2.3+Walking+for+Charity

May 25, 2009 Block 7B
 * Arfan Shayer

Big Understanding- Many real world situations can be modeled and predicted using mathematics. Essential Question- What is the relationship between a table, a graph, and an equation?

2.3 Walking For Charity

In this problem, we will refer to Leanne, Gilberto, and Alana’s suggestions as [ledge plans.

A1. Make a table showing the amount of money a sponsor would owe under each pledge plan if a student walked distances between 0 and 10 miles.

Number of Miles Leanne Gilberto Alana 0 0 0 5 1 1 2 5.50 2 2 4 6 3 3 6 6.50 4 4 8 7 5 5 10 7.50 6 6 12 8 7 7 14 8.50 8 8 16 9 9 9 18 9.50 10 10 20 10

A2. Graph the three pledge plans on the same coordinate axes. Use a different color for each plan.



A3. For each pledge plan, write an equation that can be used to calculate the amount of money a sponsor owes, given the total distance the student walks.

Leanne- y=x Gilberto- y=2x Alana- y=.5x+5

B. What effect does increasing the amount pledged per mile have on the table? The graph? The equation?

Table: The y-axis will go up with a larger number each time the x-axis goes up by 1. Graph: The slope of the line will become steeper. Equation: The co-efficient becomes larger.

C. If a student walks 8 miles in the walkathon, how much would a sponsor owe under each pledge plan? Explain how you got your answer.

Leanne- She would earn $8. 1 times 8=8 Gilberto- He would earn $16. 2 times 8=16 Alana- She would earn $9. .5 times 8 + 5=9 I used their equations to solve this problem.

D. For a sponsor to owe a student $10, how many miles would the student have to walk under each pledge plan? Explain how you got your answer.

Leanne- 10 miles. $10 divided by 1= 10 miles Gilberto- 5 miles. $10 divided by 2= 5 miles Alana- 10 miles. $10-5 divided by .5= 10 miles I used the equations to solve these problems.

E. Alana suggested that each sponsor should make a $5 donation and then pledge 50 cents per mile. How is this fixed $5 donation represented in the table. In the graph? In the equation?

Table: When the number of miles is at zero the pledge money is $5. Graph: The line enters the first quadrant at 5 on the y-axis. Equation: It has +5 in the equation.**