2.2+Day+2+Atlantic+City+to+Lewes+0910

A.A Math 7B 08/28/09 INV 2 Essential Question: What are some situations that we can describe as variable?
 * Big Idea: Observation and description of changes in the world around us are the first steps in finding and learning about patterns. **


 * Time (hours) || Distance (miles) ||
 * 0 || 0 ||
 * .5 || 8 ||
 * 1 || 15 ||
 * 1.5 || 19 ||
 * 2 || 25 ||
 * 2.5 || 27 ||
 * 3 || 34 ||
 * 3.5 || 40 ||
 * 4 || 40 ||
 * 4.5 || 40 ||
 * 5 || 45 ||

 2.2 A. **Make a coordinate graph of the (time, distance) data given in the table above.** B. **Sidney wants to write a report describing day 2 of the tour. Using information from the table or the graph, what would she write about the days travel? Be sure to consider the following questions:**

· **How far did the group travel in the day? How much time did it take them? ** · **During which time interval(s) did the riders make the most progress? ** · **Did the riders go further in the first half or the second half or the second half of the day’s ride ** The group was going okay from 12:00 to 1:00, doing 7 and 8 miles per half hour (that was their fastest), then they slowed down at 1:00, doing around 4 miles each half hour. They pushed it until 3:30, when they rested for an hour. There were only 5 miles left until the campsite. They had traveled 45 miles in 5 hours. The break took up almost half of the day, so you can say that they traveled faster during the first half of the day.

C. **By analyzing the table, how can you find the time intervals when the rides made the most progress? The least progress? How can you find these intervals by analyzing the graph?** On the table, you can subtract from each pair (ex. 8-0, 15-8, so on). On the graph, you can look at how spaced the points are and how steep they go up.

D. **Sidney wants to include either the table or the graph in her report. Which do you think she should include? Why?** I think she should include the graph, so that people can see the shape and patterns.  2.2 Follow-Up

1. **Look at the second point on your graph as you count from he left. We can describe this point with the //coordinate pair// (0.5, 8). The first number in a coordinate pair is the value for the //x-//coordinate, and the second number is the value for the //y//-coordinate. Give the coordinate pair for the third pint on your graph. What information does this point give?** (1,15). This point shows that in 1 hour the group rode 15 miles.

2. **Connecting the points on a graph sometimes helps you see a pattern more clearly. You can connect the points in situations in which it makes sense to consider what is happening in the intervals //between// the points. The points on the graph of the data for day 2 can be connected because the riders were moving during each half hour interval, so the distance was changing.** a. **Connect the points on your graph with straight line segments** (done on graph)

b. **How could you use the line segments to help you estimate the distance traveled after ¾ of an hour (0.75 hours)?** Since .75 is exactly between .5 (30 minutes) and 1 (1 hour), look between the two points to where the middle of the two points meets the distance.

3. **The straight line segment you drew from (4.5,40) to (5.0,45) gives you some idea of how the ride might have gone between the points. It shows you ho the ride would have progressed if the riders had traveled at a steady rate for the entire half hour. The actual pace of the group, and of the idividual riders, may have varied throughout the half hour. These paths show some possible ways the ride may have progressed:** 
 * Match each of these connecting paths with the following travel notes **

a. **Celia rode slowly at first and gradually increased her speed. ** ii b.<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> **<span style="line-height: 115%; font-family: 'Arial','sans-serif'; color: black; font-size: 14pt;">Tony and liz rode very quickly and reached the campsite early. **<span style="line-height: 115%; font-family: 'Arial','sans-serif'; color: black; font-size: 14pt;"> iv <span style="line-height: 115%; font-family: 'Arial','sans-serif'; font-size: 14pt;">c.<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> **<span style="line-height: 115%; font-family: 'Arial','sans-serif'; color: black; font-size: 14pt;">Malcolm had to fix a flat tire, so he started late. **<span style="line-height: 115%; font-family: 'Arial','sans-serif'; color: black; font-size: 14pt;"> iii <span style="line-height: 115%; font-family: 'Arial','sans-serif'; font-size: 14pt;">d.<span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> **<span style="line-height: 115%; font-family: 'Arial','sans-serif'; color: black; font-size: 14pt;">Theo started off fast. After a while, he felt tired and slowed down. **<span style="line-height: 115%; font-family: 'Arial','sans-serif'; color: black; font-size: 14pt;"> i

Tables
Easy to make graphs from || Change must be calculated You can't see shapes Changes aren't that obvious ||
 * PRO || CON ||
 * < Easy to read

Graphs
No need to calculate || Sometimes difficult to read numbers Can be misleading ||
 * PRO || CON ||
 * Easy to see patterns