Angles

Abstract

The following lesson is designed to introduce students to acute, obtuse, and right angles. It is also designed to introduce students to vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, same-side interior angles, same-side exterior angles, and corresponding angles.

Objectives

Upon completion of this lesson, students will:

  • identify angles as acute, obtuse or right
  • identify pairs of angles with special relationships: vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, same-side interior angles, same-side exterior angles, and corresponding angles

Standards Addressed

Grade 6

  • Geometry

    • The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.
    • The student solves problems (including real-world situations) using perimeter, area, or volume.

Grade 7

  • Geometry

    • The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.
    • The student solves problems (including real-world situations).

Grade 8

  • Geometry

    • The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.
    • The student solves problems (including real-world situations).

Grade 9

  • Geometry

    • The student demonstrates an understanding of geometric relationships.
    • The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.
    • The student solves problems (including real-world situations).
    • The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 10

  • Geometry

    • The student demonstrates an understanding of geometric relationships.
    • The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.
    • The student solves problems (including real-world situations).
    • The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 6

  • Measurement and Geometry

    • 2.0 Students identify and describe the properties of two-dimensional figures

Fourth Grade

  • Geometry

    • Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

  • Measurement and Data

    • Geometric measurement: understand concepts of angle and measure angles.

Seventh Grade

  • Geometry

    • Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Geometry

  • Congruence

    • Prove geometric theorems

Grades 6-8

  • Geometry

    • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Grades 9-12

  • Geometry

    • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Grade 6

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 2: The learner will select and use appropriate tools to measure two- and three-dimensional figures.

Geometry

  • Geometry and Measurement

    • Competency Goal 2: The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

Technical Mathematics I

  • Geometry and Measurement

    • Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.

Technical Mathematics II

  • Geometry and Measurement

    • Competency Goal 1: The learner will use properties of geometric figures to solve problems.

6th Grade

  • Geometry

    • The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry.

7th Grade

  • Geometry

    • The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. the results of the intersection of geometric shapes in a plane, and the
    • The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. the results of the intersection of geometric shapes in a plane, and the relationships among angles formed when a transversal intersects two parallel lines.

Geometry

  • Geometry

    • Standard G-2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

Grade 7

  • Geometry and Spatial Reasoning

    • 6. The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties.

5th Grade

  • Geometry

    • 5.14 The student will classify angles and triangles as right, acute, or obtuse.

8th Grade

  • Measurement

    • 8.6 The student will verify by measuring and describe the relationships among vertical angles, supplementary angles, and complementary angles and will measure and draw angles of less than 360°.
    • 8.6 The student will verify by measuring and describe the relationships among vertical

6th Grade

  • Measurement

    • 6.13b The student will measure and draw right, acute, and obtuse angles and triangles.
    • 6.13a The student will estimate angle measures, using 45°, 90°, and 180° as referents, and use the appropriate tools to measure the given angles
    • 6.13a The student will estimate angle measures, using 45°, 90°, and 180° as referents, and use the appropriate tools to measure the given angles

Textbooks Aligned

Grade Six

  • Shapes and Designs

    • Investigation Three: Polygons and Angles

7th

  • Module 6 - Flights of Fancy

    • Section 4: Parallel Lines and Angles of Polygons
      • Reason for Alignment: The Angles lesson includes a thorough review of vocabulary along with other concepts such as the angles formed by a transversal, which is the subject of this section of the textbook.

8th

  • Module 5 - Architects and Engineers

    • Section 5: Angles Formed by Intersecting Lines
      • Reason for Alignment: This lesson uses the Angles activity. Key terms from the book that are covered include vertical angles, transversal, alternate exterior and interior angles.

Student Prerequisites

  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag
    • use a browser for experimenting with the activities

Teacher Preparation

  • access to a browser
  • pencil and paper
  • copies of supplemental materials for the activities:

Key Terms

acute angle

An angle whose measure is less than 90 degrees

adjacent angles

Two angles that share a ray, thereby being directly next to each other

alternate exterior angles

Angles located outside a set of parallel lines and on opposite sides of the transversal

alternate interior angles

Angles located inside a set of parallel lines and on opposite sides of the transversal

corresponding angles

Two angles in the same relative position on two lines when those lines are cut by a transversal

obtuse angle

An angle whose measure is greater than 90 degrees

right angle

An angle of 90 degrees

same side exterior angles

Angles located outside a set of parallel lines and on the same side of the transversal

same side interior angles

Angles located inside a set of parallel lines and on the same side of the transversal

vertical angles

The two nonadjacent angles formed when two straight lines intersect

Lesson Outline

  1. Focus and Review

    Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson. Discuss key words that they're already familiar with:

    • acute angle
    • obtuse angle
    • right angle

  2. Objectives

    Let the students know what it is they will be doing and learning today. Say something like this:

    • Today, class, we are going to learn about different types of angles and the ways groups of angles can be related to each other.
    • We are going to use the computers to learn about angles, but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.

  3. Teacher Input

    Open your browser to the Angles activity in order to demonstrate it to the students. Ask students guided questions:

    • Which angles look similar?
    • Which angles look different?
    • How are the angles related?

    Lead the students through the discussion about angles.

  4. Guided Practice

    Explain to the students how to do the assignment. You should model or demonstrate it for the students, especially if they are not familiar with how to use our computer applets.

    • Open your browser to the Angles activity in order to demonstrate it to the students.
    • Show students where they select their answers for the specified angle by clicking on the pop-down menu and scrolling to the correct answer.
    • Click on the "check answer" button to see if your choices are correct.
    • When the correct answers are found, click the "new angles" button to change to a new set of angles.

  5. Independent Practice

    • Allow the students to work on their own to complete the Angles Worksheet, using the applet projected on the wall. Monitor the room for questions and to be sure that the students are on the correct web site.
    • Have students work on a computer, if it's available, to complete a self-quiz using the applet.

  6. Closure

    You may wish to bring the class back together for a discussion of the findings. Discuss with students how they went about answering questions and how they knew when they were correct. Once the students have been allowed to share what they found, summarize the results of the lesson.

Alternate Outline

This lesson can be rearranged in several ways if you have limited computer access: