Points and Lines

Grade Level: 4 – 6

Teacher Guidelines ▶ pages 1 – 2

Instructional Pages ▶ pages 3 – 4

Activity Pages ▶ pages 5 – 8

Practice Page ▶ page 9

Homework Page ▶ page 10

Answer Key ▶ pages 11 – 12

1

Classroom Procedure:

1. Ask students to give examples of the lines they can observe in the classroom.

2. Allow for responses and discussion.

3. Ask if they know the difference between the lines. Review the terms vertical and horizontal.

4. Allow for responses and discussion. Introduce points and lines.

5. Distribute Points and Lines content pages. Read and review the information with students. Use additional resources and activities to enhance understanding.

6. Review the symbols used for showing a line segment and a line.

7. Distribute the Activity page. Review the instructions with students. Distribute scissors. Allow students time to cut apart figures.

8. The teacher will randomly instruct students to create points and lines using the figures. Allow a student volunteer to show their work for each figure.

9. Check student’s work while circulating through the room.

10. Allow students to exchange ideas with a partner to make a type of line, segment, etc.

11. Distribute the Practice page. Check and review the students’ responses. Allow volunteers to share responses.

12. Distribute the Homework page. The next day, check and review the students’ responses.

13. In closing, distribute a blank white sheet of drawing paper and a ruler to each student. Give them time to create a pencil drawing/design using only points and lines.

14. Allow students to display their final drawings and to identify some of the points and lines.

Approximate Grade Level: 4 – 6

Objectives: The students will be able to identify, name, and draw points, lines, line segments, rays, and perpendicular and parallel lines. Identify these in two-dimensional figures.

Common Core State Standards: CCSS.Math.Content.4.G.A.1

Class Sessions (45 minutes): At least 2 class sessions

Teaching Materials/Worksheets: Points and Lines content pages (2), Activity pages (4), Practice page, Homework page

Student Supplies: scissors, ruler, drawing paper, handouts

Prepare Ahead of Time: Prepare some instructions for the activity based on time allotted and students’ abilities. Copy handouts.

Options for Lesson: Students may work in pairs for the activity. Take students outdoors to discover lines and points in nature, drawing what they observe. Laminate the students’ activity cut-outs for future use or for taping and removing onto or from a piece of cardboard or other background. Introduce other shapes made of line segments and lines.

2

Teacher Notes

In the lower grades, most students have been introduced to points and lines informally, but this lesson will help students identify and name the different points and lines in geometric figures. The lesson also helps students recognize the difference between perpendicular and parallel lines, and introduce intersecting lines. Understanding lines will help students with other geometry concepts. The objectives are for fourth grade students, but can be used and adapted for higher levels.

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Additional Resources:

Content: http://www.basic-mathematics.com/basic-geometry.html http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/line_shoot.htm (Interactive) https://www.mathsisfun.com/geometry/index.html (Interactive) http://math.pppst.com/points-lines-planes-angles.html (PPT options) https://www.splashmath.com/math-skills/fourth-grade/geometry/lines-rays-and-line-segments

Worksheets: http://theteacherscafe.com/teaching-4-g-a-1-draw-points-lines-line-segments-rays-angles-right-acute-obtuse-and-perpendicular-and-parallel-lines/ (and more) http://www.mathworksheetsland.com/topics/geometry/segmentsset.html http://web.cerritos.edu/dford/SitePages/Math_70_F13/Worksheet-pts-lines-planes-angles.pdf http://www.mathworksheets4kids.com/straight-lines.php http://www.commoncoresheets.com/Lines.php

Videos: https://learnzillion.com/lesson_plans/4667-identify-points-lines-line-segments-and-rays (5 min-and geometric figures) https://www.youtube.com/watch?v=NytgqC81iCo (13 min) https://www.youtube.com/watch?v=k5etrWdIY6o (8 min) https://www.youtube.com/watch?v=P3AOoLbA3us (2 min-Song, lines) https://www.youtube.com/watch?v=7U2Tk2_7F1Q (4 min-Lines) https://www.youtube.com/watch?v=4jIb2ZWFHm0 (2 min-Lines) https://www.youtube.com/watch?v=IKEihM7tthw (3 min-Lines)

3

Points and Lines

When you awoke this morning your location was at home. Now, you are in a new location, the school. Throughout the day you will be moving to several other locations too. Each location is called a point. A point is a geometric term for a location in space. In geometry each point in space is represented by a letter and a dot as shown in the very short map below. Point A is your home; Point B is the school.

The arrows at the end of a line indicate the line can go on forever. If you walked past the school, you could walk forever in a straight line, and instead of stopping at your home after school, you could go on forever in the other direction. Every line has a name, and the line above is Line AB or Line BA (AB).

