Angles and Equations


Our Angles and Equations lesson plan teaches students different ways that angles can be used to find missing angles in equations. Students also learn how to use addition and subtraction to find the measure of an unknown angle.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to have groups of students make their own angle problems using a protractor and various shapes; they can then swap them with another group’s problems and solve them.

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What our Angles and Equations lesson plan includes

Lesson Objectives and Overview: Angles and Equations explores different ways angles can be used in equations to find missing angle measurements. The lesson focuses specifically on adding and subtracting angles. At the end of this lesson, students will be able to use addition and subtraction to find the measure of an unknown angle. This lesson is for students in 4th grade and 5th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the orange box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The only supplies you will need for this lesson are charts of angles for the activity worksheet. To prepare for this lesson ahead of time, you can copy all of the materials and handouts and copy the shapes for the activity worksheet and draw in angles.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. For this lesson, one optional addition is to have groups of students make their own angle problems using a protractor and various shapes; they can then swap them with another group’s problems and solve them. You can also have older or more advanced students learn about the sum of interior angles and have them add up the sum of the interior angles for all of the shapes used during this lesson. Finally, you can have students solve more challenging problems alongside you where you add and subtract using three angles.

Teacher Notes

The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.


Angles and Equations

The Angles and Equations lesson plan includes two content pages. The lesson begins with a quick review of some information students will have already learned from a previous lesson about angles. It reiterates that a circle has 360 degrees but can be broken up into many different angles of different sizes. All of these angles added together equal 360. You can add angles together to make larger angles or divided to make smaller ones. You could also use addition and subtraction to find missing angles. You can find angle measurements using mathematical equations. We can use a variable to represent the missing angle.


Students next learn about how they can use addition to find the total number of degrees in an angle. The lesson includes some helpful diagrams and figures of angles to illustrate this concept. You can add together adjacent angles, or angles that are next to each other but don’t overlap, to make a larger angle. You can also add adjacent angles together to find the sum of the larger angle. Additionally, you can add two or more angles together for the sum of the largest angle. You can add angles if they’re independent from one another or adjacent. The lesson also notes that geometry actually uses the additive properties of angles a lot!


Students finally learn about subtraction in relation to angles. You can subtract the measurement of a smaller angle from the measurement of a larger angle in order to find the missing measurement. The lesson includes two helpful examples to illustrate this along with diagrams of shapes and angles. One of the examples shows how to solve for a missing angle in a shape. In the example, a square is shown with a line running diagonally through it. The angle on one side is marked 45°, and the angle on the other side is marked x. 45°plus x is the total measurement of the larger angle, a square has four right angles, and a right angle is equal to 90 degrees. Therefore, you can come up with the right equation to solve for x, which equals 45°!


The Angles and Equations lesson plan includes four worksheets: an activity worksheet, a practice worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.


Students can work either alone or in groups for this activity. For the activity worksheet, you will need to either provide each student with a copy of the chart showing shapes and the measurements of a single side angle of that shape or display it at the front of the room. You will also print out the shapes, draw angles with measurements, and give them to the students. They will then determine the missing angles. Students will identify the shape, find the angle measurement on the chart, and then solve for the missing measurement.


For the practice worksheet, students determine the value of x in ten different problems.


The homework assignment asks students to look at figures and both write the equation and find the missing angles.


This lesson plan also includes a quiz to test the students’ knowledge and understanding of the lesson material. For the quiz, students solve two problems where they have to determine the value of x.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet, the homework assignment, and the quiz. No answer key is provided for the activity worksheet. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

Additional information


4th Grade, 5th Grade



State Educational Standards

LB.Math.Content.4.MD.C.7, None for Grade 5

Lessons are aligned to meet the education objectives and goals of most states. For more information on your state objectives, contact your local Board of Education or Department of Education in your state.

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Nice product

A very good product that helps your kids learn about angles and equation.