Archdiocesan Schools | Livable Wage: A Matrix Analysis

Livable Wage:  A Matrix Analysis


Course Overview

This course is designed for talented 7th and 8th graders, as a supplement to their regular mathematics curriculum.  Students need not have had or currently be taking Algebra I.  This is a challenging course in problem solving, employing Excel Spreadsheet and matrix operations.  This project also challenges students to think about the social justice issue of minimum wage versus livable wage.  The course will employ Moodle, a secure online learning environment for class discussion.

Microsoft Excel are required for this project. 
 

Course Objectives

To provide an opportunity for talented math student to explore an area of mathematics (matrices) not typically covered in middle school curriculum.

To challenge high ability learners to wrestle with issues of social justice, by employing mathematical analysis.

To use interactive, web-based technology to question, share, and respond to ideas.

To prepare a final analysis, supported by mathematics, of the question at hand:  What is a fair and livable wage?


Instructional Format

This course will run for nine weeks.  Students will work independently in a library or resource setting with internet access.  Weekly tasks will be assigned.  Participation via Moodle is required.

Students will meet face to face with each other and the teacher for 3 half-day workshops.  During the workshops, students will:

  • Become familiar with the online classroom
  • Learn to use Excel Spreadsheet
  • Learn to do Matrix Operations with the TI-84 calculator
  • Collaborate with classmates
  • Present final projects
     

Introduction

Married right after high school and divorced since 2003, Jennifer went on welfare and was receiving $414 a month in assistance and $325 in food stamps.  Now she has found a job that pays $11 per hour, but she is paying $520 monthly in new child care costs, $109 each month for health insurance, and $600 a month in rent (including utilities).  She wasn't able to pay her bills when she was on welfare and she can't pay them now.  What's more, neither the welfare system nor her current job gives her the education necessary for a better job so that she can pay her bills in the future.  She is trapped!

If Jennifer, who makes $11 per hour, feels trapped, how much worse is it for someone making only the minimum wage ($7.25 an hour)?  Remember, workers still have to pay 15% of their gross pay in federal tax, 3% in state tax and 7.65% for Social Security and Medicare.  So, the minimum wage is even more "minimal" than we have been led to believe.  The typical worker earning minimum wage is not a teenager trying to earn gas money or tickets to a concert.  Nearly two-thirds of minimum wage workers are adults twenty and older and 40% of them are their family's sole breadwinner. 

In this project, you will examine the justice of minimum wage while, at the same time, learning applications of matrix analysis.  As a conclusion, you will write a 5 page reflection paper.

 

Week 1:  Understanding Minimum Wage

Activity 1:  First face to face meeting.  Assignment of partners.

Activity 2:  Go to http://www.dol.gov/whd/minwage/america.htm and complete the web search on minimum wage that can be found on the next page.

Need to write web search.  Suggested questions.

  1.  Name the states with no minimum wage law.
  2. Why do you think these states have not set a minimum wage?
  3. What is the federal minimum wage?
  4. Name the states that have a minimum wage that is lower than the federal standard.
  5. Which two states have the highest minimum wages?
  6. Why do you think these states have set their wages higher than other states?
  7. What impact does minimum wage have on small businesses?
  8. Would a stratified minimum wage based on age brackets be preferable (lower wage for 15 – 18 year olds, higher minimum wage for adults)?
  9. Look into the history of minimum wage in Wisconsin.  In 1968, did the minimum wage apply to all workers?  If not, to whom did it apply?
  10. What surprises you about your research on minimum wage.

Activity 3:  Read this article and other articles references under “More Articles”.  http://smallbusiness.chron.com/problems-minimum-wage-2692.html

Activity 4:  Minimum Wage Blog Discussion with teacher-generated blogs. 

 

Week 2:  The Problem

Let's assume that Sara is a single parent, living in Wisconsin, with two children, ages four and six.  Let's also assume that Sara's mother can take care of the children while Sara is at work.   (Thank goodness for this, because there is no way that Sara could afford to pay for child care.)

