| Lessons |
Lesson Summary
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| For
virtual manipulatives for geometry, please see: http://matti.usu.edu/nlvm/nav/grade_g_3.html |
| Geom
4.1 Circle Basics
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Students
use a Geometer’s Sketchpad “Introducing Circles”
activity. They begin a record of circle terms, concepts
and formulas.
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Geom
4.2 Measuring Circles
PDF
|
Students
derive the formulas for circumference and area of the circle.
For circumference, they measure diameters and circumferences,
create ratios and arrive at the Pi ratio. For area, they use
several strategies to observe the area of a circle as related
to a square. |
Geom
4.3 Chords, Tangents, Angles and Arcs
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Students
use Geometer’s Sketchpad or Patty Paper Geometry to
explore and write conjectures about chords, tangents, arcs
and angles. After they have written their own, they read and
compare the textbook version of the conjectures. |
Geom
4.4 More Circls Conjectures and Proofs
PDF
|
Students
use formal proofs to explore 1) whether or not the inscribed
angle conjecture works in all cases for inscribed angles,
2) inscribed angles that intersect the same arc are congruent,
3) inscribed angles in a semicircle are right angles, 4) parallel
lines intercept congruent arcs on a circle, 5) other relationships
and properties regarding intersecting chords, secants, and
tangents. |
Geom
4.5 Triangles in Circles, Circle Equations
PDF
|
Students
use Geometer’s Sketchpad to create a triangle and it’s
perpendicular bisectors, create a circle with center at the
intersection of the perpendicular bisectors, and observe that
the intersection of the perpendicular bisectors creates a
circle which circumscribes the triangle. Secondly, they use
a right triangle within a circle to develop the equation for
a circle. Third, they show how the distance formula relates
to the equation for a circle. |
Geom
4.6 Measuring the Earth's Circumference as Erastosthenes
PDF
http://www.k12science.org/noonday/
|
Students
read the book The Librarian Who Measured the Earth. Using
quotes from the books and questions on the worksheet, they
work through the process that Erastosthenes used to measure
the Circumference of the Earth. Access the website listed |
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