Linear Inequalities Investigation
Mathematics Big Idea and Major Topic: Linear Inequalities
More specific statement of the topic: Writing linear inequalities, understanding &
analyzing solution sets (is an inequality),
determining where to shade, and graphing the linear
inequalities
What the students already know: How to graph points and lines, vocabulary terms, linear
equalities (slope-intercept form, etc), and
solving/manipulating linear equations
What part will the students have to figure out on their own? The inequalities from word
problems
Context: Explain how to budget for the cost of dinner and renting a limo ($60 per hour)
for homecoming, giving them the cost for each and a budget. An extension
could be what happens if you exceed the cost of the rental agreements?
Statement of the task: Develop a visual image (a table and a graph), develop a formula to
represent the given constraints, find and explain the possible
solution set.
Where might they get stuck? The realization that the solution could potentially not equal
(don’t have to spend all the money), that the answer is a
region, the reasonability and limitations of the feasible set,
scaling the x and y axis.
What questions can I use to prompt them without giving away answers?
What if I don’t spend all of my money? What if I borrow a car and only rent the
tuxedo? Are there other restrictions on the situation?
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
1
Spending With Limits
Part 1: The Inequality Game
Play the following game with your partner.
1. For each turn roll both dice (red and blue). One roll per turn.
2. You will score one point if the sum of your dice is less than or equal to 7.
Winning example: Blue=3 and Red=2
3. Record the winning rolls in the table below.
4. The winner is the person who scores 10 points first.
BLUE
RED
TOTAL
1. On the graph paper provided, plot your winning rolls. Blue dice numbers are on
the x-axis.
2. Give an example of another roll that would win. ____________
3. Where does there appear to be a boundary line?__________________________
4. Draw the boundary line.
5. Write the equation of this line. ________________
6. Explain how you can change your equation to represent all winning rolls?
________________________________________________________________
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
2
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
3
Part 2: Going to Prom
You are going to prom. Everything is paid for except the limo and dinner. You have a
$120 budget for the limo and dinner.
You and your friends are splitting the limo so it will only cost you $10 per hour. For
dinner you are going to a Tapas restaurant. Items are $8 each at this restaurant and, of
course, you want variety!
Make a table of 15 possible ways to spend your money. Two examples are given.
LIMO HOURS TAPAS CHOICES
4
8
4
5
$ TOTAL
10(4) + 8(4) = $72
10(8) + 8(5) =$120
1. On the graph paper provided, plot your possible spending plans. The number of
Limo hours is on the x-axis.
2. Where does there appear to be a boundary line?__________________________
3. Draw the boundary line.
4. Write an equation of this line. ________________
5. Explain how you can change your equation to represent all possible spending
plans?
________________________________________________________________
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
4
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
5