Plane Figures: Two Straight Lines Lying in a Plane - Coplanar Lines

Age

6-9.

Materials

• Box of sticks
• Supplies
• Board
• Figures of children
• Red arrows
  

Presentation

First Presentation:

1. Identify the board as a plane.
2. Place a stick on the board and identify it as a line belonging to the plane.
3. We've already explored everything we can about this straight line.
4. Let's see what happens when we add another straight line.
5. Put another stick on the board so that it neither touches or crosses the first.
6. We have two coplanar straight lines; they both belong to the same plane (coplanar: Latin con, together, planus, plane; thus lying in the same plane).
7. One stick is fixed to the board horizontally.
8. Taking two small equal sticks, these are the key to the story.
9. Place them perpendicularly along one side of the first stick.
10. Move the second stick toward the first until it meets the guide sticks and fix it there.
11. Remove the guide sticks, but leave them nearby to remind the child of their importance.
12. Place the two indifferent children on either sides of the lines so that they are walking in the same direction.
13. The expressions on their faces show indifference.
14. It is as though they don't even know each other.
15. Move the figures along to the end of the line and turn them over; make them walk back.
16. They are like two people walking on opposite sides of the street.
17. They don't care to know each other. each one stays on his own sidewalk and they will never have the chance to meet.
18. We can extend these straight lines to infinity (add sticks of the same color, fixing them with the guide sticks until the lines go off the board in both directions) but these two lines will never meet.
19. Substitute the red arrows for the two children.
20. These two lines are parallel.
21. They never meet no matter how far we follow them because they are always the same distance apart (parallel: Greek parallelos < para, beside, and allelon, of one another; thus one thing beside another)

Second Presentation:

Parallel lines are parallel independently of their position

1.  Invite the child to construct two parallel lines and then to identify their position: horizontal.
2. Ask the child to construct two vertical parallel lines and then two oblique parallel lines using the same process as before.
3. All are parallel regardless of their position.
4. Remove two pairs of parallel lines.
5. Rotate the plane in its horizontal position as the child identifies the position...horizontal...oblique....vertical...etc.
6. Whenever we draw two parallel lines, the lines are also horizontal, vertical, or oblique.
7. Construct a series of parallel lines, using the same guide sticks or a pair of longer guide sticks.
8. These are called "fascial lines" because this was the symbol of fascism, first used be Julius Caesar and later by Benito Mussolini.

Variation

Find parallel lines in the environment - door frames, fence rails, telephone wires, rows in the garden, railroad tracks.