3.1+Renting+Bicycles++10-11

September 14th, 2010 M. H.

__//Big Idea: //__
Observation and description of changes in the world around us are the first steps in finding and learning about patterns.

__//Investigation 3 Essential Question: //__
How can I visually explain situations where one thing changes based on an other?

__//Notes From Class: //__
Income – Cost = Profit Cost-the amount of money to need to spend on neccesary stuff. (food, drinks, etc.) Income-money that you earn. Profit-the amount of money left after all the costs of running a business has been subtracted from the money earned. **3.1 Renting Bicycles ** **Th tour operators decided to rent bicycles for their customers rather than having customers bring their own bikes. They called two bike shops and asked for estimates of rental fees. ** **Rooky’s Cycle Center sent a table of weekly rental fees for various numbers of bikes. **
 * Number of bikes || 5  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">10  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">15  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">20  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">25  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">30  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">35  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">40  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">45  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">50  ||
 * <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">Rental Fee || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$400  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$535  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$655  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$770  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$875  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$975  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$1070  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$1140  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$1180  || <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt;">$1200  ||

**<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">Adrian’s Bike Shop sent a graph of their weekly rental fees. Since the rental fee depends on the number of bikes, they put the number of bikes on the x-axis. ** <span style="color: black; display: block; font-family: 'Vrinda','sans-serif'; font-size: 14pt; height: 320.25pt; line-height: 115%; visibility: visible; width: 366pt;">

**<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">Problem 3.1 ** **<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">A. ****<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">Which bike shop should Ocean and History Bike Tours use? Explain your choice. ** <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">I think if they want to have more people on their tour, they should definitely use Rooky’s Cycle Center, because the more number of bikes, the less money it costs. But if they want to bring less than 35 people on their tour, than they should use Adrian’s Bike Shop. **<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">B. ****<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">Explain how you used the information in the the table and the graph to make your descision. ** <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">I used the table by changing it into a graph, (You’ll see that below this answer.) and comparing it to Adrian’s Bike Shop’s graph. I used the graph by using it to compare with the table, which is shown below. (It was in the textbook.)
 * <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">Problem 3.1 Follow-up **

<span style="display: block; margin: 0cm 0cm 0pt 54pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18pt;">**<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">1. ****<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">In the graph from Adrian’s Bike Shop, would it make sense to connect the points with a line? Why or why not? ** <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">It would make sense, because you always connect the points in a continuous situation, and the variables presented in this problem (Number of bikes, and rental fee.) can go on. <span style="display: block; margin: 0cm 0cm 0pt 54pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18pt;">**<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">2. ****<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">How much do you think each company would charge to rent 32 bikes? ** <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">I think Rooky’s Cycle Center would charge $990 for 32 bikes. I think Adrian’s Bike Shop would charge $1050 for 32 bikes. <span style="display: block; margin: 0cm 0cm 0pt 54pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18pt;">**<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">3. ****<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">Recognizing patterns and using patterns to make predictions are important mathematical skills. Look for patterns in the table and graph on page 37. For each display, describe in words the pattern of change in the data. ** <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">At first, in Rooky’s Cycle Center, the price was higher than Adrian’s Bike Shop, but then when the number of bikes got higher than 35, the line started gradually sloping downwards. And it became lower than Adrian’s price. For Adrian’s, it was a straight diagonal line, no ups or downs as the number of bikes increased but the steady inrease of the price. Which means that as the number of bikes increase, the price increases too, at the same price. <span style="display: block; margin: 0cm 0cm 0pt 54pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -18pt;">**<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">4. ****<span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">Based on the patterns you found in part 3, how can you predict values that are not included in the table or graph? ** <span style="color: black; font-family: 'Vrinda','sans-serif'; font-size: 14pt; line-height: 115%;">You can predict values that are not included in the table or graph by continuing the pattern that you had noticed.