Lesson 7 | Shapes and Angles | 4th Grade Mathematics

Objective

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

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

Distinguish angle measure from other attributes, such as the length of the line segments that make up the angle, the distances between their endpoints, the area of the triangles determine by the drawn arms, etc.
Estimate the measurement of angles based on their proximity to various benchmark angles (45°, 60°, 90°, etc.).
Measure angles less than 180° with protractors, placing the middle notch on the vertex of the angle, aligning a side with the zero or base line on the protractor, and reading the number the second side length touches (MP.5, MP.6).
Measure angles with short rays by extending the rays (which can be done since the length of the rays does not determine the angle measure).
Construct viable arguments and critique the reasoning of others regarding the reasonableness of an angle measurement by comparing the estimated measurement based on benchmark angles to the actual measurement (MP.3).
See that angle measure is the same regardless of what protractor is being used to measure.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students will need a protractor for the Problem Set. It is recommended that you have students estimate all of the angle measures first, and then hand them a protractor when they are done. This will help students build visual models of benchmark fractions.
Students will need a protractor for tonight’s homework. If you do not want students to bring them home, the Homework can be cut.

Lesson Materials

180° Protractor (1 per student)
Circular protractor (1 per teacher)

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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

Below are three angles, $$\angle A$$, $$\angle B$$ and $$\angle C$$.

Which angle has the greatest measure? How do you know?

Guiding Questions

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Problem 2

a. Estimate the measure of each angle in Anchor Task 1.

b. Using a 180° protractor, find the exact measure of each angle in Anchor Task 1.

Guiding Questions

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Problem 3

a. Use a 180° protractor to find the measure of each angle in degrees.

b. Use a 180° protractor to measure the labeled angles in each figure.

Guiding Questions

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References

Illustrative Mathematics Grade 4 Unit 7 Lesson 10 Activity 1

Grade 4 Unit 7 Lesson 10 Activity 1, accessed on Oct. 16, 2023, 8:39 a.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

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

Look at #1. How did you determine the angle measure without using a protractor? How can this skill help you when using an actual protractor to measure?
In #2, which angle had the same measure as $${\angle G}$$? $${\angle I}$$?
In #2, which angles had the same angle measure but different side length measures?
For #3, discuss your experience of measuring with different protractors. Describe how the length of an arc on each protractor did or did not affect the measure of the given angle.
Take a look at your 180° protractor. Find pairs of numbers that label the two scales, such as 150° and 30°. Name other pairs of numbers. What do you notice about the pairs of numbers?

Target Task

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

First, estimate the measure of each angle below. Then, use a protractor to find their measure, in degrees.

Student Response

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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

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 6

Lesson 8

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

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Student Response

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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