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segments, it is not unusual for students to incorrect- ly visualize each line segment as a type of terrain on which Joe travels. For example, they might interpret a line segment with an increasing slope as Joe climbing a hill and a negative slope might be interpreted as Joe descending a hill. Additionally, a line segment with a zero slope may appear to repre- sent level ground. Once the observation process has been completed, I present information on the definition of a slope, the formula to find the slope of a line, and an explanation of how to find the slope of a line segment using the “rise over run” process. I then ask students to work in groups to complete a table of questions related to finding the slope of each line segment. They are asked to: determine whether each line segment represents an increas- ing, decreasing or zero slope; name the direction Joe is walking (away from his dorm, toward his dorm or standing still); and find the slope of each line segment on the “Stories and Slopes” graph using the slope formula that was introduced and the process to find the “rise over run.” Students are reminded to label their answer as a rate of change (feet/minutes). The goal of the activity is to help students gain a stronger understanding of the rate of change in distance (Y 2 -Y 1 ) over the change in time (X 2 -X 1 ). The questions and the solutions are shown below. To solidify the concept, students are then asked to create a story that describes the adventures

that the fictitious college student, Joe, encounters on his journey to his math class. They are instruct- ed to tell Joe’s story by interpreting the slopes of the line segments on the graph. To give students a starting point, the first sentence with a fill-in space for Joe’s rate of change is presented in the instruc- tions. Together, they work in groups to tell Joe’s story using the slope of each of the six line seg- ments on the graph as a basis for each related sen- tence. To include all members of the group, each student in the group must create (and share) a de- scription of at least one of the six legs of Joe’s journeys. Students collaborate with their group members to write their story of Joe’s journey and share it with the rest of the class. Through this activity, I have observed that students tend to gain a stronger and more concrete understanding of the concept of slope and rate of change. Positive and negative slopes seem to be more easily identified by students as they make the connection of Joe moving towards his math class with a positive slope and Joe travelling back to his room with a negative slope. Students are also in a position to better comprehend a “zero” slope and recognize that the horizontal lines in the graph depict Joe standing still since he is not traveling a distance while time is still continuing to pass. Perhaps, the most unexpected benefit that I discovered through the inclusion of this activity was the level of student engagement in the story- telling component. Telling stories allows us to

Stories and Slopes

1. Answer the following questions. Place your results in the table: a. Determine whether each segment is increasing, decreasing or constant b. Determine in which direction Joe is walking for each segment. c. Find the slope of each segment. Be sure to include units in your answers.

Segment

Inc/dec/constant

Direction Joe is walking

Slope (label ft/min)

1

Increasing

Away from Joe’s dorm room

(40 ft)/(2 min) = 20 ft/min

2

Constant

Standing still

(0 ft)/(2 min) = 0 ft/min

3

Walking back to Joe’s dorm room

Decreasing

(-40 ft)/(2 min) = -20 ft/min

4

Constant

Standing still

(0 ft)/(2 min) = 0 ft/min

5

Increasing

Away from Joe’s dorm room

(30 ft)/(3 min) = 10 ft/min

6

Increasing

Away from Joe’s dorm room

(100 ft)/(2 min) = 50 ft/min

Virginia Mathematics Teacher vol. 44, no. 1

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