Shapes and Angles

Lesson 10

Objective

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

Common Core Standards

Core Standards

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  • 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

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  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

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  • Students need not master 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.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 (benefits from discussion). You might decide to modify this so that it is not a partner activity, or find an online applet so that students are rotating objects on their computers instead of themselves. Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

Working in pairs, assign partners A and B. Each student represents a point and each walk represents a ray. Draw the angle each situation below creates. For each situation, start by standing next to one another.

  1. Partner A, turn 30 degrees. Walk forward in the direction you are facing.
  2. Partner B, turn 90 degrees. Walk forward in the direction you are facing.  
  3. Partner A, turn 120 degrees. Walk forward in the direction you are facing.  
  4. Partner B, turn around so you and your partner are facing opposite directions. Walk forward in the direction you are facing.

Guiding Questions

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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 The Match Foundation, Inc.

Problem 2

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

Guiding Questions

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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 The Match Foundation, Inc.

Problem Set & Homework

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

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Problem 1

Marty was doing a handstand. Describe how many degrees his body will turn to be upright again.

References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic B > Lesson 8Exit Ticket, Question #1

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..

Problem 2

Meredith faced north. She turned 90° to the right, and then 180° more. In which direction is she now facing? 

References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic B > Lesson 8Problem Set, Question #8

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..

Mastery Response

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