Linear Objects

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Warm-up

Stations

Wrap-up

Homework

Student Work Example

Objectives

· The student will be able to (TSWBAT) identify and construct lines, segments, and rays.

· TSWBAT identify and construct lines, segments, and rays as parallel, perpendicular, and skew.

Key points

Link to GSP file of Linear Objects

· Lines – infinite in length, continue “forever” in two directions, identified by two letters and corresponding symbol,

· Segments – finite in length, the part of a line between two endpoints, identified by two letters and corresponding symbol,

· Rays – infinite in length, continue “forever” in one direction, identified by two letters and corresponding symbol,

· Parallel – two lines are parallel if and only if they are coplanar and never intersect

· Perpendicular – two lines are perpendicular if and only if they intersect in a right (90˚) angle

· Skew – two lines are skew if and only they never intersect and they are not coplanar, skew lines are possible in three-dimensional space

Warm-up (5-10 minutes)

For each object, find and sketch two examples in Mrs. Love’s classroom.

1. Point

2. Line

3. Plane

4. Angle

Sample answers

1. Pencil eraser, pencil point, dot on the board, decimal point, pupil (eye), freckle

2. Flagpole, pencil, pen, table leg, stripes, edge of the board

3. White board, overhead screen, desk, poster, window, wall

4. Corner of the room, flagpole and board, overhead arm, chair seat and back

Stations (10 minutes each)

1. Using Geometer’s Sketchpad (GSP), create a picture to demonstrate your understanding of the basic geometric constructions. Your picture must include at least two (2) of each of the following:

a. Parallel lines

b. Perpendicular lines

c. Segments

d. Rays

e. Angles

(see linked example of student work)

2. Using only a compass and straightedge, construct the following:

a. Two parallel lines (p. 268)

b. Two perpendicular lines (p. 267)

c. Two congruent segments (p. 261)

d. Two congruent angles (p. 265)

3. Using the graphing calculator, determine the relationships of the slopes of parallel and perpendicular lines. (see linked investigation)

4. Using the materials provided, create a three-dimensional model of skew lines.

Materials: Spaghetti, string, straws, coat hangers, tape, paper, cardboard, transparency sheets

Wrap-up (5-10 minutes)

As a group, choose one product from each station to present at the beginning of class tomorrow. Each product must be from a different student. As a group, you should scan the compass and straightedge constructions and any hand-written work from your parallel/ perpendicular investigation. You should upload all calculator investigations to your desktop folder. You should also take two (2) digital photos of your three-dimensional skew model, one with just the model and one showing all group members.

Homework

Journal entry: Where do you see parallel and perpendicular lines in the “real world”? How would you explain to a new student the differences between lines, segments, and rays? Be prepared to enter your responses on the computers tomorrow.

p. 14 – 15: 13 – 17, 26 – 30

Student work example

Station 1

Return to Carol Love's Lesson Plan

Return to Carol Love's EMAT 6690 Page

Return to EMAT 6690 Page