the distances between landmarks “as the crow flies.”
Extension!Discuss with your students the rationale of using different units of distance – inch, foot, centimeter, mile,
etc. Why are things measured in inches as opposed to fractional feet? This is also a great time to introduce the
difference between the metric system and the U.S. measurement system. Have students perform research regarding
why the United States continues to use its system while the majority of other countries use the metric system. Provide
pros and cons to using each type of system.
Fun tip!Have students devise their own measurement device. Students can use their invention to measure a school
hallway, parking lot, or football field. Engage in a whole-class discussion regarding the results.
Refresher!Students may need a refresher regarding multiplying units. Have the students write out the complete unit,
as on page 18, and show students how units can be cross-canceled.
Look out! While the Segment Addition Property seems simple, students begin to struggle once proofs come into
play. Remind students that the Segment Addition Property allows an individual to combine smaller measurements
of a line segment into its whole.
Rays and Angles
Pacing:This lesson should take one class period
Goal:This lesson introduces students to rays and angles and how to use a protractor to measure angles. Several real
world models are used to illustrate the concepts of angles.
Real World Connection!Have students Think-Pair-Share their answers to the opening question, “Can you think of
other real-life examples of rays?” Choose several groups to share with the class.
Notation Tip! Beginning geometry students may get confused regarding the ray notation. Draw rays in different
directions so students become comfortable with the concept that ray notation always points to the right, regardless
of the drawn ray’s orientation.
Teaching Strategy!Using a classroom sized protractor will allow students to check to make sure their calculations
are the same as yours. Better yet, use an overhead projector or digital imager to demonstrate the proper way to use
a protractor.
Teaching Strategy!A good habit for students is to name an angle using of all three letters. This becomes important
when labeling vertices of triangles and labeling similar and congruent figures using the similarity statement. Further-
more, stress to students the use of double and triple arcs to denote angles of different measurements. Students can get
caught up in the mass amounts of notation and forget this important concept, especially during triangle congruency.
Stress the parallelism between the Segment Addition Property and Angle Addition Property. Students will discover
that many geometrical theorems and properties are quite similar, with perhaps one words changed. Yet, the meaning
remains the same.
Arts and Crafts Time!Have students take a piece of paper and fold it at any angle of their choosing from the corner
of the paper. Open the fold and refold the paper at a different angle, forming two “rays” and three angles. Show
how the angle addition property can be used by asking students to measure their created angles and finding the sum
- they should equal 90 degrees!
Physical Models! The angle formed at a person’s elbow is a useful physical model of angles. Have the students
put their arm straight out, illustrating a straight angle. Then have the student gradually turn their arm up (or down)
gradually to demonstrate how the degree changes. Use several students as examples to show that the length of the
forearm and bicep do not change the angle measurement.
Chapter 1. Geometry TE - Teaching Tips