Angles, Angles, and More Angles

Learning Resource Type

Lesson Plan

Subject Area

Mathematics

Grade(s)

7, 8

Overview

This lesson is designed to develop knowledge about the angles of a triangle. This lesson will prove that the interior angles of a triangle will have a sum of 180 degrees. This lesson will prove that an exterior angle is the sum of the remote interior angles. This lesson will show the relationships of the angles of parallel lines and transversals.

This lesson results from the ALEX Resource Gap Project.

Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.38

Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.

UP:MA19.7A.38

Vocabulary

  • Transversal
  • Corresponding Angles
  • Vertical Angles
  • Alternate Interior Angles
  • Alternate Interior Angles
  • Supplementary
  • Adjacent

Knowledge

Students know:
  • that a straight angle is 180 degrees.
  • That a triangle has three interior angles whose sum is 180 degrees.
  • The definition of transversal.
  • how to write and solve two-step equations.

Skills

Students are able to:
  • make conjectures about the relationships and measurements of the angles created when two parallel lines are cut by a transversal.
  • Informally prove that the sum of any triangle's interior angles will have the same measure as a straight angle.

Understanding

Students understand that:
  • missing angle measurements can be found when given just one angle measurement along a transversal cutting through parallel lines.
  • Every exterior angle is supplementary to its adjacent interior angle.
  • parallel lines cut by a transversal will yield specific angle relationships that are connected to the concepts of rigid transformations (i.e. vertical angles are reflections over a point. corresponding angles can be viewed as translations).
Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.38a

Use informal arguments to establish that the sum of the interior angles of a triangle is 180 degrees. [Grade 8, 25]
Mathematics (2019) Grade(s): 8

MA19.8.25

Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.

UP:MA19.8.25

Vocabulary

  • Transversal
  • Corresponding Angles
  • Vertical Angles
  • Alternate Interior Angles
  • Alternate Interior Angles
  • Supplementary
  • Adjacent

Knowledge

Students know:
  • That a straight angle is 180 degrees
  • That a triangle has three interior angles whose sum is 180 degrees.
  • The definition of transversal.
  • How to write and solve two-step equations.

Skills

Students are able to:
  • Make conjectures about the relationships and measurements of the angles created when two parallel lines are cut by a transversal.
  • Informally prove that the sum of any triangle's interior angles will have the same measure as a straight angle.

Understanding

Students understand that:
  • Missing angle measurements can be found when given just one angle measurement along a transversal cutting through parallel lines.
  • Every exterior angle is supplementary to its adjacent interior angle.
  • Parallel lines cut by a transversal will yield specific angle relationships that are connected to the concepts of rigid transformations (i.e. vertical angles are reflections over a point. corresponding angles can be viewed as translations).
  • The sum of the interior angles of a triangle is 180 degrees.
Mathematics (2019) Grade(s): 8

MA19.8.25a

Use informal arguments to establish that the sum of the interior angles of a triangle is 180 degrees.

Primary Learning Objectives

The student will be able to explain the sum of the angles in a triangle equals 180 degrees.

The student will be able to calculate the measure of an exterior angle of a triangle.

The student will be able to calculate the measure of an interior angle when given the exterior and remote interior angle.

Procedures/Activities

Before:

1. As the students enter the room, the teacher will have the bell ringer displayed on the interactive whiteboard, “How can you prove that a triangle has 180 degrees?”

2. After a couple of minutes, the teacher will ask some of the students to respond to the question.

3. The teacher will poll the class to see how many students agree with the given suggestions.

During:

4. The teacher will ask the students to get into groups of three.

5. The teacher will give students a sheet of copy paper. Each group will receive a pair of scissors and three colored pencils or crayons.

6. With a ruler, the students will be instructed to draw a triangle. The group will decide who will draw an acute, obtuse, and right triangle. The students will cut out their triangles.

7. The teacher will instruct the students to color the angles of the triangle with different colors.

8. The student will cut off just the angles.

9. With a sheet of notebook paper, the teacher will instruct the students to place the angles with the point on the blue line. The angles should line up on the line.

10. The teacher will ask the question, “A line has what degree measure?” The response should be 180 degrees.

11. The teacher will elaborate that the angles are along the line, thus the angles together are 180 degrees.

12. The teacher will ask the groups to discuss, “What happens when the triangles are acute, obtuse or right?” The response is that all types of triangles will be 180 degrees.

13. The teacher will use the video on Youtube to review triangles and parallel lines. https://www.youtube.com/watch?v=bBt6IPkZd-8

14. The teacher will hand out the worksheet, "Exterior Angles".

15. The teacher will monitor the students and check with each group to answer any questions. This is the informal assessment.

16. After completion of the worksheet, the students will move out of the groups.

17. The teacher will assign one student from each group to turn in the scissors and colored pencils or crayons.

18. Students will work independently on the worksheet for the formal assessment. The worksheet comes from the website Math Aids. http://www.math-aids.com/Geometry/Triangle/Triangle_Exterior_Angle_Theorem.html

After:

The students will complete an Exit Slip called 3-2-1. They will write the answers on the back of the worksheet. The teacher will write the following on the interactive whiteboard:

3 – List three things that you have learned today.

2 – List two things that you would like to know more about.

1 – Write a question from the material that you did not understand.

Assessment Strategies

Informal:

The teacher will complete an informal assessment as he/she walks around the room monitoring the students. During the lesson, the teacher will randomly select students to determine if the student is engaged and understanding the material.

Formal:

The teacher will create an assessment sheet for the class using the website, http://www.math-aids.com/Geometry/Triangle/Triangle_Exterior_Angle_Theorem.html. The teacher will use the 3-2-1 exit slip to make an assessment about how well he/she presented the lesson.

Acceleration

The accelerated student will be assigned a more challenging worksheet with multi-step algebra problems. The worksheet is called "Exterior Angle Accelerated".

Intervention

Students who require intervention can be placed with a peer-tutor. During the lesson, the teacher can work one-on-one with the students. The teacher does have the option to reduce the number of problems or give the students more time to complete the assignment.

Total Duration

31 to 60 Minutes

Background/Preparation

The teacher will need to preview the websites. The teacher will need to have colored pencils or crayons, scissors, and rulers for students to use. The teacher will need to know the ways to prove the sum of angles in a triangle. The teacher will need to know the culture of the class to keep students engaged during the group project. The teacher will need to know which students are the best peer-tutors. The teacher will click on the link to make original worksheets on Math Aids (http://www.math-aids.com/Geometry/Triangle/Triangle_Exterior_Angle_Theorem.html).

The student will need to know that a line is 180 degrees. The student will need to know how to write and solve multi-step equations. The student will need to know the terms exterior and remote interior angles.

Materials and Resources

Pencils

Three colored pencils or crayons

Notebook paper

Calculator

Exterior Angle with Answers worksheet (make enough copies for all students)

Website to make more worksheets: http://www.math-aids.com/Geometry/Triangle/Triangle_Exterior_Angle_Theorem.html

One sheet of copy paper for all students

Scissors

Technology Resources Needed

https://www.youtube.com/watch?v=bBt6IPkZd-8

The teacher will need to make his/her own worksheets. Just click on the link below and follow the steps on the page.

http://www.math-aids.com/Geometry/Triangle/Triangle_Exterior_Angle_Theorem.html

Desktop Computer/Interactive whiteboard

Students will need a calculator.

Approved Date

2017-06-22
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