Lesson 9 | Shapes and Angles | 4th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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:

Measurement and Data

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.

Measurement and Data

4.MD.C.6 — Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

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).
See that “turns” can be made in two directions, clockwise and counterclockwise.
Understand what portion of a turn happens when degree measures are given in real-world contexts (a car “does a 360,” etc.) (MP.4).
Determine the direction a person or object is facing after one or more turns of varying degrees.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

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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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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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic B > Lesson 8 — Concept 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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Problem Set

Problem Set

Answer Keys

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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

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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?

Problem 2

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

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 8

Lesson 10

Lesson Map

Topic A: Lines and Angles

Identify and draw points, lines, line segments, rays, and angles.

4.G.A.1 4.MD.C.5

Identify and draw right, obtuse, and acute angles.

4.G.A.1

Identify and draw perpendicular lines.

4.G.A.1

Identify and draw parallel lines.

4.G.A.1

Topic B: Measures of Angles

Use iteration with one physical nonstandard unit to measure benchmark angles.

4.MD.C.5 4.MD.C.6

Understand that an angle that turns through $${{1\over360}}$$ of a circle is called a “one-degree angle” and can be used to measure angles. Use a makeshift protractor to measure benchmark angles.

4.MD.C.5 4.MD.C.6

Measure angles that are less than 180° using a 180° protractor. Distinguish angle measure from other attributes.

4.MD.C.5 4.MD.C.6

Sketch angles of specified measure using a 180° protractor.

4.MD.C.5 4.MD.C.6

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

4.MD.C.5 4.MD.C.6

Topic C: Measures of Adjacent Angles

Decompose angles using pattern blocks.

4.MD.C.7

Solve problems involving the measure of two adjacent angles.

4.MD.C.7

Solve problems involving the measure of more than two adjacent angles.

4.MD.C.7

Measure and sketch angles that are greater than 180°.

4.MD.C.5 4.MD.C.6 4.MD.C.7

Topic D: Shapes and Lines of Symmetry

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

4.G.A.1 4.G.A.2

Draw triangles from given criteria.

4.G.A.1 4.G.A.2

Analyze and classify quadrilaterals based on parallel and perpendicular lines and the presence or absence of angles of a specified size.

4.G.A.1 4.G.A.2

Draw quadrilaterals from given criteria.

4.G.A.1 4.G.A.2

Identify and draw lines of symmetry in two-dimensional figures.

4.G.A.3

Shapes and Angles

Objective

Common Core Standards

Core Standards

Measurement and Data

Measurement and Data

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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