Mathematics Senior Level Capstone Course Unit Overview
Title of Unit: Summer Jobs Unit Designers:
Javornda Ashton Sharon Daniel Adam Letizia Gliziel Gonzales
Northumberland County Public Schools/Middlesex County Public Schools
Amy S. Lamb, Editor Context:
Summary of the issue, challenge, investigation, or problem.
Many high school students have summer jobs. As high school seniors approach graduation and entering college, they should anticipate expenses they will face. Students will analyze the income generated from summer jobs to determine if they will earn enough money to meet their financial obligations of their first semester of college.
Number of Class Hours:
9 hours
Unit
Design: ___Task Based __X_Project Based
Other Subject Areas/Disciplines Addressed:
Personal Finance, Writing for a Specific Purpose [Summaries and Interview Questions], Decision Making
Driving Question: How does a college students spend the summer to avoid being broke in the spring? Mathematics Content
Addressed:
Transfer between and analyze multiple representations of a function to make a decision, collect and analyze data to solve real world problems and to generate a mathematical model to represent a situation
MPE Addressed:
Problem Solving, Decision Making and Integration; Applying and Understanding Functions Assumption of Prior
Knowledge:
College and Career Readiness/21st Century Skills to be taught (T) during this unit or expectation (E) for student use during this unit and assessed (A): BIE Page 35-37
Collaboration- E Research T, E
Communication (Oral and/or Written)- E, A Technology -Excel for spreadsheets and graphical representations
T, E, A
Critical Thinking/Decision Making E, A Other: (Describe)
Major Products and/or Performances:
Group: Presentation Audience:
X Class
School Individual: Excel Spreadsheets, Interview Results, Journal
entries, Presentation with Summary
Expert Community Other: Launch: Event or
experience used to engage the students interest and inquiry:
Have students imagine it is 1911 instead of 2011. What career choices would be available to them? Have students brainstorm some ideas about what choices they would have. Have a discussion on what career and educational opportunities are available in 2011 that were not available in 1911?
Evaluation: Formative Assessments (During the Unit)
Interview Practice Presentations
Mathematicians Journal X Notes
Preliminary
Plans/Outlines/Prototypes
Checklists
Rough Drafts Concept maps
Field Tests Other: Interview Notes X
Summative Assessment (End of Project)
Written Products, with a rubric X Peer Evaluation, with a rubric
Oral Presentation with a rubric X Self Evaluation, with a rubric
Other Product(s) or
Performance(s), with a rubric
Resources Needed: On-site people, facilities: Instructors
Equipment/Technology: Computers, Excel Files, place to save files [jump drive or student-shared files]
Materials: Handouts, Chart Paper
Community Resources: Local Community College with the time to be interviewed
Reflection Methods: Individual, Group, and/or Whole Class
Mathematicians Journal X Small/Focus Groups X
Whole Class Discussions X Fishbowl Discussions
Survey Other:
Material Adapted From:
Algebra, Functions, and Data Analysis: A Virginia Course by The Consortium for Foundation Mathematics
Virginia’s Senior Level Capstone Course Instructional Plan
Unit Title: Summer Jobs
Driving Question: How does a college student spend the summer to avoid being in the spring?
Task/Project/Problem: Many high school seniors are not aware of all the living expenses associated with living away from home for their first semester of college. Students will examine these costs in relation to analyzing income from various summer jobs in order to make informed financial decisions. ENGAGE
How will student’s interested be peaked so they want to engage in the inquiry in this unit? Number of hours: 1.5
Prior to starting the unit, students will have had some basic practice on using Excel spreadsheets. Students will also receive HO#1A to assess prior knowledge. HO #1B provides students with a listing of resources that will review the mathematical knowledge assessed on HO#1A.
Engage #1: Students will share their plans for their first semester of college/vocational training and their future career goals. HO#1 A discussion will be held in which students can share their plans. A class poster can be developed that lists where students plan to go after graduation for college or career training.
Engage #2: Linking the discussion of the Launch section to the Explore section, students will complete the Women in College Task. HO #2
Mathematician Journal Prompts
List some goals of your
classmates that you heard during the discussion.
EXPLORE Teacher provides guidance for the explorations to prepare students with the
knowledge and skills to engage in the task. Students will self-assess on the prior knowledge and skills assumed for the unit
Number of hours: 2-3 hrs
Explore #1: Working in small groups, students will make a decision on what car they will rent to visit the college of their choice. HO #3
Explore #2: Field Trip to a local Community College Students will travel to a local community college to interview college personnel, such as advisors, counselors, professors, and students about the expenses associated with college attendance and living expenses of young adults. HO#4
Prior to starting the explain section, students will have had some basic practice on using Excel spreadsheets. Students will also receive HO#5A to assess prior knowledge. HO #5B provides students with a listing of resources that will review the mathematical knowledge assessed on HO#4A.
Mathematician Journal Prompts
Write a brief summary on what you learned during your visit to the community college. What types of
expenses do you think you will have that you didn’t think of before your visit?
