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Modeling Circular Motion
Lesson Plan
with formative assessment
Iowa Core Math
Essential
Characteristics
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Teaching for Understanding
Problem-Based Instructional Tasks
Mathematical Modeling
Connected and Coherent Content
Iowa Core Math
Essential Skills
• Problem Solving
• Ability to Construct and Apply
Multiple Connected
Representations
• Deep Conceptual and
Procedural Knowledge
• Rigor and Relevance
• Effective Use of Technology
• Ability to Recognize, Make,
and Apply Connections
• Communication
• Reasoning and Proof
Iowa Core Math
Essential Strand(s)
Algebra
Geometry
Iowa Core Math
Essential
Concept(s)
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Functions
Trigonometric Relationships
Iowa Core Math
Sub-Concept(s)
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Understand, apply, and analyze trigonometric functions
Use functions to represent and reason about patterns of change and
relationships between quantitative variables.
Analyze functions in terms of zeros and maximum and minimum
Model and solve problems with functions, including in real-world
situations
Understand and apply trigonometry with respect to right triangles,
general triangles, circles, and periodic phenomena
Understand, apply, and analyze the formulation of sine and cosine
with respect to the unit circle (in terms of the x and y coordinates
of a point on a unit circle)
Recognize periodic phenomena and model them appropriately
with trigonometric functions
Reason about, reason with, and apply fundamental trigonometric
relationships, including sin2x + cos2x = 1
Use trigonometry to solve problems
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Prerequisite
Knowledge
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Learning Goals
Right triangle trigonometry
(See associated Meaningful Distributed Practice tasks to address
this prerequisite knowledge.)
Pythagorean theorem
Measuring in metric units
Understand that:
Iowa Core Mathematics / Every Student Counts
Problem-Based Instructional Task Lesson Plan
11/15/09
Page 1 of 3
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The horizontal and vertical directed distances exhibited in circular
motion can be represented using trigonometry.
The learning goal above may be presented to students at the beginning of
the lesson.
The learning goals below may be shared with students and discussed at
the end of the lesson. It will detract from student learning if these goals
are shared at the beginning of the lesson.
Understand that:
 The horizontal and vertical components of circular motion exhibit
a periodic pattern of change.
 The x-coordinate of a point on a unit circle can be represented as
cos  (where  is the measure of the angle between the positive xaxis and the ray through the origin and point on the unit circle).
 The y-coordinate of a point on a unit circle can be represented as
sin .
 The fundamental trigonometric identity sin2 + cos2 = 1 is
evident as an example of the Pythagorean theorem in a unit circle.
Success Criteria
I can:
1. Visualize, predict, measure, plot, and explain the pattern of change
of the vertical directed distance of a seat on a Ferris wheel as it
rotates counterclockwise.
2. Visualize, predict, measure, plot, and explain the pattern of change
of the horizontal directed distance of a seat on a Ferris wheel as it
rotates counterclockwise.
3. Write an equation using a trig ratio that will precisely determine
the vertical directed distance of a seat on a Ferris wheel as it
rotates counterclockwise, and explain why the equation makes
sense.
4. Write an equation using a trig ratio that will precisely determine
the horizontal directed distance of a seat on a Ferris wheel as it
rotates counterclockwise. Explain why the equation makes sense.
5. Represent the x and y coordinates of a point on a unit circle using
trigonometric ratios, and explain why this representation makes
Iowa Core Mathematics / Every Student Counts
Problem-Based Instructional Task Lesson Plan
11/15/09
Page 2 of 3
sense.
6. Demonstrate and explain how the Pythagorean theorem is
expressed using trigonometry.
7. Demonstrate and explain the periodic pattern of change of the x
and y coordinates of a point on a unit circle as it rotates
counterclockwise.
Note: Do not share all these success criteria with students at the beginning
of the lesson. You might share them at appropriate places throughout the
lesson, just after students have worked on that associated part of the
lesson. You might share and discuss at the end of the lesson as part of the
lesson summary.
Evidence of
Essential Skills
linked to Success
Criteria
Focus Question(s)
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Problem Solving – Success Criteria 1–5
Reasoning and Proof – Success Criteria 1–6
Communication – Success Criteria 1–7
Connections – Success Criteria 3, 4, 5, 6
Representation – Success Criteria 3, 4, 5
Think about sitting in a particular chair on a Ferris wheel.
 How can trigonometric ratios be used to find vertical and
horizontal directed distances of the chair as the Ferris wheel
rotates?
In general:
 How can trigonometry be used to model aspects of circular
motion?
Iowa Core Mathematics / Every Student Counts
Problem-Based Instructional Task Lesson Plan
11/15/09
Page 3 of 3