standard_description: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
- An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
problem_activity: Narrative
In this warm-up, students practice estimating a reasonable angle measurement based on their knowledge of angles so far and their familiarity with clocks. Later in the unit, students will take a closer look at the angles in an analog clock and apply their understanding of angles to solve more sophisticated problems.
Launch
Groups of 2
Display the image.
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time
Activity
1 minute: partner discussion
Record responses.
Draw an arc to show the clockwise turn of the minute hand from the hour hand (label the
\(143^\circ\)
measurement with an arc).
“Your estimate should show the size of this angle in degrees. If you need to, revise your estimates.”
As needed, record any revisions.
Student Facing
How many degrees is the angle formed by the long hand and the short hand of the clock?
[IMG]
Make an estimate that is:
|                    too low                     |                  about right                   |                    too high                    |
|------------------------------------------------|------------------------------------------------|------------------------------------------------|
| \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) |
Student Response
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Activity Synthesis
Consider asking:
“Is anyone’s estimate less than _____? Is anyone’s estimate greater than _____?”
“How did you go about making an estimate? How did you know that _____ must be too low and _____ must be too high?”
“Based on this discussion does anyone want to revise their estimate?”
Consider revealing the actual measurement:
\(143^\circ\)
.


aligns: yes