Lesson 4

Measuring and Estimating Angles

Est. Class Sessions: 1–2

Developing the Lesson

Part 1. Estimating Angles

Sort Angles. Display ∠F and ∠B from the Angle Sort Cards pages of the Student Activity Book. Ask students to describe the size of each angle. After a few minutes, ask students to tell their neighbor how they chose their estimate. Ask a few students to share their estimation strategies with the class. Look for a student who is using the 90° square corner as a benchmark to estimate the size of each angle.

Ask:

X
  • Describe the size of ∠F. (∠F is greater than zero and less than 90°. But it is a small angle so it is close to 0°.)
  • Describe the size of ∠B. (∠B is greater than 90° but smaller than 180°. It is really close to a straight angle. So it is a little smaller than 180°.)
  • What type of angle is ∠F? (acute)
  • What type of angle is ∠B? (obtuse)

Ask students to take out the Angle Sort Cards they used in Lesson 1. Ask them to find groups of angles that will help them describe the approximate size of an angle. See Figure 1 for one possible sort. Note that ∠J belongs in the “More than 180°” category if we are considering reflex ∠J. Ask students to describe to their partners how they sorted the Angle Sort Cards and discuss a few different sorts with the whole class.

Order Angles by Size. Display and ask students to take out ∠D, ∠K, ∠C, and ∠M from the Angle Sort Cards. Ask students to put these angles in order from smallest to largest.

Ask:

X
  • What is similar about the size of all these angles? (These are all about 90°).
  • How do you know which angle is the smallest?
    (∠D is smaller than a right angle).
  • Describe the size of ∠D. (∠D is a little smaller than a right angle, so a little less than 90°).
  • Describe the size of ∠M. (∠M is a little larger than a right angle, so a little more than 90°).

Describe Angle Size. Ask student pairs to work together to describe the approximate size of each angle on the Angle Sort Cards. Students record their descriptions on the back of each card.

While they are working, circulate and ask students to explain their estimates; for example:

X
  • How did you decide that angle was larger than 90°?
  • How did you decide that angle is close to 180°?

After students have written descriptions, ask them to sort the angles by type of angle: acute, obtuse, right, and reflex.

Ask:

X
  • Which angle measures describe each type of angle? (Acute angles are smaller than 90°, obtuse are larger than 90° but smaller than 180°, right angles are 90°, and reflex angles are larger than 180°.)

Add to the Geometry Word Chart. Lead the class to refine their definitions of angle types by adding this angle measure information to the angle type descriptions on the Geometry Word Chart you created in Lessons 1 and 3.

Introduce Mrs. Dewey's problem in the vignette on the Measuring and Estimating Angles pages in the Student Guide. Ask student pairs to answer and discuss Questions 1–4. Circulate and listen to students describe the size of an angle and ask students to justify those descriptions using the benchmarks. Students can put their Angle Sort Cards in an envelope for now. They will use them again in the next part of the lesson.

Assign the Homework section in the Student Guide after Part 1.

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Developing Estimation Skills. Students develop the ability to estimate angle measures through experiences with measuring and with describing angles using benchmarks. Students are asked to either describe the angle size using benchmarks (e.g., That angle is a little smaller than a straight angle or 180°.) or select a best estimate from a list of possible estimates (e.g., Is the angle about 50°, 90°, or 120°?). With experience, students will be able to choose an appropriate estimate on their own (e.g., About how big is ∠Y? About 60°.). That is not expected during these early experiences with measuring angles.

Student Guide: 384 385
Answers
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SG_Mini
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SG_Mini
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Student Activity Book:
Master:
One possible sort of the Angle Sort Cards
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