2.2+++Changing+the+Walking+Rate+10-11

Josh Hufemia May 14, 2011

Big Idea:

Many real world situations can be modeled and predicted using mathematics.

 __ Essential Question #2: What is the relationship between a table, a graph and an equation? __ **Problem 2.2 Changing the Walking Rate**
 * A. In Problem 2.1, each student walked at a different rate. Use the walking rates given in that probem to make a table showing the distance walked by each student after different numbers of seconds. How does the walking rate affect the data in the table?**

The table is affected by the rate in that the meters each student walked increases as the time increases.
 * Time(sec) || Terry(m/sec) || Jade (m/sec) || Jerome (m/sec) ||
 * 0 || 0 || 0 || 0 ||
 * 1 || 1 || 2 || 2.5 ||
 * 2 || 2 || 4 || 5 ||
 * 3 || 3 || 6 || 7.5 ||
 * 4 || 4 || 8 || 10 ||
 * 5 || 5 || 10 || 12.5 ||
 * 10 || 10 || 20 || 25 ||
 * 20 || 20 || 40 || 50 ||
 * 30 || 30 || 60 || 75 ||
 * 40 || 40 || 80 || 100 ||
 * 50 || 50 || 100 || 125 ||

The rate affects the graphs in that each graph is steeper if the rate is higher. Terry: d = t / y = x Jade: d = 2t / y = 2x Jerome: d = 2.5t / y = 2.5x
 * B. Graph the time and distance data for the three students on the same coordinate axes. Use a different color for each students data. How does the walking rate affect the graphs?[[file:save (3).svg]]**Black: Terry ;Red: Jade; Blue: Jerome
 * C. For each student, write an equation that gives the relationship between the time and the distance walked. Let //d// represent the distance in meters and //t// represent the time in seconds. How does the walking rate affect the equations?**

The equations are affected by the rate in that the slope or coefficient of x (or t in this case) is different from the other two equations.

On the table, the time increases only by 1 second. In the distance column, the meters increase by two until 2 seconds, and then by 4 on 3 seconds. After that it increase by 5 meters in one second, and then by four meters in the next second. So because of the change of increase of distance as time went up by one second, I know that if I graph this information, the points will not lie in a straight line.
 * Problem 2.2 Follow-up**
 * While reading a sports magazine, Abby finds the following time and distance data for an athlete in an Olympic race. She wonders whether the data represent a linear relationship. Abby knows that if the relationship is linear, the data will lie on a straight line when graphed.**
 * Time (sec) || Distance(m) ||
 * 0 || 0 ||
 * 1 || 2 ||
 * 2 || 4 ||
 * 3 || 8 ||
 * 4 || 13 ||
 * 5 || 17 ||
 * 1. Use the table to determine how the distance changes as the time increases. How can you use this information to predict whether or not the data will lie on a straight line when graphed?**


 * 2. Describe the race that might have produced these data.**

These data could have been produced by a 50 meter sprint or a 100 or 200 meter run where the the athlete ran slow at the start of the race. But as time was increasing, and the race getting nearer to the end, the athlete started speeding up and then slowed down a little to get the finish line.