Marie Curie Math & Science Center
 
Dr. Mary Ellen Ferraro
St. Thomas Aquinas College
GROUP I

Coordinate Graphing and Linear Equations
Grade 9, 11 and College Algebra



COMMENCEMENT CONTENT STANDARDS

  • Students will use mathematical analyasis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.
  • Students will access, generate, process, and transfer information using appropriate technologies.
  • Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions.

BENCHMARK STANDARDS
CONTENT STANDARDS
 

  • Students will use mathematical modeling/multiple represaentation to provide a means of presenting, interpreting, communicating and connecting mathematical information and relationships
  • Students will usae graphing utilities to model real-world problems with linear equations and tables to analyze mathematical phenomena.

PERFORMANCE STANDARDS

  • Students will be able to take raw data and express it in the form of a table and as a linear equation
  • Using the models they created, students will make decisions and predictions of future events
  • Students will use a graphing calculator to help them to form mathematical models and to make informed decisions.


CONTENT STANDARDS

  • The TI-82 calculator will be instrumental in helping the students graph a given a set of coordinates Cartesian Plane, determine the slope of a line numerical and graphical methods, and information obtained in the local or newspapers students will develop linear models use these models to evaluate situations and make predictions for the future.

 PERFORMANCE MEASURES

Students will be marked on a scale ranging from 1 to 4. The grades will be assigned in the following fashion:
 

  • 1 Completing task A
  • 2 Completing tasks A, 8 and C
  • 3 Completing tasks A, 6, C and D
  • 4 completing tasks A, B, C, D, E and F
  • A Students will be able to graph a set of coordinates and connect the points and create a picture
  • B Students will be able to find the slope of a line numerically
  • C Given a picture of a variety of lines, students will be able to determine if the slopes are negative, zero or if the lines have an undefined slope
  • D Given equations of lines, the students will be to determine if the lines are parallel or perpendicular
  • E Given real-life data, students will represent them in a tabular format
  • F Given real-life data, students will create a model to represent the data and to make predictions.


ENABLING ACTIVITES
    This two week lesson plan will cover material concerning coordinate graphing and the creation of linear equations. The content of this unit will be developed using the TI-82 calculator.  Time will be sent having the students and graph points in the Cartesian Plane using the calculator. The students will be introduced to the concept of the slope of a line.  They will be asked to represented slopes of different lines both numerically and graphically. Slopes of lines which are parallel and perpendicular will be discussed, as well as lines that have slopes which are positive, negative, zero and lines whose slopes do not exist. The students will be introduced to the concept of writing equations of lines.  They will then be given situations from real-life problems and they will be asked to represent this data in both a tabular form and as a linear model. Using the model which they created they will be asked make predictions concerning possible outcomes of future events.



 WORKSHEET 1

1. Simplify the expressions in both the x and y column and place the answers in a second t-chart

 2. Using your TI-82, graph the coordinates which you found in question 1.

3. Which coordinates are located in Quadrant I? II?  III? IV?

4. Change the type of graph from one where you just points to one where you connect the points.  What have you drawn?



WORKSHEET II

You are in need of a new car since your old car has died, so on Monday you stop at a dealership which offering a 42 month lease.  The salesperson tells you the terms of the lease will require you to pay $159 a month.
In addition you will be required to pay $1000 down, a $ bank fee and a $200 security deposit.

  • Write an equation which will represent the terms of this lease.
  • Using the equation which you just formed, how money will you have paid at the end of:

6 months
15 months
26 months
36 months
42 months

On Tuesday you decide to try another dealership who is offering another deal on the exact same car you yesterday.  This salesperson offers you a 36 month lease for $199 a month.  The security deposit here is $400 and bank fee is $798.

  • Write an equation which will represent the terms of this lease.
  • Using the equation which you just formed, how money will you have paid at the end of

6 months
15 months
26 months
36 months.
 

  • Using your graphing calculator, graph each equation and determine at what point have you paid the same amount of money on both of the leases.


WORKSHEET III

According to the National Association of Scholars, the average number of instructional days at a college in the year 1914 was 204.  During the academic year 1993, the number of days had decreased to 156.  If you represent this information as order pairs in the form (year, days in class)

  • Determine the slope of the line which can be drawn between these two points.
  • Using the slope which you just found, write the equation of the line which can be drawn between these two points(Round all decimals to ten-thousandths).
  • Use this equation to answer the following
  • What is the coordinate of the x-intercept?
  • What is the coordinate of the y-intercept?
  • The slope of this line is
  • Using this equation and assuming that nothing differs, in what year will a student not have to go to class?

While the number of days that a student spends in formal classes have decreased, the average tuition paid by have increased.  In 1914 the average daily cost was $7.lS
while in 1993 the average cost was $100.  If you this information as an order pair in the form (year,  cost)

  • Determine the slope of the line which can be drawn between these two points.
  • Using this slope, write the equation of the line which can be drawn between these two points(Round all decimals to the nearest ten-thousandths).
  • Using this equation, determine
  • The x - intercept.
  • The y - intercept.
  • The slope of this line is
  • If the rate of inflation continues, in what will students be paying an average of $200 a day for college?


WORKSHEET IV

You are a little short of cash so you decide to turn your hobby of making holiday ornaments into a money proposition by selling them at a flea market.  The first day you are there you sell 3S items and you make a profit $20.  The next time that you sell the items you sell lS2 the profit you make is $254.  The third time you sell ornaments you sell 98 of them and the profit you make is $146.

  • Express this information in a t-chart.
  • Use,the TI-82 calculator and form a linear which can be used to express this information.
  • If you sold 163 ornaments, how much profit would you have made?

  • You need $600 to cover the cost of your car and insurance this month.  How many ornaments do you need to sell to cover these two expenses?

 

St. Thomas Aquinas College, 125 Route 340, Sparkill NY 10976-1050