Sara works eight hours per day, 5 days per week, earning the minimum wage.  Before deductions, her weekly pay is 8 x 5 x $7.25, which equals $290.  From this amount, there are three payroll deductions: 15% of gross pay in federal tax, 3% for state tax and 7.65% for Social Security and Medicare. 

Activity 1:  What are the essential expenses that Sara needs to meet in order to provide for her family?  List these now – you will investigate them later.

Activity 2: You need to do some nutrition research.  Go to your local grocery store and gather data on common healthy foods.  You may select generic / least expensive brands as long as you to not compromise nutritional quality.  For each food, record nutrients, calories, serving size, servings per package, and cost.  You will need to read nutrition labels that look like this:

Activity 3:  Share your findings via the course blog.

 

Week 3:  Creating a Basic Matrix

Activity 1:  As you learned last week, Sara’s gross weekly pay is 8 x 5 x $7.25, which equals $290.  From this amount, there are three payroll deductions: 15% of gross pay in federal tax, 3% for state tax and 7.65% for Social Security and Medicare.  Also subtract $17.50 per week for bus fare.  Assume that Sara lives in subsidized housing and pays 1/3 of her gross monthly income in rent.  This includes heating, water and electricity, but not a telephone or TV.  Do these calculations on a spreadsheet and use absolute addresses for all of the above information.  This will be demonstrated via moodle. (Microsoft built-in tutorials and you-tube may also be employed for teaching basic Excel skills.)

Activity 2:  Put the results of your food research from last week into a Nutrition Matrix.  It could look something like this:

 

Bread

Cereal

Milk

Coffee

Carrot

Potato

Tomato

Ground Beef

Orange

Cake

Calories

70

110

150

0

30

145

25

245

60

445

Protein (grams)

3

2

8

0

1

3

1

20

1

4

Calcium (mg)

20

1

291

0

19

8

9

9

52

61

Iron (mg)

1

108

0.1

0

0.4

0.5

0.6

2.1

0.1

1.2

Vitamin A

Vitamin C

Serving Size

Servings per package

Cost

 

 

 

 

 

 

 

 

 

 

 

 Activity 3:  Weekly Menu

nutrient (units)

Child 1–3

Female 4–8

Male 4–8

Female 9–13

Male 9–13

Female 14–18

Male 14–18

Female 19–30

Male 19–30

Female 31–50

Male 31–50

Female 51+

Male 51+

Macro
nutrients

 

Protein (g)

13

19

19

34

34

46

52

46

56

46

56

46

56

(% of calories)

5–20

10–30

10–30

10–30

10–30

10–30

10–30

10–35

10–35

10–35

10–35

10–35

10–35

Carbohydrate (g)

130

130

130

130

130

130

130

130

130

130

130

130

130

(% of calories)

45–65

45–65

45–65

45–65

45–65

45–65

45–65

45–65

45–65

45–65

45–65

45–65

45–65

Total fiber (g)

14

17

20

22

25

25

31

28

34

25

31

22

28

Total fat (% of calories)

30–40

25–35

25–35

25–35

25–35

25–35

25–35

20–35

20–35

20–35

20–35

20–35

20–35

Saturated fat (% of calories)

<10%

<10%

<10%

<10%

<10%

<10%

<10%

<10%

<10%

<10%

<10%

<10%

<10%

Linoleic acid (g)

7

10

10

10

12

11

16

12

17

12

17

11

14

(% of calories)

5–10

5–10

5–10

5–10

5–10

5–10

5–10

5–10

5–10

5–10

5–10

5–10

5–10

alpha-Linolenic acid (g)

0.7

0.9

0.9

1.0

1.2

1.1

1.6

1.1

1.6

1.1

1.6

1.1

1.6

(% of calories)

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

0.6–1.2

Cholesterol (mg)

<300

<300

<300

<300

<300

<300

<300

<300

<300

<300

<300

<300

<300

Minerals

 

Calcium (mg)

