Download lesson design std21.0geom

Lesson Design
Subject Area: Geometry
Grade Level: 9th grade.
Benchmark Period 4
Duration of Lesson: 1 hour.
Standard(s): Students prove and solve problems regarding relationships among chords, secants,
tangents, inscribed angles, and inscribed and circumscribed polygons of circles.(21.0)
Learning Objective: Solve for missing sides and angles of inscribed and circumscribed polygons of
circles.
Big Ideas involved in the lesson: Know the relationships between angles in triangles and quadrilaterals
and how to use the Pythagorean theorem to find missing sides of right triangles.
As a result of this lesson students will:
Know: circle, triangle, right triangle, quadrilateral, angles, supplementary angles, vertex, interior of a
circle, exterior of a circle, hypotenuse, Pythagorean theorem, opposite angles, inscribed polygon,
circumscribed polygon, circumference, chords, diameter, radius.
Understand: A right triangle is circumscribed in a circle when the diameter of the circle constitutes the
hypotenuse of the triangle. A quadrilateral can only be inscribed in a circle if and only if its opposite
angles are supplementary.
Be Able To Do: Recognize right triangles from other triangles inscribed in circles. Find missing angles of
quadrilaterals inscribed in circles.
Assessments:
What will be evidence
of student
knowledge,
understanding &
ability?
1
Formative: - CFU questions.
- ABWA
Summative: Quiz, cloze
activity, test, homework
worksheet.
CFU Questions:
Define “inscribed”.
Define “circumscribed”.
Define polygon.
What is the condition for a polygon to be
inscribed in a circle?
(answer: all the vertices must be on the circle.)
Is the radius half of the diameter?
What do you call the longest side of a right
triangle?
How many sides does a quadrilateral have?
What is the sum of the angles in a quadrilateral?
How do we know that a quadrilateral is inscribed
in a circle?
What does “supplementary angles” mean?
How do you know that an inscribed triangle is a
right triangle? Which theorem do you use to
prove that it is a right triangle?
Lesson Design
Anticipatory Set:
a. T. focuses students
b. T. states objectives
c. T. establishes purpose of
the lesson
d. T. activates prior knowledge
Lesson Plan
Pair students. Pass out compasses and protractors. Have students
alternately draw a circle and a quadrilateral (instruct them to draw ANY
quadrilateral, not a perfect rectangle) such that the vertices are on the
circle. Have them measure the angles of the quadrilateral using
protractors and specifically look at the opposite angles. What can you
conclude? Are they supplementary? If you move the lines around and
move in or out of the circle, would the opposite angles still add up to 180
degrees? (This activity included in power point).
And / or
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
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
2
Exploration activity see word document or PowerPoint
Present power point (attached).
Draw three inscribed triangles on the board. One is a regular triangle, so
it is isosceles. One is right, and one is scalene. It is easier for the
students to see how they can identify the right triangle by showing that
its hypotenuse will BE the diameter. The scalene will not even cross the
center and its sides will be chords of the circle.
Give an example of a right triangle with legs equal to 3 and 4 units
(always start by giving Pythagorean triples) and ask them to find the
hypotenuse, using the Pythagorean theorem. The diameter (or
hypotenuse) will be 5 units. Ask them if they would have been able to
find the radius of the circle with having only the values of the legs of the
triangle. (Yes, because once we find the hypotenuse, we will have found
the diameter, and then we can divide it by 2 and obtain the value of the
radius).
Have the students draw an inscribed right triangle using their tools.
Label the legs of the triangle with 6 and 8 units. Ask them to find the
circumference of the circle.
Walk around and, for those who need help, hint that to find the
circumference of a circle, you need to know the diameter (or the radius,
depending on what they were taught; C=2πr, or C=πd. Explain both.)
How would you find the diameter of a circle in which a right triangle is
inscribed?
Draw 2 sets each of inscribed right triangles and quadrilaterals, and label
respective sides. Ask students to come to the board and solve missing
sides, or hypotenuse, or legs, or find the circumference.
Lesson Design
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
3
Hands on activities, taking notes, answering questions, working in pairs.
Individual activity:
Problem 1: If the radius of a circle is 6.5 inches, and one leg of an
inscribed triangle is equal to 5 inches, find the value of the other leg.
Problem 2: If a quadrilateral has 3 angles measuring 102, 78, and 89
degrees, what should the measure of the missing angle be for it to be
inscribed in a circle?
Homework page 617, #16,18,19,20,22,23,24,26,28 and challenge problems
#44 and 45.