EXPLAIN Teacher introduces the main task of the unit and prepares students to in small group independent work...
Number of Hours: 0.5 hr
Students can work with a partner or in a group of most of this project until they have to work with the data for their own summer job.
Students will be given HO #6, which explains the project. The teacher will explain the project directions and share the rubric with the final product requirements. The teacher will explain where the Excel Files can be located and the procedure for saving their work. [Copies of Excel files attached for reference.]
Materials/Equipment/Resources Needed: Handouts, Computers, and Excel Files
Mathematician Journal Prompts What are the benefits of having a summer job? How can summer jobs and temporary jobs help you reach your long-term goals? ELABORATE The student groups are working independently with teacher consultations.
While students are working on the project, the teacher will be available to assist students who may require assistance using Excel. The teacher will monitor student progress by asking questions as students work and keeping students on the project calendar.
Formative Assessments:
Anticipated Products and Artifacts Described HO# 6
Rubric(s) for self-evaluation of product and/or presentation, etc.
Number of Hours: 2 hrs
HO# 7 earned and
personal satisfaction? EVALUATE
Working groups submit products or make
presentations Number of Hours: 2 hrs
Students will present their final products, which should include a written summary of which job presented would help them meet their financial obligations. The summary should include their budget, the amount of money they would save, and if they can make enough money during the summer to pay their expenses for their first semester of college. Excel files can be printed or saved and turned in with their written summaries and budgets.
Students should also take notes in their journals on their
classmates’ presentations to be able to answer the journal prompt for this section.
Mathematician Journal Prompts While your classmates are presenting, take notes on any key points that you would like to ask them to clarify. Was any information given during the presentations that you omitted from your presentation? Would you change your decision based on this
information?
Map the Unit Task:
KNOWLEDGE AND SKILLS NEEDED Assumed
already learned
Students will self-assess
Will be taught during the unit
2. Write equations to model a situation or write a system of equations to graph
X X
3. Solving equations with variables on both sides of the equals sign
X X
4. Solving formulas/equations for a specified variable
X X
5. Determining a Break-Even Point X
6. Writing X
7. Oral Presentation X
8. Decision-Making/Making predictions X
9. Using Excel/spreadsheets to calculate earnings, to make a budget and a circle graph
X
10.Research X
11.
What project tools will student’s use? Know/need to know lists Daily goal sheet
X Mathematician’s Journals Briefs/Memos
Task lists
X Planning Calendar
□ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________
Attachments: Handouts With Title and Numbered Sequentially as H0# 1-7
HO#1
What Are Your Future Plans?
to learn a new trade? No matter where you are going, or what you want to do, list your plans for
next year, September 2012-December 2012.
Be ready to share your thoughts with your classmates. Plan to share at least three ideas of where
your will be, what you will be doing, and how you are going to meet your financial obligations.
Idea #1
# Idea 2
Idea #3
HO#2
Year
1970
1975
1980
1985
1990
1995
2000
2001
Number
Enrolled
in
Millions
3.54
5.04
6.22
6.43
7.54
7.92
8.59
8.97
Source: U.S. Dept. of Education, National Center for Education Statistics
Let t represent the number of years since 1970. The number N (in millions) of women enrolled in
college can be modeled by the formula below.
N = 0.158t + 4.092
A. Estimate in what year women’s college enrollment will reach 10 million.
B. Solve the equation N = 0.158t + 4.092 for t.
C. Use the new formula in part B to estimate the year in which women’s enrollment will reach
11 million.
Rental HO #3
Visiting In Style
Deal-a-Car: $39.95 per day, plus $0.19 per mile
On The Move Rental: $19.95 per day, plus $0.49 per mile.
Let x represent the number of miles driven in one day and C represent that total daily rental cost ($).
Write an equation that represents the total daily rental cost from Deal-a-car in terms of the number of miles driven.
Write an equation that represents the total daily rental cost from On The Move Rental in terms of the number of miles driven.
Write an equation and solve the equation to determine for what mileage the one-day rental cost would be the same.
HO #4
Field Trip to the Community College
During the visit to the Community College on _____________________, you will be provided the opportunity to interview several college students and employees of the community college system to determine the expenses that young adults encounter during their first semester of college.
You want to ask questions that are not too personal of individuals. For example, you can ask students to list what types of items they need for college, the categories of their living expenses, and “average” amounts they spend on these items each month.
HO#5
Assessment of Mathematic Skills Needed for Summer Job Project
Look at the concepts below and determine if you need to review any of the skills associate with these concepts.
Skill/Concept Yes, I need to review this concept.
No, I’m okay with this concept.