700

1,000

1,000

1,300

1,300

1,300

1,300

1,000

1,000

1,000

1,000

1,200

1,200

Iron (mg)

7

10

10

8

8

15

11

18

8

18

8

8

8

Magnesium (mg)

80

130

130

240

240

360

410

310

400

320

420

320

420

Phosphorus (mg)

460

500

500

1,250

1,250

1,250

1,250

700

700

700

700

700

700

Potassium (100 mg)

30

38

38

45

45

47

47

47

47

47

47

47

47

Sodium (100

mg)

<15

<19

<19

<22

<22

<23

<23

<23

<23

<23

<23

<23

<23

Zinc (mg)

3

5

5

8

8

9

11

8

11

8

11

8

11

Copper (mcg)

340

440

440

700

700

890

890

900

900

900

900

900

900

Selenium (mcg)

20

30

30

40

40

55

55

55

55

55

55

55

55

vitamins

 

Vitamin A (mcg RAE)

300

400

400

600

600

700

900

700

900

700

900

700

900

Vitamin Dh (mcg)

15

15

15

15

15

15

15

15

15

15

15

15

15

Vitamin E (mg AT)

6

7

7

11

11

15

15

15

15

15

15

15

15

Vitamin C (mg)

15

25

25

45

45

65

75

75

90

75

90

75

90

Thiamin (mg)

0.5

0.6

0.6

0.9

0.9

1.0

1.2

1.1

1.2

1.1

1.2

1.1

1.2

Riboflavin (mg)

0.5

0.6

0.6

0.9

0.9

1.0

1.3

1.1

1.3

1.1

1.3

1.1

1.3

Niacin (mg)

6

8

8

12

12

14

16

14

16

14

16

14

16

Folate (mcg)

150

200

200

300

300

400

400

400

400

400

400

400

400

Vitamin B6 (mg)

0.5

0.6

0.6

1.0

1.0

1.2

1.3

1.3

1.3

1.3

1.3

1.5

1.7

Vitamin B12 (mcg)

0.9

1.2

1.2

1.8

1.8

2.4

2.4

2.4

2.4

2.4

2.4

2.4

2.4

Choline (mg)

200

250

250

375

375

400

550

425

550

425

550

425

550

Vitamin K (mcg)

30

55

55

60

60

75

75

90

120

90

120

90

120

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Use the Nutrition table above to create a daily menu in EXCEL for Sara and her family.  Females 25 to 50 need from 1500 to 3000 calories per day, depending on activity level.  Children ages 4 – 6 need from 1200 to 2000 calories per day.  Make sure that your menu satisfies the minimum daily requirements for calcium, iron, protein, and Vitamins A and C.  Use trial and error until you achieve a menu plan that provides acceptable nutrition for Sara and her children. 

Your menu table should include at least 12 different food items.  It might look something like this: (You may include different foods or more foods on your list – this is just an example.)

Menu Matrix

 

Adult

Child

 

Breakfast

Lunch

Dinner

Breakfast

Lunch

Dinner

Bread, 1 slice

 

 

 

 

 

 

Cereal, 1 oz

 

 

 

 

 

 

Whole Milk, 1 cup

 

 

 

 

 

 

Coffee, I cup

 

 

 

 

 

 

Carrot, 1

 

 

 

 

 

 

Potato, 1

 

 

 

 

 

 

Tomato, 1

 

 

 

 

 

 

Ground Beef, 3 oz

 

 

 

 

 

 

Orange, 1

 

 

 

 

 

 

Cake, 1 slice

 

 

 

 

 

 

 



Week 4:  Refining Menus

Activity 1:  Share your proposed menus with classmates.  Refine menus as appropriate.

Activity 2:  Discuss what is missing from your menus?  Why do you think that obesity and poor diet is most common among those who live in poverty?

Activity 3:  Now that you have a healthy menu, create a shopping list.  Make sure that your list includes enough of each item to last for seven days. 

