ARE YOU WORTH YOUR SALT?
Enduring Understanding: Develop a better understanding that using systems of equations in graphical form is appropriate in determining a solution.
Essential Questions:
· What is an informative title for a graph?
· What is an appropriate interval for the x- and y-axes?
· How is a fitted line determined?
· How is an equation of a fitted line determined?
· What do the intercepts of a graph represent in the context of a given situation?
· How can a graph be used to make predictions?
· How are percentages used to determine an increase in value?
· How can a conclusion be supported using mathematical information and calculations?
Lesson Overview:
· Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to how people get paid—hourly, yearly contract, combination of hourly/monthly plus commission, straight commission, etc.
· What is meant by “base salary”? Are there advantages/disadvantages to getting a base salary plus commission?
· Discuss a “fitted line”—What is it? How would a person use a fitted line? How would you show an understanding of a fitted line? Why do you think a fitted line is used? What would happen if a person inaccurately used a fitted line? What operations are necessary to create a fitted line?
· When reading a graph, where are the x- and y-intercepts? What is the relationship between the intercepts and the context of any problem?
· What is meant by receiving a yearly salary increase of a certain percent?
· What is meant when two graphs intersect?
· A good warm-up could be Payday or Ernie Elephant or Patience’s Patience.
· How can you support a conclusion that you make? What evidence from graphs can be used to support/justify your conclusion?
· Use resources from your building.
EALRs/GLEs:
1.1.6
1.4.4
1.5.2
1.5.6
2.2.2
3.3.2
5.1.2
5.2.1
Item Specifications: NS02; PS03; AS03; SR02; SR05; MC01
Assessment:
· Use WASL format items that link to what is being covered by the classroom activity
· Include multiple choice items
Are You Worth Your Salt?
Staci has graduated from school and is working in sales. Each month she earns a base salary, plus commission (therefore the monthly variation). Below is Staci’s income after taxes for the first 24 months.
Staci’s Monthly Take Home Pay During Her First 24 Months
Pay Period
/ Take-home Pay(in dollars)
Month 1 / 1500
Month 4 / 1600
Month 8 / 1700
Month 12 / 1850
Month 16 / 2000
Month 20 / 2050
Month 24 / 2200
1. Graph this data. Make the graph large enough to include Staci’s first 60 months of work.
______
2. Draw a line that fits the data (fitted line) displayed on your scatter plot.
3. Write an equation that describes your fitted line. ______
4. What is the y-intercept? ______What does the y-intercept represent in the
context of this situation? ______
______
5. What is the slope? ______What does the slope represent in the context of this
situation? ______
______
6. Based on your model, how much take-home pay would you predict Staci to make in month
14? ______; During month 32? ______.
7. What is the x-intercept? ______Does the x-intercept have any real meaning
in the context of this situation? Explain your answer.______
______
______
______
8. Staci’s friend, Derek, started working for another company on the same day that Staci started her job. Derek did not receive an increase in pay during his first year. He started making $2,250 per month in take-home pay and still made $2,250 per month during his first 12 months on the job. He received a 5% increase in his monthly salary at the end of each year that he worked. On the same graph depicting Staci’s earnings, graph Derek’s monthly take-home pay for the first 2 years that he worked.
9. The trend of their yearly earnings continues for Staci and Derek for the first 4 years of their employment. Who will be making more money per year after the fourth year? Use information from the graphs and/or equations to support your answer.
______
______
______
______
______
______
10. On June 1, Mary had a balance of $50 in her bank account. During June she made the following four transactions:
· deposited $25
· withdrew $30
· wrote a check for $60
· paid a bank fee of $25
There were no other transactions.
Which was the balance in Mary’s bank account on July 1?
O A. -$90
O B. -$40
O C. +$10
O D. +$190