The Best Summer Job Offer Ever!
 
 
TEACHERS: The Best Summer Job Offer Ever!
Overview:
Answers to the student questions are provided below.  See also an Excel attachment that shows what the graphs should look like once students have finished them. 

Topics covered:

  • Solving equations (with 2 variables)

  • Problem solving

  • Slope

  • Graphing

  • Spreadsheets

  • Equation of a line

NJ Core Curriculum Content Standards:

  • Standard 1
  • Standard 2

Materials:

  • Material 1
  • Material 2
  • Handout 1: handout.doc

Suggested Classroom Environment:

  • One computer classroom, classroom lab

  • Depending on student ability this can be made into a one period lesson or more likely a period and then some.  Alternatively students could finish parts of the assignment for homework.

Procedure:

  1. Give each student a student worksheet.
  2. Read directions and outline the problem for the students.
  3. Have students select a payment plan.  Have volunteers voice their opinion regarding a couple different plans.   Answer questions 1-4 as a class before working on computers.
  4. Have students work in individually or in pairs to develop a spreadsheet and answer the rest of the questions 5-9.
    1. For accountability, you can have students print their data table and graphs. 
  5. As a class you may decide to go over answers or have students had in their charts, graphs and answers to questions 1-9 as a graded assignment.
  6. Optional: Have students answer the homework question and submit their report.

Extensions / Related Activities:

  • You may want to take a look at the Jinx Puzzle as a one lesson introduction to 2 variable equations and a more guided implementation of using spreadsheets for solutions to equations.

  • Link 2
Questions:
1. Which plan did you choose? Why?  Students may select any of the plans.  Encourage them to voice differing opinions.
2. How much will you make on the 5th day under each of the payment plans?  How did you calculate that?  A class determine how the first 3 or 4 days were determined.  In other words, what is the pattern?  From there students should see how the 5th day can be determined. 
3. For payment plan 1, how would you figure out how much you make on the nth day where n is any number of days from 1 to 22?
Students should try to verbalize that they would take the number of days worked and multiply by 2 and add 50 to it.  That is close but keep in mind that it will not work for the first day!  If they try 48 instead they will get the right answer.
4.

For payment plan 3, how would you figure out how much you make on the nth day where n is any number of days from 1 to 22?

 This one is tougher.  If students know their squares then they might recognize that their pay would be the square of the number of days worked.  Basically they are discovering equation building.  Next they will see the power of computers in performing all the calculations for each day. 

  The excel file answer key should compare to what students developed and be useful as a guide for some of the questions.  Be sure to scroll down to see al the graphs.  Encourage skill building such as color coding lines and graphs and labeling axes.  This will enhance the illustration and give students access to these skills in the future.
5. Which plan will make you the most money after 22 days? How much money will you make? Plan 2, $41,943.03
6. If you planned to quit after 7 days of work, which plan should you use?  How much money will you make?  Plan 1, $392
7. If you plan to quit after 14 days of work, which plan should you use?  How much money will you make? Plan 3, $1015
8. According to your graph and equation of the line, why do you have different answers for questions 3, 4 & 5?  Because the slope of each line is different. 
9. According to the graph of all 3 payment plans, on what day is the total money earned for payment plan 1 and 2 equal?  (You may have to change the scale of the y-axis on your graph to 0-500 or something like that in order to improve your resolution.)  Confirm that with your data table.  Approximately how much is the daily pay?   Somewhere on the 17th day, at about $1200.
10. According to the graph of all 3 payment plans, on what day is the total money earned for payment plan 2 and 3 equal? Confirm that with your data table.  Approximately how much is the daily pay?

 Somewhere on the 18th day, at about $2000.
Advanced question:
11. Using the equations of a line, when are the equations for payment plan 1 and 3 equal?  How many days of work?  Confirm that with your data table and graph. Students may take the next step and equate one equation with the other understanding that  would be the equality that is being asked for.  Also, students may look at the equations or the Excel file and determine the answer.  Effort should be made to link all these modes of understanding together.
   

 

 

 

 
 
 

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