Activity 4:  Second face-to-face meeting.  Instruction on using functions and formulas in EXCEL.  Instruction on performing matrix operations with TI-84 calculator.


Week 5:  Computing the Cost of Feeding Sara’s Family

Activity 1:  Create a spreadsheet to compute the total cost of one week’s worth of groceries.  Multiply the weekly cost by 4.33 to find the average monthly cost.  Use built-in EXCEL functions

Activity 2:  Calculate the cost in another way, using matrix multiplication. 

 

Cost Matrix (It's a ROW MATRIX!)  – (This part is to be completed AFTER meeting with the high school teacher.)

 

Bread

Cereal

Milk

Coffee

Carrot

Potato

Tomato

Ground Beef

Orange

Cake

Cost per serving

0.05

0.14

0.18

0.15

0.06

0.13

0.25

0.39

0.17

0.42

 

Using a menu that meets the RDAs, use matrix multiplication to figure out the cost of food for a week.  Remember that Sara has TWO children. 

Activity 3:  Take the average of the two methods you used to calculate monthly food costs.

Activity 4:  Discussion:  Does this “average” cost surprise you?  Can Sara afford to feed her family?  Share thoughts on class blog.


Week 6:  This week is set aside for help with your matrices.


Week 7:  Expanding the question.

Activity 1:  Compute how much Sara has left over for clothing, medicine, entertainment, telephone and anything else.  Investigate the costs of some of these items.  Insert a new worksheet and create a "spending plan" for Sara's family.

Copy your original spreadsheet onto Sheet 3.  Change the minimum wage to an amount that you think would be a "living wage" for a family of 3. 

Copy your original spreadsheet on to Sheet 4.  Change the minimum wage to an amount that you think would be a "living wage" for a family of 4 (two adults and two children).  Remember to adjust the food costs to reflect two adults.  Assume the nutritional requirements stay the same.

Activity 2:  Now assume that Sara's family encounters a crisis.  One of her children is injured in an accident and requires medical treatment.  Sarah does not have insurance and so she is forced to put a $3000 charge on her credit card.  She pays the minimum payment each month ($30) with an interest rate of 13.9%.  Create a spreadsheet that shows the balance after each payment.  How long will it take Sarah to pay off this bill?  What will Sarah's family have to give up as a result of this accident?

Activity 3:  Discuss findings and respond to teacher-generated prompts. 


Week 8:  The Final Analysis

Activity 1:  Submit your Excel file to instructor.  Make sure both partners’ names on listed in the file.  You will receive instructions for doing this.

Activity 2:  Begin rough draft of reflection paper as described below. 

Write a five page reflection paper on what you have learned about poverty from this project.  (Note:  even though the Excel project was done with partners, each individual student should write his/her own reflection paper.)

Address each of the following questions:  (These may be modified by instructor.)

  1. How do people in poverty get out of the trap? 
  2. Why do you think children of poverty are at a disadvantage in our educational system? 
  3. What would you recommend to your elected officials as a way to begin to solve the problem in our country?
  4. What do you think is a fair and livable wage?  What factors need to be considered in determining this number? 

Activity 3:  Make corrections to spreadsheets based on feedback from instructor.


Week 9:  Wrapping Up the Project

Activity 1:  Final face-to-face meeting. Present projects.

Activity 2:  Reflection paper due to instructor.

Activity 3:  Discussion – what did you learn?  Share final thoughts


Please wait while we gather your results.

Discovery Project Forms

Click here to access forms

(login required)

To access Discovery Project forms, click "log in" in the upper right hand corner of the screen and enter username and password.

Next click the "Educators" icon and return to the Discovery Project page.

Note to Parents: Registration forms are available at your participating Catholic elementary school office.

 


Discovery Project Contacts


Brenda White

Associate Superintendent
414-758-2252
whiteb@archmil.org

Janelle Luther
Administrative Assistant
414-758-2256
lutherj@archmil.org

© 2016 - Archdiocese of Milwaukee | 3501 S. Lake Dr., Milwaukee, WI 53207