Download Lesson Plan: Inscribing Figures - Howard County Public School

Lesson Title: G.CO.D.13 Lesson Inscribing Figures
Date: _____________ Teacher(s): ____________________
Course: CC Geometry Unit 3
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
G.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
MP1:
MP3:
MP5:
MP7:
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Look for and make use of structure.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Give students paper plates, and instruct them to draw
and label all of the parts of a circle that they know.
Have them form small groups and get as many parts as
they can. Place a paper plate under the document
camera. Call on groups one at a time to send a
representative to draw and label on of the parts that
they had. Keep going from group to group until groups
are out of ideas. Be sure that radii, chords, diameters,
inscribed angles, and central angles have been added.
As a class, discuss the properties of each part.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
Have students complete the 3-2-1 Closure.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. Assign students to pairs and give each pair multiple paper plates. Have students try to construct the following
shapes, inscribed in the circle formed by the plate, by folding: equilateral triangle, square, regular hexagon. As
you circulate the room, be sure to ask students how they know their shapes are truly regular.
2. As a class, compare the constructions and methods used. Have pairs share which shape they thought was the
most difficult to create and why. In addition, students should justify how they know each of their shapes is
regular.
3. Assign each pair one of the shapes: equilateral triangle, square, and hexagon. Pairs will explore the properties of
the shape they have been assigned and their relationships to the parts of a circle. Students will try to justify
properties of these shapes based on the properties of circles.
 Equilateral Triangle Pairs – Have students explore the angles in an equilateral triangle and their
relationship to the circle. They should recognize that each angle in their equilateral triangle is 60
degrees and is inscribed in the circle. The triangle divides the circle into three different arcs of equal
measurement, which would be 120 degrees. This is a justification that inscribed angles are equal to one
half the measurement of the arc they intercept.
 Square Pairs – Have students explore the diagonals of the square and their relationship to the circle.
Students may easily recognize that the diagonals of the square are the diameters of the circle and must be
congruent. Encourage them to also explore the angles created by the diagonals. Since the diagonals
form central angles that divide the circle into four equivalent arcs, this can be used to justify that they
intersect at a 90-degree angle. Conversely, if students already know that the diagonals are
perpendicular, they could justify that the central angles are equivalent to the measurements of the arcs
they intercept.
 Hexagon Pairs – Have students explore the triangles formed by the diagonals of the hexagon. Students
should see that the diagonals are congruent, since they are diameters. In addition, they may be able to
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: G.CO.D.13 Lesson Inscribing Figures
Course: CC Geometry Unit 3
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
explore the triangles formed based on the fact that the radii are all equivalent, or the relationship
between the central angles formed by the diagonals and the arcs they intercept.
4. Once pairs have explored and discussed the relationships between the properties of their shape and the circle,
regroup the class by shape and allow the larger groups to consolidate their thoughts. Encourage the larger
groups to verify everything using multiple methods. Once groups have become experts in their figures, have
each group present their findings to the rest of the class.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Students should be able to relate the properties of inscribed polygons to the parts of a circle, using the appropriate
terminology and definitions.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Students will be exploring relationships using circle vocabulary such as radius, diameter, chord, inscribed angle, and
central angle. They will make connections with properties of polygons, which may have already been explored in
either Unit 2 or in middle school.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Paper Plates
Document Camera
Have students complete various central and inscribed
angle problems.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Can students accurately name and describe relationships between the parts of a triangle?
Can students use the parts of circles to articulate justifications for properties of regular polygons inscribed within the
circle?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.