Shapes and Angles

Lesson 13

Math

Unit 8

4th Grade

Lesson 13 of 18

Objective


Measure and sketch angles that are greater than 180°.

Common Core Standards


Core Standards

  • 4.MD.C.5 — Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
  • 4.MD.C.6 — Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
  • 4.MD.C.7 — Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Criteria for Success


  1. Measure angles that are greater than 180° by:
    1. Understanding that the interior and exterior angles composed of three points must add up to 360°. Thus, finding the angle measure of the smaller angle will allow one to find the angle measure of the larger one by subtracting the smaller angle’s measure from 360° (MP.2, MP.3, MP.5); or
    2. Breaking the large angle into two pieces, one of which is a straight angle. Since straight angles are 180°, one must only measure the non-straight angle of the pair and add its measure to 180° to find the angle measure of the large angle (MP.2, MP.3, MP.5). 
  2. Sketch angles that are greater than 180° by:
    1. Sketching an angle whose sum with the desired angle measure is 360°, but designating the exterior angle as the desired angle; or
    2. Finding how much greater than 180° the desired angle is, then sketching an angle of that measure plus an adjacent straight angle.

Tips for Teachers


  • Both strategies for measuring and sketching angles greater than 180° using a 180° protractor are dependent on students understanding that angle measure is additive, which explain this lesson’s placement in the unit. 

Lesson Materials

  • 180° Protractor (1 per student)
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Anchor Tasks

25-30 minutes


Problem 1

Estimate the measure of $$\angle QRS$$ indicated by the arc below.  Then, find the actual measure of $$\angle QRS$$ using a protractor.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic B > Lesson 7Concept Development Problem 2 and 3

Grade 4 Mathematics > Module 4 > Topic B > Lesson 7 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Measure each of the following angles.

Guiding Questions

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Student Response

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Problem 3

Sketch angles with each of the following measures.

a.   245°

b.   307°

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • It is important to learn to use the 180° protractor because it is the one you will see everywhere.  Explain to your partner how to measure an angle greater than 180° with a 180° protractor.
  • Which strategy did you use the most for #1 and why did you choose that?
  • What mistake did Maria make in #2?

Target Task

5-10 minutes


Use a protractor to measure the following angles.

a.   Measurement: __________

b.   Measurement: __________

c.   Measurement: __________

d.   Measurement: __________

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Analyze and classify triangles based on side length, angle measure, or both.

Lesson 14
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Lines and Angles

Topic B: Measures of Angles

Topic C: Measures of Adjacent Angles

Topic D: Shapes and Lines of Symmetry

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