Shapes and Angles

Lesson 12

Math

Unit 8

4th Grade

Lesson 12 of 18

Objective


Solve problems involving the measure of more than 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. See 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. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems that involve more than two adjacent angles, e.g., by using an equation with a symbol for the unknown angle measure (MP.2, MP.4).
  3. Write an equation to represent the unknown angle measure in a compound angle (MP.2).
  4. Know the angle measure of common angles (a straight angle, a right angle, a full circle) and use that knowledge to solve for missing angle lengths (MP.3).

Tips for Teachers


Lesson Materials

  • pattern blocks (Various quantities per student or small group) — See Anchor Task 1 for more information.
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Anchor Tasks


Problem 1

Use patterns blocks of various types to create a design in which you can see a decomposition of 360°.  Which shapes did you use? Write an equation to show how you composed 360°.

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic C > Lesson 11Application Problem

Grade 4 Mathematics > Module 4 > Topic C > Lesson 11 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

Find the measure of the missing angles in the following figures.

a.

b.

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic C > Lesson 10Concept Development Problem 3

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.
EngageNY Mathematics Grade 4 Mathematics > Module 4 > Topic C > Lesson 11Concept Development Problem 1

Grade 4 Mathematics > Module 4 > Topic C > Lesson 11 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 Set


Answer Keys

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Discussion of Problem Set

  • How does your knowledge of a line assist you in solving #1 and #2? 
  • How does your knowledge of a circle assist you in solving #3 and #4?
  • What was the correct equation in #5 part (a)? How did that help you solve part (b)? 
  • In #6, what vocabulary term did you need to know to be able to solve?  
  • What made #7 different from previous problems? How was it similar to and different from some problems in Lesson 12? 
  • How did #8 differ from the previous problems? How does #8 demonstrate the importance of reading carefully?

Target Task


$${\angle XYZ}$$  is a straight angle.

a.   Write an equation that can be used to solve for the measure of $$\angle VYW$$.

b.   Find the measure, in degrees, of $$\angle VYW$$.

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

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 11

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Lesson 13

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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