ALEX | Alabama Learning Exchange

Writing and Solving Equations Using Angle Terminology

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This lesson provided by:

Author:	Morgan Boyd
Organization:	Retirement

General Lesson Information

Lesson Plan ID:	35591
Title:	Writing and Solving Equations Using Angle Terminology
Overview/Annotation:	This lesson will enhance mathematical vocabulary knowledge and reinforce basic skills for solving equations. Mathematical vocabulary is a vital part of this lesson. The lesson will challenge the minds of seventh-grade students with the theory of angles. The student will use the information in the diagram to write an equation and solve for the variable. Terms that will be identified in the lesson are as follows: supplementary, complementary, adjacent, parallel lines and transversal, and vertical angles. This lesson results from the ALEX Resource Gap Project.

Associated Standards and Objectives

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 7

21. Use facts about supplementary, complementary, vertical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure.

Unpacked Content

Evidence Of Student Attainment:

Students:

Find the values of angles using complementary and supplementary angle relationships and equations.
Identify angle relationships in angle diagrams involving vertical, supplementary, and complementary angles.
Write equations to represent relationships between known and unknown angle measurements.
Determine the measures of unknown angles and judge the reasonableness of the measures.

Teacher Vocabulary:

Supplementary angles
Complementary angles
vertical angles
Adjacent angles

Knowledge:

Students know:

supplementary angles are angles whose measures add to 180 degrees.
Complementary angles are angles whose measures add to 90 degrees.
vertical angles are opposite angles formed when two lines intersect.
Adjacent angles are non-overlapping angles which share a common vertex and side.

Skills:

Students are able to:

write a simple equation to find an unknown angle.
Identify and determine values of angles in complementary and supplementary relationships.
Identify pairs of vertical angles in angle diagrams.
Identify pairs of complementary and supplementary angles in angle diagrams.
Use vertical, complementary, and supplementary angle relationships to find missing angles.

Understanding:

Students understand that:

vertical angles are the pair of angles formed across from one another when two lines intersect, and that the measurements of vertical angles are congruent.
Complementary angles are angles whose measures add up to 90^o, and supplementary angles are angles whose measures add up to 180^o.
Relationships between angles depends on where the angles are located.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.7.21.1: Define supplementary angles, complementary angles, vertical angles, adjacent angles, parallel lines, perpendicular lines, and intersecting lines.
M.7.21.2: Discuss strategies for solving multi-step problems and equations.
M.7.21.3: Identify all types of angles.
M.7.21.4: Identify right angles and straight angles.

Prior Knowledge Skills:

Model using a protractor to draw angles.
Draw points, lines, line segments, and parallel and perpendicular lines, angles, and rays.
Define vertex/vertices and angle.

Alabama Alternate Achievement Standards

AAS Standard:
M.AAS.7.21 Classify angles as acute, obtuse, right, or straight.

Local/National Standards:

Primary Learning Objective(s):

The student will write an equation from the given information in a figure.

The student will solve equations using inverse operations.

The student will determine if unknown angles in a figure are supplementary, complementary, or equal.

Additional Learning Objective(s):

The student will be able to label and determine if angles are equal, complementary, or supplementary.

Using the pictures, the student will be able to explain if the sum of the angles is 180 degrees, 90 degrees, or equal.

Preparation Information

Total Duration:	31 to 60 Minutes
Materials and Resources:	Website: Khan Academy https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-unknown-angle-algebra/v/solving-for-unknown-angles "Web 2.0 Scientific Calculator" Web 2.0 is a website that can be saved to Apple or Android devices. If the program cannot be used on the school network, then just use the website. A regular scientific calculator can also be used. Notebook paper Pencil Bell Ringer Angles (place on interactive whiteboard - See attached document) Worksheets that can be made by the teacher are from the website http://www.commoncoresheets.com/Angles.php ("Finding Missing Angles" and "Finding Complementary and Supplementary Angles") Worksheet for Exit Slip Copy for all students -- Exit Angles with Answers (see attached document)
Technology Resources Needed:	Desktop computer with interactive whiteboard for teacher and lesson iPad, Chrome book, or MacBook for all students Web 2.0 Scientific Calculator website Web 2.0 is a website that can be saved to Apple or Android devices. If the program cannot be used on the school network, then just use the website. A regular scientific calculator can be used. Khan Academy Website "Missing Angles" interactive lessons: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-unknown-angle-algebra/v/solving-for-unknown-angles http://www.commoncoresheets.com/Angles.php for worksheets to copy for all students ("Finding Missing Angles" and "Finding Complementary and Supplementary Angles")
Background/Preparation:	Teacher: The teacher will need to preview the video to determine good places to stop and ask questions and allow the students to ask questions. The teacher will need to adjust the vocabulary of the student to the vocabulary of college and career ready standards. Students in different locations may use different vocabulary words for the types of angles. The angles are listed in the bell ringer attachment. The teacher can develop a word wall with the names of the different angles such as complementary angles, supplementary angles, vertical angles, adjacent angles, exterior angles, and remote interior angles. The teacher will need to visit the website http://www.commoncoresheets.com/Angles.php for worksheets for the students ("Finding Missing Angles" and "Finding Complementary and Supplementary Angles"). Student: The student will need to understand the meaning of the following terms: complementary angles, supplementary angles, parallel lines with a transversal, and vertical angles. The student will need to have experience in writing multi-step equations.

