Lines, Rays, and Angles
Modeling and describing lines, rays, and angles are part of the 3rd Grade Geometry section of the West Virginia Contents Standards and Objectives. I have chosen to focus on these three specific concepts because lines, rays, and angles are commonly used in geometric applications and reasoning. The instructional methods that I have chosen in this lesson will fulfill two West Virginia Content Standards and Objectives in Geometry.
II. Goals and Objectives
A. Instructional Goals: Students will be able to model and describe lines, rays, and angles
B. Specific Objectives: Students will be able to accurately describe parallel and perpendicular lines. Students will also be able to understand that two rays joining together in a vertex make an angle. At the completion of this lesson, students should be familiar with the terms in order to create their own lines, rays, and angles.
C. West Virginia Content Standards and Objective: Standard 3: Geometry
MA 3.3.5 Model and describe lines and rays
MA 3.3.6 Identify and draw right, obtuse, and acute angles
III. Essential Question(s): None
A. Lesson Introduction
Children will sit around the teacher while he or she reads the book: Pigs on the Ball by Amy Axelrod
This book will briefly introduce the basic concepts of geometry.
B. Lesson Development
1. After the completion of the book, teacher can ask the students questions about the book. Teacher can also use this time to relate the story to today's geometry lesson: lines, rays, and angles.
Lines: Parallel and Perpendicular
Line: goes on forever in both directions
Ask the students if they can name a line.
Examples: Lines on the highway
Parallel Lines: two lines (that go on forever) beside each other that never intersect or touch each other
Example: Lines on the highways
2. After the completion of the discussion (above) over lines and parallel lines, the teacher can pass out 2 Twizzler strips to each student. Explain to the students that they will be using these 2 Twizzler sticks to show what parallel lines look like. Note: The samples should not intersect.
3. Once the students understand what parallel lines are discuss perpendicular lines.
Perpendicular lines are two lines that intersect or cross to make right angles. Tell the students to make a "T" with their Twizzler strips
4. Use the next few minutes to reinforce the concept of lines by asking the students questions about what has just been covered. Ask students to describe and make examples in their own words of what lines, parallel, and perpendicular lines are.
5. Finally, allow the students to eat their Twizzlers.
Rays, Angles: Acute, Right, and Obtuse
6. For the next lesson, have the students sit around the teacher while he or she asks the students questions about rays and angles from the book. Question the students to see if anyone knows or remembers what rays and angles are.
Ray: has one endpoint and goes on forever
Teacher then can draw a ray on the board.
Ask the students to compare a line and a ray.
What is the difference?
Angle: is the joining of two angles together at the vertex
Teacher can draw an angle on the board.
Ask the students if they can look and find anything around the room that is an angle. If the students do not find anything, the teacher can find many examples in the classroom.
Ask the students how a ray and an angle are similar?
How are they different?
7. Explain to the students that there are many types of angles. However, today we are only going to learn about acute, right, and obtuse angles.
Acute: angle that measures less than 90 degrees
Right: angle that measures exactly 90 degrees
Obtuse: angle that measures more than 90 degrees
8. Give each student a pipe cleaner that they can manipulate to make the three types of angles. Reinforce the fact that an angle is composed of two rays with one endpoint that is the vertex.
9. Once each student has a pipe cleaner:
Direct each student to hold the pipe cleaner flat
Tell each student to work with their neighbor to make a parallel line
Tell each student to work with their neighbor to make a perpendicular line
10. Explain to the students that acute angles are smaller that right angles and that right angles are smaller that obtuse angles. Show them the pictures of characters from a handout which reinforces the definitions of these terms.
11. Have the students manipulate the pipe cleaners to make acute, right, and obtuse angles. The students will enjoy manipulating the pipe cleaners as they develop a greater spatial sense with this lesson.
C/F. Lesson Closure/List of Questions
12. As a review and a closure for this lesson, the teacher can ask the students the following questions over the material covered.
Does a line have a beginning or an end?
Lines go on forever so therefore they do not have a beginning or an end.
Can someone show me an example of parallel lines?
Parallel lines are two lines that go on forever and never intersect.
Can someone show me perpendicular lines?
Perpendicular lines are two lines that intersect like a "T" to make right angles.
Can someone show me a right angle?
Can someone show me an acute angle?
Can someone show me an obtuse angle?
13. Finally direct the students back to their seats, where the entire class will complete a worksheet together.
E. Lesson Contingency
If there is additional time, teacher can pass out a worksheet that the students can complete on their own to test their understanding of lines, rays, and angles. Teacher can also choose to play a fun game with the students to reinforce lines, rays, and angles.
V. Daily (Formative) Student Assessment
Listen to the different responses of the students.
Watch the students to see that they are accurately participating and correctly completing the concept or concepts being taught
Constantly quiz the students verbally over the concept that was just taught in order to keep them involved.
Use worksheets and fun activities to assess individual students learning
VI. Materials, Equipment, and Resources
A. Readings: Pigs on the Ball by Amy Axelrod
B. No outside facilities will be needed for this lesson
C. There is no procedure for bringing people into class and/or visiting community events, people, or places.
Note: Other materials needed are Twizzlers, Worksheets, Activity Worksheets, and Math Games