Points, Lines, & Planes

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Objective

SWBAT identify points, lines, and planes as two-dimensional and illustrate them.

Big Idea

Points, Lines, and planes are two-dimensional figures that have special attributes.

Opener

5 minutes

In today's lesson, the students learn to identify and draw points, lines, and planes. This aligns with 4.GA.1 because the students will be able to identify these in two-dimensional shapes.  This is an important skill for the students because this is the first lesson in our Geometry unit and it leads into identifying shapes by their lines and angles.  

 To get started, I probe the students to identify things in the real-world that relates to this skill.  "Name things that you have seen that form a straight line."  I let the students think about the question.  "Share your answer with your neighbor."  By doing this it allows students to share their way of thinking, as well as helps some students who do not know how to come up with the answer.  I take a few student responses.   Some of the student responses:  roads, pencils, and poles.  I tell the students, "Today, we will learn to identify and draw points, lines, and planes.  These are basic skills needed to understand geometry."

Whole Class Discussion

10 minutes

I call the students to the carpet as we prepare for a whole class discussion. The Points, Lines, and Planes power point is already up on the Smart board.  I like for my students to be near so that I can have their full attention while I'm at the Smart board.  

I begin by going over important vocabulary for this lesson.  The students will have to know these terms to understand the lesson.

Vocabulary:

A point is an exact location in space.

A line is a straight path of points that goes on and on in two directions.

A plane is an endless flat surface.

Parallel lines never intersect.

Intersecting lines pass through the same point.

Perpendicular lines are lines that form square corners.

Let's see how these things are important to understanding geometry.

Sometimes, students enjoy learning from others instead of listening to their teachers all the time.  Therefore, to the give the students a visual of the skill, I show the students the following:

Points 

Planes 

Lines 

I feel that the videos give the students a real-world sense of points, lines, and planes.  I explain to the students that this is just an introductory lesson on geometry.  We will use this information and expand on it in other upcoming lessons.

Group or Partner Activity

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others.

For this activity, I put the students in pairs.  I give each group a Group Activity Sheet Points, Lines, and Planes. The students are allowed to use their math book to help with the activity.  The students must work together to identify points, lines, and planes.  They must draw the points lines, and planes (MP4).  They must communicate precisely to others within their groups. They must use clear definitions and terminology as they precisely discuss this problem

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students.  From the video,  you can hear the students discuss the problem and agree upon the answer to the problem.  As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill.  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.  

As they work, I monitor and assess their progression of understanding through questioning. 

1. What are the characteristics of this figure?

2. Does it have an end point?  Does it have arrows on both ends?

3. Do they intersect?  Do they form corners when they meet?

As I walked around the classroom, I heard the students communicate with each other about the assignment. From the video, you can hear the classroom chatter and constant discussion among the students. Before Common Core, I thought that a quiet class working out of the book was the ideal class. Now, I am amazed at some of the conversation going on in the classroom between the students.  

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing.

My Observations:

As I walked around to monitor and listen in, I noticed that the majority of the students were doing well with this lesson.  I feel that a big part of this is because of the resources that they were allowed to use.  This lesson was to introduce the students to points, lines, and planes as a basis for future lessons. By having the students draw out the figures, this would help the students remember and understand the concept.  With that being said, one area that a few students need to improve upon is drawing straight lines for the figures.  This will be addressed as we continue working with lines.

Closure

15 minutes

To close the lesson, I have one or two students share their answers.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples Student Work, as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.  

Misconception:

We need to work on drawing straight lines.  In the Student Work, you can see the lines are not straight.  When the student extends these lines, they would meet.  I will work with the students next time by letting them use rulers to draw lines.  Also, I will make sure that the students understand that the lines have to be straight or they will meet when they are extended.