Shapes and Angles

Lesson 9

Math

Unit 8

4th Grade

Lesson 9 of 18

Objective


Identify and measure angles as turns and recognize them in various contexts.

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.

Criteria for Success


  1. Understand that angles are portions of turns, not just the fraction of a circle between their two rays (i.e., angles can describe an action, with the starting “ray” being the direction something faces at the start of the action and the ending “ray” being the direction something faces at the end of the action).
  2. See that “turns” can be made in two directions, clockwise and counterclockwise.
  3. Understand what portion of a turn happens when degree measures are given in real-world contexts (a car “does a 360,” etc.) (MP.4).
  4. Determine the direction a person or object is facing after one or more turns of varying degrees.

Tips for Teachers


  • Students need not be proficient with the language of clockwise and counterclockwise. 
  • “Given the complexity of angles and angle measure, it is unsurprising that students in the early and elementary grades often form separate concepts of angles as figures and turns, and may have separate notions for different contexts (e.g., unlimited rotation as a fan vs. a hinge) and for various ‘bends’” (MD Progression, pp. 23-24). Thus, this lesson serves to deepen and add nuance to students’ understanding of angles not just as static wedges, but also as portions of turns and rotations.
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Anchor Tasks

25-30 minutes


Problem 1

Work with a partner. Each of your walks represents a ray. Draw the angle each situation below creates.

a.   Stand next to your partner. Partner A, turn 30 degrees. Both walk forward in the direction you are facing.

b.   Stand next to your partner. Partner B, turn 90 degrees. Both walk forward in the direction you are facing.

c.   Stand next to your partner. Partner A, turn 120 degrees. Both walk forward in the direction you are facing.

d.   Stand next to your partner. Partner B, turn around so you and your partner are facing opposite directions. Both walk forward in the direction you are facing.

Guiding Questions

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Student Response

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References

Howard County Public School System Going Different Directions

Going Different Directions is made available by the Howard County Public School System under a CC BY-NC-SA 4.0 license. © 2013-2014 Elementary Mathematics Office Howard County Public School System. Accessed March 5, 2019, 11:19 a.m..

Modified by Fishtank Learning, Inc.

Problem 2

What examples of angles as turns can you find in the real world?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic B > Lesson 8Concept Development Problem 3

Grade 4 Mathematics > Module 4 > Topic B > Lesson 8 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 3

A clock changes from 3:00 to 3:15. 

a.   How many degrees has the minute hand turned?

b.   CHALLENGE: How many degrees has the hour hand turned?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • Why was there confusion with turning 90° but not with turning 180° or 360°?  How can the terms “clockwise” and “counterclockwise” be used in #6?
  • Why is there more than one answer for #6? 
  • Does it matter in #7 if you turned 180° to the right or 180° to the left?  Explain.
  • What do you notice about the terms used to tell time?  (All of the benchmark angles have terms, i.e., half past, quarter of, quarter past.)
  • Stand face-to-face with your partner.  Ask your partner to turn to the left.  Why does it appear to you that she turned to the right?  In each problem in this lesson, when someone turns to the right or left, it is from his or her perspective.  What does this mean? 

Target Task

5-10 minutes


Problem 1

Dario is trying to hang a piece of art on his wall. He accidentally hangs it upside down. How many degrees does Dario need to turn the painting so that it is hanging right side up? 

Student Response

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Problem 2

Giovanna is facing north. She turns 90° to the right three times. Which direction is she now facing? 

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

Decompose angles using pattern blocks.

Lesson 10
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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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