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# Angles, Arcs, and Circles

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Common Core Standards
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An exploration into the relationship between circles and angles. This can be done after students have become familiar with angles and able to use a protractor to measure and draw angles.

It begins with the connection between angles and arcs: angles define or “cut out” parts of circles. Students measure the central angles that divide a circle into 3, 4, 5, 6, 8, and 10 equal angles, implicitly inscribing those polygons in the circle.

Next, students find patterns for the angles formed by the hour and minute hands of a clock for particular times. Student clocks would be helpful to do this last part. Geared clocks are not necessary. Following from the fact that a circle includes 360º, a one-hour interval includes an angle of 30º. Students use protractors to measure such angles, but then go on to infer other angle measurements.

Last, students use a compass rose and a protractor for an introduction to the idea of compass bearing.

All told:
- 4 pages on measuring central angles of polygons
- 4 pages measuring and discovering angles formed by clock hands
- 2 pages on angles related to direction and the compass

Common Core Standards:

4.MD.5: “…understand concepts of angle measurement:
a. An angle is measured with reference to a circle….by considering the circular arc between the points where the two rays intersect the circle…”
4.MD.6: “Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.”

A Smart Notebook 10 file is included.

Double-click the Zip icon and open the PDF and Notebook files separately.
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