However, since you did start from home and ended at the school you actually walked a line segment. A line segment is a part of a line that has two endpoints. A and B are the endpoints in the line segment above. When you start at home and walk to school it is line segment AB (𝐀𝐁̅̅ ̅̅ ), for the trip home, it is called line segment BA.

Here are more examples of points, lines, and line segments: POINTS: Points C, D, K, P

LINES:

X Line XY Y S Line ST T

LINE SEGMENTS:

Line segment CD Line segment KP

Every point, line, and line segment can be named. There is also one other type of line called a ray. A ray contains one endpoint and extends forever in one direction. Think about your home being the endpoint and your path into outer space goes on forever like this:

A

B

C. .D K. .P

C. .D K. .P . . . .

4

PERPENDICULAR INTERSECTING LINES PARALLEL LINES

Parallel lines are two or more lines that will never meet in space or on a plane. It does not matter how long the lines are, they will never meet. An example are the vertical lines in each corner of the room.

Intersecting lines do the opposite of parallel lines. They will meet or cross in space or on a plane. Sometimes intersecting lines look as if they will not meet, but if they both continue on forever, they will meet.

Perpendicular lines meet at right angles, like those in the corners of the classroom. A line that meets another line at a right angle is called a perpendicular line. Other examples include lines in a square or rectangle.

Planes

Another term you will read about in geometry is a plane. A plane is simply a flat surface, like a piece of paper, that goes on forever in all directions:

Points and lines are everywhere. There are lines running along the corners of a room, on the sides of a computer screen, and a line is used to cut across the center of a pizza. You can draw many lines simply by connecting any two points. Some lines cross each other, some do not, and there are some that connect at 90 degree angles like in the corners of a room.

There are three basic types of lines:

Different types of points and lines are used by architects, builders, engineers, artists, and nearly everyone else in the world for an infinite number of purposes. You most likely have used points and lines when drawing a picture. Every time you write the letter X you draw intersecting lines. The letter H includes parallel lines, and the letter T is an example of perpendicular lines. Lines and points are everywhere.

How many different types of lines can you identify in the photo?

5

Activity Name __________________________ Date ________

Instructions

1. Cut apart each of the points and lines.

2. Create the different types of points, lines, and line segments using the cut-outs.

3. Draw and label your points, lines, and line segments using the spaces provided.

4. The teacher will then give instructions to create more points, lines, and line segments.

5. Be prepared to share with the class.

Label your lines, segments, etc.

6

7

A B C D

8

E F

9

Practice Name __________________________ Date ________

1 Intersecting Lines A

2 Line B

3 Line Segment C

4 Parallel Lines D

5 Perpendicular Lines E

6 Plane F

7 Point G

8 Ray H

11 14

.

.10 13 16

9 12 15

Lines that meet at right angles.

Lines that meet or cross in space or on a plane.

Match the term with the correct definition.

Write the name for each of the following figures:

.

A flat surface that goes on forever in all directions.

Contains one endpoint and extends forever in one direction.

Collection of points that could extend forever in either direction.

A location in space.

Two or more lines that will never meet in space or on a plane.

A part of a line that has two endpoints.

10

Homework Name __________________________ Date ________

11

ANSWER KEY

Practice Name __________________________ Date ________

1 H Intersecting Lines A

2 C Line B

3 F Line Segment C

4 E Parallel Lines D

5 G Perpendicular Lines E

6 A Plane F

7 D Point G

8 B Ray H

10 Perpendicular Lines 13 Line Segment 16 Parallel Lines

11 Line 14 Plane

9 Ray 12 Intersecting Lines 15 Point..

A part of a line that has two endpoints.

Lines that meet at right angles.

Lines that meet or cross in space or on a plane.

Write the name for each of the following figures:

.

Match the term with the correct definition.

A flat surface that goes on forever in all directions.

Contains one endpoint and extends forever in one direction.

Collection of points that could extend forever in either direction.

A location in space.

Two or more lines that will never meet in space or on a plane.

12

ANSWER KEY

Homework Name __________________________ Date ________

T V X

A Q

A C

X P

C Y

R S

D E

A B K

L

C D

C D

Two lines intersecting two other

lines

Two parallel lines perpendicular

to line segment CDOne point labeled M Two rays making an angle

M

A planeTwo parallel lines intersecting

one line

Make a square using Line

segments AB, CD, AC, BD

Show point J and point K on a

line

Three parallel lines A ray perpendicular to a lineThree points connected by three

line segments

Parallel line segments labeled

RS and DE

Sketch and correctly label each of the following.

Three points in space, labeled T,

V, and XLine AC Line segment FG

Intersecting lines, one XY, the

other PQ