A Math Forum Web Unit
Tom Scavo's

Lines

Contents || Math Lessons

[Materials] [Length] [Area] [Pick's Theorem] [Dot Paper] [Epilogue]

[Lines] [Squares] [Rectangles] [Parallelograms] [Right Triangles] [Bibliography]

## Find all line segments

### Objectives

• to develop a sense of length on the geoboard
• to associate attributes of line segments with appropriate terminology (e.g., horizontal, parallel, intersecting, perpendicular, congruent)
• to develop a working knowledge of order attributes (e.g., less than, greater than, between) with respect to length of line segments
• to experiment with geometric pattern making

### Materials

• 5 x 5 geoboards (the kind that fit together to make a 10 x 10 geoboard) and rubber bands (various sizes and colors)
• at least five geoboards for the teacher and one for each student
• 5 x 5 geoboard dot paper (two sheets for each student)
• 10 x 10 geoboard dot paper (for extended activities)
• overhead projector; transparent geoboard or dot paper (with marking pens)

### Warm-up activities

1. Make a horizontal line segment that touches 3 pegs. What is the length of this line segment?
2. Make another line segment that touches 3 pegs, but with different length. Is the length of this new line segment less than or greater than the previous one?
3. Can you find a third line segment that touches 3 pegs, but with length different than the other two. Is the length of this line segment less than or greater than the previous ones?
4. Find the shortest line segment on your geoboard.
5. Find the next shortest line segment.
6. Find the longest line segment on your geoboard.
7. Find the next longest line segment.

### Main activity

Find all possible line segments on a 5 x 5 geoboard. (There is a total of 14 such line segments.)

### Homework

Order each of the line segments in the main activity by length. (In order, the 14 line segments have lengths sqrt(1), sqrt(2), sqrt(4), sqrt(5), sqrt(8), sqrt(9), sqrt(10), sqrt(13), sqrt(16), sqrt(17), sqrt(18), sqrt(20), sqrt(25), and sqrt(32) units.)

### Extended activities

1. On a 5 x 5 geoboard, there are five line segments with length greater than 4 units. Can you find them?
2. Find three line segments with length less than 3 units. Are there others?
3. Find two line segments with length between 3 and 4 units.
4. With two rubber bands, make two line segments that touch a total of 9 pegs.
5. Make two parallel line segments that touch a total of 9 pegs.
6. Make two perpendicular line segments that touch a total of 9 pegs.
7. Make two intersecting line segments that touch a total of 9 pegs, but are not perpendicular.
8. Make two congruent line segments that touch a total of 9 pegs. Do these line segments intersect?
9. Make two congruent line segments that touch a total of 8 pegs. Do these line segments intersect?
10. Continue each pattern on a 10 x 10 geoboard:
11. How many different line segments are there on a 10 x 10 geoboard?
12. Order each of the line segments in the previous activity by length.

[Materials] [Length] [Area] [Pick's Theorem] [Dot Paper] [Epilogue]

[Lines] [Squares] [Rectangles] [Parallelograms] [Right Triangles] [Bibliography]

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The Math Forum * * Tom Scavo * * 3 August 1997