Shapes and Angles

Lesson 11

Math

Unit 8

4th Grade

Lesson 11 of 18

Objective


Solve problems involving the measure of two adjacent angles.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 1.OA.D.8

Criteria for Success


  1. Understand that angle measure is additive (i.e., 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).
  2. Understand that adjacent angles are angles that share a vertex and a side.
  3. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems that involve two adjacent angles, e.g., by using an equation with a symbol for the unknown angle measure (MP.2, MP.4).
  4. Write an equation to represent the unknown angle measure in a compound angle (MP.2).
  5. Know the angle measure of common angles (a straight angle, a right angle) and use that knowledge to solve for missing angle lengths (MP.3).

Tips for Teachers


Lesson Materials

  • Square-sized paper (2 per student)
  • 180° Protractor (1 per student)
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Anchor Tasks

25-30 minutes


Problem 1

a.   Take a square piece of paper and fold it along the diagonal. What is the measure of each of the angles created by the fold at each corner? What is the measure of the angle of the whole corner?

b.   Take another square piece of paper and fold it so that there is a crease from one corner to another point on an opposite side that is not the diagonal corner.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic C > Lesson 10Concept Development Problem 1

Grade 4 Mathematics > Module 4 > Topic C > Lesson 10 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

a.   In the figure below, $$\angle ABC$$ measures 60°.

In the figure above, draw an angle that measures 25°. It should have the same vertex and share side $$\overrightarrow{AB}$$.

b.   How many angles are there in the figure you drew in Part (a)? What are their measures?

c.   Below is a copy of $$\angle ABC$$. Draw a different angle that measures 25° and has the same vertex and also shares side $$\overrightarrow{AB}$$.

d.   How many angles are there in the figure you drew in Part (c)? What are their measures?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Measuring Angles

Measuring Angles, accessed on March 7, 2018, 1:52 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

In the figure, $$ABCD $$ is a rectangle and $$B$$$$E$$, and $$C$$ lie on a line.

a.   $$\angle BAE=37^{\circ}$$ Find $$\angle EAD$$.

b.   $$\angle BEA=53^\circ$$.  Find $$\angle AEC$$.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Finding an Unknown Angle

Finding an Unknown Angle, accessed on Feb. 20, 2019, 12:40 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes


Discussion of Problem Set

  • For #1–4, why is it important to know that we are starting with a right angle or a straight angle?
  • For #5, why is it important to know that ACDE is a rectangle?
  • What was different about #6 compared to the other problems on the Problem Set? 
  • What new (or significant) math vocabulary did we use today to communicate precisely?

Target Task

5-10 minutes


$${\angle ADC}$$ is a right angle. 

a.   Which of the following equations can be used to find the measure of $$\angle ADB$$?

  1. a.   $${34+z=90}$$

  2. b.   $${z-34=90}$$

  3. c.   $${34\times z=90}$$

  4. d.   $${90\div34=z}$$

b.   What is the measure, in degrees, of $${{\angle ADB}}$$?

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

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

Lesson 12
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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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