles of a polygon
using triangles.
Assign the following problems:
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Ruler
Whiteboard & marker
Index Cards
Overhead projector