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Figure 2: Four representations of the Water Tank. Photo by Dan Meyer (2011) used with permission

Act Two: The students request additional infor mation about filling the water tank as they work with their partners to answer the question. Subse quently, dimensions given in the video, and the time it took to fill the tank, are used to find the equation of a line representing the relationship be tween the volume of water in the tank versus time. Some students have time to complete the Sequel , which asks: How long will it take to empty the tank? In this lesson they are exposed to the concept of negative slope as the water tank is emptied. Act Three: The students see the answers and dis cuss and compare their solutions. This discussion includes Sequel values, even though some students did not discover these themselves. Once the stu dents have completed the Water Tank activity, they are introduced to the multiple representations of the linear function (see Figure 2) (Leinwand, 2009). This activity is followed by a Green Screen activity where the students work in pairs to explain various

tomed to problem solving, it is helpful to explain the process and goals of the three act learning mod el before the lesson begins. Students may need to be reminded that they can derive the formula for the area of a regular polygon by breaking the poly gon down into a set of n isosceles triangles, where n is the number of sides, and multiplying the area of one triangle by n . Students may also need to be reminded to keep their units consistent, either sec onds or minutes and either cubic centimeters or ounces.

Activity 2: Using a Motion Detector to Reinforce Slope

This is an activity using a motion detector device to help students connect the rate and type of physical movement to slope.

Supplies:

a) 1 motion detector (often available from the physics teacher in your school). b) 1 copy of the software (free with the motion detector or it can be downloaded from the com pany website). It displays the graph for an ob jects motion as it moves in front of the detector. c) 1 computer d) 1 computer projection unit a) Lesson handout for students to record motion graphs produced in class and to summarize the most important ideas learned from the lesson. The motion detector is connected to the computer and placed on the edge of a chair pointing outward toward an unobstructed path in the classroom (see Figure 3). Per student:

real world graphs by identifying and explaining the meaning of the la bels on the x - and y - axis, the x - and y - intercepts, the slope and a coordi nate pair of their choice. Common Difficul ties and Challenges If students have difficulties because they are unaccus

Figure 3: Student walking in front of a motion detector

Virginia Mathematics Teacher vol. 46, no. 2

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