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Technology Infused Lesson
Title: Circles
Subjects: Mathematics
Learning Level: High School Mathematics Geometry
Abstract:
Instruction of an introductory unit on circles was enhanced using
Geometer's
Sketchpad. Geometer's Sketchpad allows for the creation of an infinite
number of examples leading students to conjecture about the relationships between
parts of circles. Lack of computer access required that the material be presented
in a discussion/lecture format. Looking for patterns, predicting and making
conjectures was an important part of the lessons. Part of each class period
was allocated for students to do daily work and ask individual questions.
Objectives/Outcomes:
Students will:
- Define and identify parts of a circle - center, radius,
chord, diameter, semicircle, major and minor arcs, central angle.
- Develop and
apply a theorem regarding the relationship between the measure of a central
angle and its intercepted arc.
- Create and use a method to calculate
the length of an arc given the radius and measure of the central angle
intercepting the arc.
- Develop and apply a theorem concerning the relationship of congruent
chords, and arcs.
define and identify - secant, tangent, point of tangency.
- Develop and
apply a theorem concerning radii that are perpendicular to chords.
- Develop
and use a theorem regarding radii and tangents that intersect at the
point of tangency (Tangent Theorem).
- Define and identify an inscribed angle
and its intercepted arc.
- Develop a theorem concerning the measure of an inscribed
angle and its intercepted arc.
Invitation:
Students have an informal understanding of circles, angles,
and segments related to the circles. Use Geometer's Sketchpad to
enhance formal instruction in introductory lessons on circles. The lessons
compliments
Lessons 9.1, 9.2, and 9.3 from the text Geometry, by Holt, Rinehart, Winston.
Tasks:
- Students participated in a discussion/lecture class. Geometer's
Sketchpad was used in these discussions. Sketches were projected on a
screen using a LCD Projector.
- Students completed daily assignments concerning the
concepts being studied.
- Assignment #1 Page 474 1-12, 15-21, 24-25.
- Assignment #2 Page 481 1-10, 12-16.
- Assignment #3 Practice and Apply Worksheets
9.1 and 9.2.
- Assignment #4 Page 489 1-23.
- Assignment #5 Practice and Apply Worksheet 9.3.
(Assignments taken from Geometry, by Holt, Rinehart, Winston).
- Students took
a quiz on the concepts taught.
Situations:
Sample sketches and details for creating them are provided. During
this unit, spend:
- Day One: Lesson 1 Sketches 1, 2, 3, and 4 - Traditional
examples concerning the concepts - and Assignment #1.
- Day Two: Lesson 2
Sketches 1, 2, and 3 - Traditional examples concerning
the concepts - and Assignment #2.
- Day Three: Review of Lessons 1 and 2 - Traditional
examples - and
Assignment #3.
- Day Four: Lesson 3 Sketch 1 - Traditional examples concerning
the concepts - and
Assignment #4.
- Day Five: Review of Lesson 3 - Traditional examples - and
Assignment #5.
- Day Six: Written Quiz concerning Lessons 9.1, 9.2, and 9.3.
Interactions:
Described
in situations. Please keep in mind that these students have used Geometer's
Sketchpad extensively through the school year. They are active in giving instruction
as to the next step to be taken during the discussion/lecture.
Tools:
- Geometer's Sketchpad.
- Previous hands on use of Geometer's Sketchpad.
- LCD projector (or other
means of projecting sketches)
- Overhead, chalkboard or whiteboard
- Calculators (helpful in second lesson)
- Text used was Geometry, by Holt, Rinehart and
Winston (1997).
Assessment:
- Daily assignments assessed students understanding of the concepts.
- Classroom discussions revealed student knowledge of concepts. Dialog and
multiple examples were used to reinforce instruction.
- A written quiz provided a formal assessment of the outcomes.
Standards: (Minnesota Graduation Standards and ISTE)
Minnesota Standards Shape, Space and Measurement
"New" Standards (draft standards dated May 19, 2003)
SPATIAL SENSE, GEOMETRY AND MEASUREMENT
b. Geometry
Standard: Apply basic theorems of plane geometry, right triangle trigonometry,
coordinate geometry, and a variety of visualization tools to solve real-world
and mathematical problems.
The student will:
- Know and use theorems about circles to justify geometrical facts and solve
real-world and mathematical problems. These theorems include the relationships
involving tangent lines, and radii, the relationship between inscribed
and central angles and the relationship between the measure of a central
angle
and arc length.
ISTE:
- Basic Operations and Concepts (Students demonstrate a sound understanding
of the nature and operation of technology systems. Students are proficient
in the use of technology).
- Technology Productivity Tools (Students use technology tools to enhance
learning, increase productivity and promote creativity).
- Technology Research Tools (Students use technology tools to process data
and report results).
Author(s): Deb Halver, Ben Pany, Karen Plass, Kay Wohlhuter (TechnoRooters
Collaboratory).
Submitted by: Deb Halver and the TechnoRooters Collaboratory, Arrowhead "Preparing
Tomorrow's Teachers to Use Technology" Project, Dept. of Education, University
of Minnesota Duluth.
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