Download When is a circle a line?

2012
When is a circle a line?
Class/Course Title:
Applied Robotics
Duration/Time Frame:
Full class period or 50 min.
CTE/Core Standards:
Core Geometry-Circles: MACC.912.GC.2, MACC.912.GC.5 and
Modeling with Geometry: MACC.912.GMG.1
CTE 06.0 Demonstrate an understanding of engineering
principles.
09.0 Build, program, and configure a robot to perform predefined
tasks
Teacher:
Fred Urquhart
Lesson Objective:
Students will be able to relate problems involving finding a
distance line in Robotics to the circumference formula in
Geometry.
Materials:
Cloth style tape measure, 3 different diameter Styrofoam wheels
CTE/Core Benchmark(s):
Core:
MACC.912.GC.2 Understand and apply theorems about circles.
Identify and describe relationships among inscribed angles, radii,
and chords. Include the relationship between central, inscribed,
and circumscribed angles; inscribed angles on a diameter are right
angles; the radius of a circle is perpendicular to the tangent where
the radius intersects the circle.
MACC.912.GC.5 Find arc lengths and areas of sectors of circles.
Derive using similarity the fact that the length of the arc intercepted
by an angle is proportional to the radius, and define the radian
measure of the angle as the constant of proportionality; derive the
formula for the area of a sector.
MACC.912.GMG.1 Apply geometric concepts in modeling
situations. Use geometric shapes, their measures, and their
properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder).*
CTE:
06.03, Name the six simple machines(i.e., lever, inclined plane,
wheel and axle, screw, wedge, and pulley) and describe their
application to robotics.
09.05, Formulate examples of how the robot might be used or
adapted for use in a manufacturing or other environment.
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2012
When is a circle a line?
09.06, Create and present a proposal, including drawings and
specifications, describing the robot, the tasks and rationale, and
the results.
Key terms/vocabulary:
Core: Perimeter, circumference, radius, diameter, arc, arc length
CTE: Wheel and axle, rotations, circumference, diameter, distance
line, calculate, predict, degrees
Anticipatory
Set/Introduction:
How do changes in the drive wheel circumference affect the
distance the robot travels?
Exploration/Investigation:
CTE: Build a data table that describes the circumference
measurement/distance line of each of the 3 wheels.
Practice/Problem
Solving/Applications:
CTE: How many revolutions of each wheel will be necessary for
the robot to travel 28 inches? How can you measure a partial turn
of the wheel? Convert to degrees.
Check for
Understanding/Justification:
CTE: Students should explain the correlation between moving the
drive wheel and movement of the robot.
Closure/Summary:
CTE: Students use their table to calculate the distance a robot will
travel when the drive wheel is turned a specific number of
degrees.
Reflections:
Modifications and/or
Accommodations:
CTE: Students will give a real world example of why it is important
to know how far a robot will travel for each turn of the drive wheel.
CTE/Core Students work in pairs/teams to measure the 3 foam
wheels as a class then the pairs/teams complete the rest of the
calculations.
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