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 reallife 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 realworld 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 TI82
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
reallife data, students will represent them in a tabular format
 F Given
reallife 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 TI82 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 reallife
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 tchart
2.
Using your TI82, 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 tenthousandths).
 Use this
equation to answer the following
 What is
the coordinate of the xintercept?
 What is
the coordinate of the yintercept?
 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 tenthousandths).
 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 tchart.
 Use,the
TI82 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?
