1.1+Preparing+for+a+Bicycle+Tour+10-11

CO(Chae Un Ok)  Math 7B August 26, 2010

Big Idea:

Observation and description of changes in the world around us are the first steps in finding and learning about patterns.
 * INVESTIGATION 1 Essential Question: **What are some of the variables around us?

**Notes from the class:** - The scale of a graph should always have the same interval.  - Variables are something that can change.

**New vocabulary:** Variable

 1. If you have unusal condition, will it affect the distance you ride, and why or why not?  2. How is a jumper and a timer related together? __** 1.1 - Preparing for a Bicycle Tour **__
 * Questions: **

<span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;">The popularity of bicycle tours gave five college student-Sidney, Celia, Liz, Malcom, and Theo-an idea for a summer business. They would operate bicycle tours from school and family groups. They chose a route from Philadelphia, Pennsylvania, to Williams burg, Virginia, including a long stretch along the ocean beaches of New Jersey, Delaware, and Maryland. They decided to name their business Ocean and History bike Tours. While planning their bike tour, the five friends had to determine how far the touring group would be able to ride each day. To figure this out, they took test rides around their hometowns.

__**<span style="color: #000000; font-family: 'Arial Black',Gadget,sans-serif; font-size: 140%;">Problem 1.1 **__

<span style="font-family: Tahoma,Geneva,sans-serif;">This experiment requires for people:
 * <span style="font-family: Tahoma,Geneva,sans-serif;">A jumper (to do jumping jacks)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">A timer (to keep track o time)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">A counter (to count jumping jacks)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">A recorder (to write down the number of jumping jacks)

<span style="font-family: Tahoma,Geneva,sans-serif;"> As a group decide who will do each task. <span style="font-family: Tahoma,Geneva,sans-serif;"> Prepare a table for recording the total number of jumping jacks after every 10 seconds, up to a total time of 2 minutes (120 seconds).


 * <span style="font-family: Tahoma,Geneva,sans-serif;">Time (seconds) || <span style="font-family: Tahoma,Geneva,sans-serif;">0 || <span style="font-family: Tahoma,Geneva,sans-serif;">10 || <span style="font-family: Tahoma,Geneva,sans-serif;">20 || <span style="font-family: Tahoma,Geneva,sans-serif;">30 || <span style="font-family: Tahoma,Geneva,sans-serif;">40 || <span style="font-family: Tahoma,Geneva,sans-serif;">50 || <span style="font-family: Tahoma,Geneva,sans-serif;">60 || <span style="font-family: Tahoma,Geneva,sans-serif;">70 || <span style="font-family: Tahoma,Geneva,sans-serif;">80 || <span style="font-family: Tahoma,Geneva,sans-serif;">90 || <span style="font-family: Tahoma,Geneva,sans-serif;">100 || <span style="font-family: Tahoma,Geneva,sans-serif;">110 || <span style="font-family: Tahoma,Geneva,sans-serif;">120 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Total number of jumping jacks ||  ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||

<span style="font-family: Tahoma,Geneva,sans-serif;">Here’s how to do the experiment. When the timer says “go,” the jumper begins doing jumping jacks. The counter jumps the jumping jacks out loud, Every 10 seconds, the timer says “time” and the recorder records the total number of jumping jacks the jumper has done so far, Repeat the experiment four times so that everyone has a turn at each of the four tasks.


 * <span style="font-family: Tahoma,Geneva,sans-serif;">1.1 Solution **
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Time (seconds) || <span style="font-family: Tahoma,Geneva,sans-serif;">0 || <span style="font-family: Tahoma,Geneva,sans-serif;">10 || <span style="font-family: Tahoma,Geneva,sans-serif;">20 || <span style="font-family: Tahoma,Geneva,sans-serif;">30 || <span style="font-family: Tahoma,Geneva,sans-serif;">40 || <span style="font-family: Tahoma,Geneva,sans-serif;">50 || <span style="font-family: Tahoma,Geneva,sans-serif;">60 || <span style="font-family: Tahoma,Geneva,sans-serif;">70 || <span style="font-family: Tahoma,Geneva,sans-serif;">80 || <span style="font-family: Tahoma,Geneva,sans-serif;">90 || <span style="font-family: Tahoma,Geneva,sans-serif;">100 || <span style="font-family: Tahoma,Geneva,sans-serif;">110 || <span style="font-family: Tahoma,Geneva,sans-serif;">120 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Total number of jumping jacks ||  || <span style="font-family: Tahoma,Geneva,sans-serif;">20 || <span style="font-family: Tahoma,Geneva,sans-serif;">36 || <span style="font-family: Tahoma,Geneva,sans-serif;">50 || <span style="font-family: Tahoma,Geneva,sans-serif;">63 || <span style="font-family: Tahoma,Geneva,sans-serif;">76 || <span style="font-family: Tahoma,Geneva,sans-serif;">90 || <span style="font-family: Tahoma,Geneva,sans-serif;">103 || <span style="font-family: Tahoma,Geneva,sans-serif;">114 || <span style="font-family: Tahoma,Geneva,sans-serif;">126 || <span style="font-family: Tahoma,Geneva,sans-serif;">138 || <span style="font-family: Tahoma,Geneva,sans-serif;">151 || <span style="font-family: Tahoma,Geneva,sans-serif;">167 ||

__<span style="font-family: 'Arial Black',Gadget,sans-serif; font-size: 130%;">1.1 Follow Up __


 * <span style="font-family: Tahoma,Geneva,sans-serif; letter-spacing: 0px;">Use your table of jumping jack data to answer the questions: **


 * <span style="font-family: Tahoma,Geneva,sans-serif;">1. How did you jumping jack rate (the number of jumping jacks per second) change as time passed? How is this shown in your table? **

<span style="font-family: Tahoma,Geneva,sans-serif;">My rate of jumping jack dropped after 20 seconds. I seconds. I steadily dropped till 60 seconds. Since then, my jumpihng jack rate was stable on average. My table shows the rate of change and that shows the pattern. I got tired towards the end, so I gave everything I had and sped up.


 * <span style="font-family: Tahoma,Geneva,sans-serif;">2. What might this pattern suggest about how bike-riding speed would change over a day's time on the bicycle tour? **

<span style="font-family: Tahoma,Geneva,sans-serif;">This pattern suggests that bike-riding speed changes a lot during the earlier part of the day and stabilizes during the later parts of the day. In other words, the rider tries putting different levels of effort during the earlier part of the day. When the rider finally finds the right rhythm, he sticks with it till the end. That is why he stabilizes during the later parts of the da y.