Lesson 13 | Shapes and Angles | 4th Grade Mathematics

Objective

Measure and sketch angles that are greater than 180°.

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.
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.

Measurement and Data

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

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

Measure angles that are greater than 180° by:

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
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).

Sketch angles that are greater than 180° by:

Sketching an angle whose sum with the desired angle measure is 360°, but designating the exterior angle as the desired angle; or
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

Suggestions for teachers to help them teach this lesson

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

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

Problem 1

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

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic B > Lesson 7 — Concept 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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Problem 3

Sketch an angle with the following measure:

a. 245°

b. 307°

Guiding Questions

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Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

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

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

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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 12

Lesson 14

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

Measurement and Data

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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