Review Resources
Determining a Break-Even Point
http://tutor2u.net/business/production/break_even.htm
Graphing a System of Equations; writing systems
http://www.khanacademy.org/video/solving-systems-by-graphing? playlist=Algebra+I+Worked+Examples
(there are many other videos on systems in Khan Academy)
Solving for a specified variable in an equation or formula
http://www.analyzemath.com/Equations/literal_equations.html
http://www.virtualnerd.com/algebra-1/linear-equations-solve/ literal-equation-definition.php
http://www.nwscc.edu/nsfdc/tgh/Physical%20Science/Worked-out %20problems/Literal%20Tutorial.pdf
http://regentsprep.org/Regents/math/ALGEBRA/AE4/litless.htm
Solving for a variable when it is on both sides of the equal sign
http://www.onlinemathlearning.com/equations-variables-both-sides.html
Finding the percent of a number
HO#6
Summer Jobs Project -How Should a Senior Spend Their Summer to Avoid Going Broke at College?
Scenario: You will investigate the earnings of three summer jobs advertised in the newspaper for a ten-week period during the summer before you leave for college. You will also investigate one job of your choice. All positions will involve the same 10-week period during the summer. You will make an informed decision in choosing one of the jobs for the summer. Although you may like one job over another for personal reasons, keep in mind you need to earn the maximum amount possible to pay your estimated expenses for the fall semester at college.
For each of the three jobs listed below, and the summer job you choose to investigate, design an Excel Spreadsheet that will calculate the “typical” weekly paycheck for each week and the total amount of earnings accrued as the summer progresses for the ten week period. Keep in mind you have to pay taxes and your will have a gross income and a net income. You will also complete an Excel Spreadsheet that will help you determine the amount of money you need to save for the time period of September through December [your first college semester.] You will need to make an informed decision of which job you will work during the summer so that you don’t go broke!
Job #1: SALES: A sales job opened at a computer store. The hourly rate is $7.50 per hour plus a 3% commission on your total weekly sales. You would be given between 30 and 40 hours per week. You’ve been told that sales people typically make between $3,000 and $6,000 in sales per week.
Job #2: PARK WORKER: The parks department hires a graduating senior each summer to help with outdoor summer projects. The hourly rate is $12.50. You can work up to 40 hours each with but if the weather is good, you can expect to work an extra 10 hours per week in overtime. For overtime, you earn time and a half. Remember, though, it may rain and then you wouldn’t be able to work. Research the weather for June-August for last summer and make a decision about how many days overtime you could earn and how many days you would not work.
HO #7 Rubric for Project
Assessment Rubric
1-Insufficient Understanding
2-Fair 3-Good 4-Excellent
Understanding of Concept
(Writing and Solving Linear Equations)
Demonstrates no understanding of the main concept.
Demonstrates little understanding of the main concept.
Demonstrates partial understanding of the main concept. Demonstrates mastery knowledge of the main concept. Accuracy Excel spreadsheets Demonstrates no understanding of excel.
Accuracy is weak with very little correct calculations.
Accuracy needs to improve with most of the correct calculations . Mastery of concept with accurate solutions and correct usage of excel.
Summary No organization of work or support for final decision.
Very weak evidence of organization or support for final decision.
Organization needs to improve and some support for final decision.
Well organized with clear understanding and detailed support of final decision.
Presentation Demonstrates no knowledge of concept with no explanations of final decision.
Demonstrates very little understanding of concept and explanations are not very clear.
Demonstrates partial understanding of concept and some explanations are clear.
Knowledgeable of concept and clear
explanations of decision making process.
HO # 8a Sales
Heathsville Computer Store
Employee Name:
Week Hourly Rate WorkedHours Basic Pay
Weekly
Sales Commission
Gross Weekly
Pay
1 $7.50
2 $7.50
3 $7.50
4 $7.50
5 $7.50
6 $7.50
7 $7.50
8 $7.50
9 $7.50
10 $7.50
Total
Enter hours worked in Column C. Enter Weekly Sales in Column E. Calculate the
following:
Basic Pay = Hourly Rate * Hours Worked Commission = Weekly Sales * 3%
HO # 8b Park Worker
Kings Dominion
Employee name:
Week Hourly Rate WorkedHours
Hours Worked
< or = to 40
Hours Worked
in excess
to 40
Basic
Pay OvertimePay
Gross Weekl y Pay
1 $12.50
2 $12.50
3 $12.50
4 $12.50
5 $12.50
6 $12.50
7 $12.50
8 $12.50
9 $12.50
10 $12.50
Total
Enter hours worked in Column C.
Copy data entered in column C to column D if hours worked is < or equal to 40.
Enter 40 in Column D and enter the excess of 40 to column E if data in column C is > 40.
Calculate the following:
Basic Pay = Hourly Rate * (Hours Worked < or equal to 40)
Overtime Pay = (Hourly Rate)*(Hours worked in excess to 40)*( 1.5 ) Gross Weekly Pay = Basic pay + Commission
HO # 8c Wait Staff
The Cull Ring
Employee Name:
Week Hourly Rate WorkedHours Basic Pay WeeklyTips
Gross Weekl y Pay
1 $3.75
2 $3.75
3 $3.75
4 $3.75
5 $3.75
6 $3.75
7 $3.75
8 $3.75
9 $3.75
10 $3.75
Total
Enter hours worked in Column C. Enter Weekly Tips in Column E Calculate the following:
