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2.2 TeachingWith strong middle-grades focus on linearity, students should learn about the idea that slope represents the constant rate of change in linear functions and be ready to learn in high school about classes of functions that have non-constant rates of change. NCTM Standards 2000, page 40Suppose a student asks you if the slope of a line is like the slope of a hill. Write a response to this question. List several “every day” (non-mathematical) examples of the word slope. Compare these uses of slope to the mathematical use of the slope of a line. What are some similarities and differences? 2.2 Concepts As they progress from preschool through high school, students should develop a repertoire of functions. In the middle grades, students should focus on understanding linear relationships. NCTM Standards 2000, page 38Eldino always walks at the same speed. One day she walked in the park from point A to point B in 5 minutes (B is 300 feet east of A and 400 feet north). There she stopped for 3 minutes to look at the view. Then she walked from B to C in 10 minutes (C is 600 feet east of B and 800 feet north). Sketch the following two graphs of her trip: (1) graph the east distance along the x-axis and the north distance along the y-axis; and (2) graph the time along the x-axis and the distance along the y-axis. Discuss similarities and differences in the information from these two graphs. 2.2 Concepts A car travels at the constant speed of 60 miles per hour for 3 hours. Sketch the following three graphs, each of which have time on the x-axis: (1) distance on the y-axis; (2) speed on the y-axis; and (3) acceleration on the y-axis. Discuss the information shown by each graph. Create a question for each graph that could be answered by using that graph. |