Angles with Circles


In our Angles with Circles lesson plan, students learn about how circles and angles are related. Students learn how to measure angles using circles and also learn other relevant lesson vocabulary. They will also learn that the hands of a clock create angles and will learn to identify those angles.

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 students find angles throughout the classroom and draw them inside of a circle.

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What our Angles with Circles lesson plan includes

Lesson Objectives and Overview: Angles with Circles reviews angles, introduces the concept that angles can be measured using circles, and provides relevant vocabulary. It includes the names of several types of angles, such as acute and obtuse, with illustrations and descriptions. At the end of the lesson, students will understand that an angle is measured with reference to a circle such that the center is the common endpoint of the rays and understand that the measurement of the angle is the fraction of the circular arc. 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 supplies you will need for this lesson are straws and a pipe cleaner. To prepare for this lesson ahead of time, you can gather the supplies and copy the lesson materials.

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. One suggested alteration to the activity worksheet is to have students use a paper with many circles on it if no pipe cleaners or straws are available. You can also have them draw or estimate the current time on the clock and name the angle. An optional addition to the lesson would be to have students find angles throughout the classroom and draw them inside of a circle.

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 with Circles

The Angles with Circles lesson plan includes two content pages. The lesson begins with some basic definitions. It states that an angle is a shape that is formed by two lines or rays that start from a common point. We call the common point of the two lines or rays the vertex, and we call each line the side of the angle. The lesson includes a helpful diagram of an angle with vertex, side, and angle labelled. You can measure angles using a circle with a center point. There’s a vertex, or center point, and rays (or sides) that touch the circle at two points. We measure the circular arc between the two places as a fraction of the whole circle, which is 360 degrees (°).

The lesson then illustrates how we form a 360° circle from angles. The degree measurement inside a circle can be anything from 0° to 360°, with a full rotation being 360°. The lesson shows various angles, from 0° to 30° to 135° to 270° to 360°, and many more in between! It also shows circles with 180°, 90°, and 45° from their centers.

Names of Angles

Next, students will learn about the names we use for different angles. These names are based on the number of degrees within a circle. The lesson includes both pictures of the different types of angles and a chart that lists the type of angle and a description. It also notes that you can find angles all around you, like the right angle on the edge of a book.

The types of angles that students will learn about are acute, right, obtuse, straight, reflex, and full rotation. Acute angles are greater than 0° and less than 90°. Right angles are exactly 90°, which obtuse angles are greater than 90° but less than 180°. Straight angles are exactly 180°. Reflex angles are greater than 180°, and full rotation angles are exactly 360°!


The Angles with Circles lesson plan includes three 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.


For the activity worksheet, students will create their own “angle explorer” to use. Students will make this using two straws and a pipe cleaner. They will bend the pipe cleaner and put the straws on either end. You can go over lesson vocabulary and reiterate that angles are formed by two rays sharing an endpoint, like the hands on a clock. You can also have students identify the vertex and the two rays on their angle explorer. Students will then use the angle explorer to create obtuse, acute, right, and straight angles. They will also use it to show time, like they would on a clock, and identify the types of angles formed by each time.


The practice worksheet has students draw the hands on blank clocks based on the time listed next to the clock. They will then identify the angles as acute, right, straight, or acute.


Students will find examples of different types of angles in their home, neighborhood, or online for the homework assignment. They will draw or print out a picture of each. The types of angles they must find are acute, straight, right, reflex, obtuse, and full rotation.


This lesson includes a quiz to test students’ knowledge and understanding of the lesson material. For the quiz, the students will match terms to their definitions. The terms include acute, obtuse, right, side, straight, and vertex.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the quiz. No answer keys are provided for the activity worksheet or the homework assignment. 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

None for Grade 3, LB.Math.Content.4.MD.C.5.A

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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Elham E.


I really loved the lesson plans, it is really detail and guide you perfectly. I could find lot's of lesson plans and sure I will find more.