Procedures/Activities:

Before:

Bell Ringer:

The teacher will have the bell ringer, “Bell Ringer Angles” (see attached document), on the interactive whiteboard for the students to begin working as they come into the classroom. The teacher will have students to write their answers on the interactive whiteboard. The teacher should encourage students to explain their reasons behind their answers.

During:

Review the vocabulary and illustrations of the different types of angles. The teacher should point out each type of angle and also show the terms on the word wall. The teacher can also have labeled pictures of the angles on the wall.
After the discussion about the angles, the teacher will go to the website for Khan Academy: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-unknown-angle-algebra/v/solving-for-unknown-angles. The students can follow the lesson on their device. The teacher will stop the video and ask questions to see if the students are engaged. The website is interactive and will allow the students to type in their answers.
As the first two sections are being completed, the teacher will show the class how to write an equation to represent the missing measure.
Example: Find the missing measure. Draw a picture of supplementary angles. The angle on the left is x – 48 and the angle on the right is 4x + 53. The problem is asking to find the measure of the angle on the right.

Write the equation (x – 18) + (4x + 53) = 180.
The sum has to be equal to 180 degrees.
Simplify x + 4x and -18 +53.
5x + 35 = 180.
Subtract 35 from both sides.
5x = 145.
Divide both sides by 5.
X = 29
With x = 29 then replace x in the angle on the right.
4(29) +53 = 116 + 53 = 169.
The measure of the angle on the right is 169 degrees.

The teacher will draw a picture of complementary angles and vertical angles. The teacher will label the angles with expressions that he/she can make up.
The sum of the complementary angles will equal 90 degrees.
If the angles make a “v” shape, vertical, then the angles are equal.
The teacher will continue to guide the students through the website and the interactive segments.
The teacher will hand out the worksheets that the teacher located from the website http://www.commoncoresheets.com/Angles.php ("Finding Missing Angles" and "Finding Complementary and Supplementary Angles").
The teacher will read the following instructions for the worksheet: "Use the definitions of the angles to write equations and solve."
If the students need intervention, then the teacher will allow students to work in groups with a peer-tutor.
As the teacher walks around the room, an informal assessment will be taking place. The teacher will be able to work one-on-one with students that need help. Also, the teacher can see if the students are mastering the concept.
As time is drawing to a close, the teacher will select only four problems from each page. The teacher will select at random the eight students to work the problems on the interactive whiteboard. The teacher will make sure the students are explaining each step of the solution.

After:

While the students are checking their work, hand out the exit slip. The exit slip is in the attachments section called "Exit Angles with Answers". The students will turn in the exit slip as they leave the room.

If students finish early, then the assignment is a worksheet called "Early Finishers Angles" in the attachment section.

Assessment

Assessment Strategies

Informal:

The teacher will ask questions to check for understanding of the standard. While visiting the website, Khan Academy, the teacher will select students to come to the Smart board to answer problems. Informal assessments are constantly being made as the lesson is taught.

Formal:

After the students complete the exit slip, the teacher will check for mastery of the content.

Acceleration:	The accelerated students will have a challenging assignment. The problems have multiple variables and steps. The name of the worksheets is Early Finishers (see attached document).
Intervention:	The intervention for the students is to allow more time to complete the worksheets. The students can work in groups of 3 or 4 students. The teacher can assign an accelerated student to be the peer tutor for the group. The teacher can also modify the assignment by removing some of the questions.

View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.

ALEX Lesson Plan

Writing and Solving Equations Using Angle Terminology