Lesson: Points, lines, segments, rays
STUDENTS PERFORMANCE OBJECTIVES:
1. Students will be able to construct and identify points, segments, rays, and lines.
2. Students will measure segments a) using the computer
b) using a ruler (to 1/16 of an inch)
3. Students will be able to explain that an infinite number of lines may pass through
one point; only one line may pass through two points.
CRITICAL MATHEMATICS EXPLORED:
Establishing these geometric terms is critical to later understanding of geometric
shapes. Students need to understand that two points define a line and a segment, that
there is an infinite number of points in a line, that a segment has two endpoints, a ray one
endpoint.
TEKS: 6.7 A,
HOW WILL STUDENTS ENCOUNTER THE LESSON?
First by demonstration by instructor using geometer’s Sketchpad and projector.
On the screen will be points, segments, rays, and lines. These will be identified by
students. (What is this?) as teacher points to different items on screen. If students can
not identify the elements, just say they will know what to call these elements before the
lesson is finished. (Define/reinforce during construction)
Secondly, these items will be constructed (by small groups at computers, if possible)
As the instructor “talks it through” using a projector, having students go through the
construction of point A, a line passing through point A, construction of point B,
construction of points C and D and the construction of segment CD; construction of
segment EG, ray EG, segment HI, ray IH. On the projector, the instructor will start
hiding elements to go from line to segment, questioning students as to what shows.
The third part of this lesson is where students individually draw segments AB, line
CD, ray EF, and ray HG (rays to go in different directions) using the computer as a
learning center.
EQUIPMENT NEEDED:
Geometer’s Sketchpad on individual computers, display system and screen for
instructor; textbook for supplementary practice, directions for computer as a learning
center practice.
QUESTIONS TO ASK STUDENTS:
How many points do you need to construct a line?
Can you have points A, B, and C on the same line?
Must you have points A, B, and C on the same line?
What defines which way a ray points?
How many endpoints does a line have? A segment? A ray?
SUGGESTED HOMEWORK ASSIGNMENT:
Find three instances at home where objects define a line segment.
Find two instances where objects suggest a line (seem to go until out of sight).
Find three separate instances where objects define a point.
Give an example of an object that seems to define a ray.
Supplementary questions in textbook.
EXTENSION/RELATED MATERIALS
Demonstrate how you could use a segment to define a circle.
Why do we say “line” when we mean “segment”, and where is it appropriate to use
the word line for segment?
Discuss a “ray” of light and how long it takes to get from the surface of the sun to the
surface of the earth. (If it is “absorbed” or “reflected”, is it still a ray?)