2.2+Day+2+Atlantic+City+to+Lewes+10-11

**K.F.** Big Idea: Observation and description of changes in the world around us are the first steps in finding and learning about patterns. Essential Question: What are some situations that we can describe as variable? Notes: We learned a new vocabulary word. The vocabulary is coordinate pair. Coordinate pair means a set of numbers usually in parentheses except when they're in a table. The coordinate pair represents the place that the dot would go on a scatter plot.
 * August 30, 2010**


 * A: Make a coordinate graph of the (time, distance) data given in the table.**



**B: Sidney wants to write a report describing day 2 of the tour. Using information from the table or the graph, what could she write about the day's travel? Be sure to include the following questions.** The group traveled 45 miles in five hours. They made the most progress in the first half-hour, when they traveled eight miles. The least progress was made from 3.5 to 4 and 4 to 4.5. They traveled much more in the first half. The average for the first half is 5.4 miles per half hour, but for the second half is 3.8. The overall average is 4.5 per half hour. This is down from Day 1, because Day 1 the overall average was 5.6 miles per half hour. **C: By analyzing the table how can you find the time intervals when the riders made the most progress? The least progress? How can you find these intervals by analyzing the graph?** You can find the time intervals when the riders traveled the most/least by adding a third column with the distance traveled during the interval. On the graph, you can just look at distance between the two points. **D:Sidney wants to include either the table or the graph in her report. Which do you think she should include? Why?** I think the graph should be included, because it is more visual, and can be looked over quicker for easy information.
 * **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? The least progress?**
 * **Did the riders go further in the first half or the second half of the day's ride?**

Problem 2.2 Follow-up

The coordinate pair for the third point is (1.0, 15) this tells you that 1 hour into the trip the riders had traveled 15 miles.
 * 1. Look at second point on your graph as you count from the 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 point on your graph. What information does this point give?**

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.** You could draw a straight line from where 0.75 hrs is to the line, and from that point to the y-scale. So, about 11 miles. The one that best matches is ii. The one that best matches is iv. The one that best matches is iii. The one that best matches is i.
 * A: Connect the points on your graph with straight line segments.**
 * B: How could you use the line segments to help you estimate the distance traveled after 3/4 of an hour (0.75 hours)?**
 * 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 how the ride would have progressed if the riders had traveled at a steady rate for the entire half-hour. The actual of the group, and of the individual riders, may have varied throughout the half-hour. These paths show some possible ways the ride may have progressed:**
 * A: Celia rode slowly at first and gradually increased her speed.**
 * B: Tony and Liz rode very quickly and reached the campsite early.**
 * C: Malcolm had to fix a flat tire, so he started late.**
 * D: Theo started off fast. After a while, he felt tired and slowed down.**