1. How Do Different Rates Affect The Graphs

2. How Do Different Rates Affect the Graphs? Collecting Data – Mark a 12 m segment at 1 m intervals. – Have the 1st walker start at the 1 meter mark from the starting line (position 0) and walk toward the 12 m mark (finishing line) at a speed of 1 m/s. Have the 2 nd walker start at the 4 m mark from the starting line (position 0) and walk toward the 12 m mark (finishing line) at a speed of 0.5 m/s.

3. – Have a timekeeper count 1 second counts out loud. (This does not have to be in real time.) – Have two walkers model the situation on a large number line. – Record both the time and position of the first walker and second walker on a chart.

4. Analyzing the Data – What does the Position of the Two Walkers Template illustrate? What information don’t you observe as the walkers are modeling the situation? What can you observe from the modeling of the situation?

5. Analyzing the Data – What does the data in the Time/Position Chart illustrate? – Did you observe this during the modeling? 0 1 2 3 4 1 2 3 4 5 4.5 4 5 5.5 6 5 6 6 7 6.5 7

6. Analyzing the Data – Enter the data from the Time/Position Chart in the lists of the graphing calculator. L1 = time L2 = position of walker A L3 = position of walker B 0 1 2 3 4 1 2 3 4 5 4.5 4 5 5.5 6 5 6 6 7 6.5 7

7. – Create two scatter plots: one for walker A (L1 vs. L2) and one for walker B (L1 vs. L3). Create a graph. – What is the rate of change of walker A? How does this match what the problem described? – What is the rate of change of walker B? How does this match what the problem described? – Explain how the graph illustrates what was modeled on the number line. – Explain why the two walkers eventually meet.

8. Extending the Question – Keep the starting locations the same as described for walker A and walker B. Suppose that walker 1 walks faster than 1 m/s. Select a new rate of change that is slightly faster. Change the values in your chart and lists. – Conjecture how the graph of will be different. Confirm your conjecture by graphing the new data. How is the rate of change of the walkers reflected in the graph?

9. – Keep the starting locations the same as described for walker A and walker B. Suppose that two people walk at the same speed and direction from their starting positions. Change the charts and lists to reflect that each walker is walking at the same rate. – Conjecture what the graph and table will illustrate in this new situation. Check both the graph and table for this new situation. Explain what the table is illustrating. Explain what the graph is illustrating. Explain what happens with the point of intersection.

10. – Suppose that two people walk at the same speed in the same direction from the same starting mark. Change the charts and lists to reflect that each walker is walking at the same rate of change and starting at the same location. – What does this graph of this situation look like? Explain why the two walkers will never meet.