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Investigating Proportional Relationships via a cool Laser Activity

Fortunately, I got involved with one of the group for Math Night at Clark Middle School, 1235

Baxter Street, Athens on 01.15.2013. Math Night is a community outreach program funded by

NCTM organized by Mathematics Education Student Association (MESA) of The University of

Georgia. Math Night includes collaboration between graduate students and pre-service teachers,

the school math coach and mathematics teachers to host an evening for students to come with

their parents and both participate in mathematics related activities. All the activities are aligned

with the Common Core State Standards for Mathematics.

Our group prepared an activity for 8 graders. The theme of the activity was to investigate

proportional relationships and to make connections between the graph and algebraic equations.

Below is the lesson plan:

Laser Activity for Proportional RelationshipsJiyoon Chun, Sayonita Ghoshhajra, Hamilton Hardison, Kassie Smith

Grade Standard

8 8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare

two different proportional relationships represented in different ways. For example, compare a

distance-time graph to a distance-time equation to determine which of two moving objects has greater

speed.

Materials:Each group of two to four students will need two yardsticks, masking tape, the attached handout,

and a laser pointer. The laser pointer must be capable of projecting a line segment instead of themore common dot. A calculator is considered optional for this activity.

Logistics:Place one end of a yardstick on the floor and tape it to a wall (or to the edge of a table). The

yardstick should be perpendicular to the floor. Students should place the laser flat against the

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yard stick so that the end of the laser that emits light is five inches from the floor. The laser

should be rotated so that the line segment of light projected onto the floor is parallel to the wall.Another student should use a second yardstick to measure the length of the beam projected on

the floor.

Students should repeat this procedure when the height of the laser is 10 and 15 inches. Students

should record measurements in the table in the attached worksheet. Points for each ordered pair

can be plotted on the attached coordinate system. Students can take turns measuring the beam,

recording the measurements, and holding the laser.

After documenting three ordered pairs, students should make a prediction for the length of the

beam that will be projected on the floor when the laser is 12 and 20 inches high. After recordingtheir predictions, students should investigate the accuracy of their predictions through

measurement. The height and measured length ordered pairs should also be recorded on the

table and coordinate system.

Students should predict the length of the beam projected on the floor when the laser is 100 inches

high.

Students should predict the height of the laser when the length of the laser is 20 inches and 150

inches. Students may check their prediction for 20 inches via measurement.

At this point in the activity, students should try and relate the height of the laser and the length ofthe beam projected using an equation.

Possible Extensions:Students might repeat the activity with the laser rotated so that the beam is perpendicular to the

wall. It is up to the students to decide whether to include the portions of the beam projected ontothe yardstick and the floor or to include only the portion projected onto the floor.

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Tape a square onto the wall and challenge four groups of students to predict an appropriate

distance away from the wall so that when they turn on their lasers they can form a square withthe line segments projected onto the wall. As different lasers will result in different linear

equations, students will be standing at different distances from the wall. Note that height and

angle at which the lasers are held must be considered.

Activity Sheet:

The length of the beam projected on the floor varies according to the distance from the floor to the tip of a

laser.

H: distance from the floor to the tip of a laser

L: the length of the beam projected on the floor

1. Please measure L where H is 5, 10 and 15 inches. Fill in the blanks of the table below and plot the

corresponding points on the graph paper.

H L

5

10

15

2. Based on the measurements in the table above, predict the length of the beam when H is 12 and 20

inches. Check the accuracy of your prediction by measuring the length of the beam for 12 and 20 inches

high.

H Prediction of L Measured L12

20

Were your predictions close to the measurements?

Describe the process that you used to make your prediction?

Can you predict L when H is 100?

3. Predict H when L is given as 20 and 150. After the prediction, you can check your prediction by

measuring H when L is 20.

H L

20

150

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4. Let H is h. Then what amount of H will be L?

H L

h

Can you express the relationship between H and L using an equal sign?

A graph paper was provided, so that students can see the relationship between height and the length.

5555 10101010 1 51 51 51 5 2 02 02 02 0 2 52 52 52 5 30303030 35353535

5555

1 0101 010

1 5151 515

2 0202 020

2 5252 525

3 0303 030

3 5353 535

Height

Length