Algebra 1
Project Based Summative Assessment
Name
Objective: Students will apply functional relationship concepts to a real-life situation and use vocabulary and learned
concepts to communicate mathematical information about the situation.
Steps:
1)
2)
3)
4)
5)
6)
7)
8)
Determine the independent and dependent variables for your situation.
Create a table of values representing this situation, including the variables.
Determine whether this represents a functional relationship or not.
Determine whether the graph would be discrete or continuous. (Flip this page over for definition on discrete vs.
continuous)
Determine the domain and range for the table of values you created.
Create your poster:
a) Title your poster at the top (NEATLY)
b) Write your scenario below that (don’t write the question)
c) Copy your table of values onto your poster (NEATLY) including your variables
d) Answer question 3 using a complete sentence and using a dependency statement
e) Answer question 4 using a complete sentence and tell why
f) List the domain and range
g) Identify variables for independent and dependent variables
h) Create a function rule
i) Answer the question to your scenario using a complete sentence
j) Decorate---Make your poster look good!
Make sure your NAME is on the back of your poster
Glue or tape your scenario and question to the back of your poster.
*** You can use your computer to create the poster or make one using markers, colored pencils, and paper. It is your
choice, but you are responsible for 2 posters.
Ways to write Domain and Range: {(2, –3), (4, 6), (3, –1), (6, 6), (-2, 3)}
1. List the values: Domain: x = {-2, 2, 3, 4, 6}
Range: y = {-3, -1, 3, 6}
When listing the domain and range go in order from least to greatest and if a number repeats you don’t need to write it
again.
2. Inequalities:
Domain: -2 ≤ x ≤ 6
Range: -3 ≤ y ≤ 6
When writing the inequality start with the minimum number on the left, the maximum on the left, the x or y in the
middle means that the domain or range is between the minimum or maximum. Use the ≤ symbol because the domain
or range can be that minimum or maximum number.
Continuous
Discrete
Definition: A set of data is said to be continuous if the
values belonging to the set can take on ANY value
within a finite or infinite interval.
Definition: A set of data is said to be discrete if the
values belonging to the set are distinct and separate
(unconnected values).
Examples:
• The height of a horse (could be any value within the
range of horse heights).
• Time to complete a task (which could be measured
to fractions of seconds).
• The outdoor temperature at noon (any value within
possible temperatures ranges.)
• The speed of a car on Route 3 (assuming legal speed
limits).
Examples:
• The number of people in your class (no fractional
parts of a person).
• The number of TV sets in a home (no fractional
parts of a TV set).
• The number of puppies in a liter (no fractional
puppies).
• The number of questions on a math test (no
incomplete questions).
NOTE: Continuous data usually requires a measuring
device. (Ruler, stop watch, thermometer,
speedometer, etc.)
NOTE: Discrete data is counted. The description of
the task is usually preceded by the words "number
of...".
Function: In the graph of a continuous function,
the points are connected with a continuous line, since
every point has meaning to the original problem.
Function: In the graph of a discrete function,
only separate, distinct points are plotted, and only
these points have meaning to the original problem.
Graph: You can draw a continuous function
without lifting your pencil from your paper.
Graph: A discrete graph is a series of unconnected
points (a scatter plot).
Domain: a set of input values consisting
ofall numbers in an interval.
Domain: a set of input values consisting of only
certain numbers in an interval.
In Plain English: A continuous function allows the xvalues to be ANY points in the interval, including
fractions, decimals, and irrational values.
In Plain English: A discrete function allows the xvalues to be only certain points in the interval,
usually only integers or whole numbers.
Why do we care? When graphing a function, especially one related to a real-world situation, it is important to
choose an appropriate domain (x-values) for the graph. For example, if a function represents the number of
people left on an island at the end of each week in the Survivor Game, an appropriate domain would be positive
integers. Hopefully, half of a person is not an appropriate answer for any of the weeks. The graph of the people
remaining on the island would be a discrete graph, not a continuous graph.
TITLE
Chuck charges $6 per hour to haul junk.
# of Hours
Amount of
(Independent)
$ Made
(h)
(Dependent)
(a)
0
0
1
2
6
12
3
4
18
24
5
6
7
8
30
36
42
48
This is a functional relationship because the amount of
money Chuck makes depends on the number of hours
Chuck spends hauling junk. The graph would be
continuous because he could work part of an hour.
Domain: 0 ≤ x ≤ 8
Range: 0 ≤ y ≤ 48
h = number of hours
a = amount of money made
a = 6h
Chuck would make $48 if he hauled junk for $48 hours.
Grading Rubric (23 points)
Independent and Dependent variables are identified correctly (2 points)
Table of values is correct (4 points)
Variables identified and labeled (2 points)
Functional relationship statement is correct and written as a complete sentence (2 point)
Discrete or continuous is correct and written as a complete sentence (2 points)
Domain and range is correct and written correctly (2 points)
Title is appropriate, creative, and neat (2 points)
Scenario written completely and neatly (2 points)
Question from scenario is answered correctly and in a complete sentence (2 points)
Function rule is correct (1 point)
Decorated/creative/neatly completed (2 points)
Name on back (1 point)
Scenario and question taped or glued to the back (1 point)