Level: This lesson is intended for students in
an algebra class. Before beginning the lesson, students will
need an understanding of how to graph inequalities.
The purpose of this activity is for students to
TI-Nspire handhelds to explore the properties of graphs of
inequalities, and to gain an appreciation for the real-life
applications of the topic. This lesson represents an
use of technology because it helps students develop the skills needed
to work with complex problems that can be solved using systems of
inequalities. When moving on to these more involved
situations, the calculator takes care of tasks
and shading the equations and finding the points of intersections; this
leaves students with more time for critical thinking and higher-level
State Standards of Learning (SOLs) Addressed:
Algebra 9: The
student will solve
systems of two linear equations in two variables both algebraically and
graphically and apply these techniques to solve practical problems.
calculators will be used both as a primary tool for solution and to
Geometry 2: The
student will use pictorial representations,
including computer software, constructions, and coordinate methods, to
problems involving symmetry and transformation.
AFDA 5: The student
will determine optimal values in problem
situations by identifying constraints and using linear programming
- Review each of the three student activity
worksheets from the Resources section above. Each
one discusses a different aspect of graphing inequalities.
Since the worksheets are independent of one another, you can
choose any or all of them to be used in your class. For this
document, though, we will focus mainly on the second worksheet (linear
- For each of the activities you have chosen to give to your
class, make copies of the student directions. Note: each of
the three activities contains the student directions, followed by the
teacher notes, both in the same file. You will probably want
to ensure that your students don't have the teacher notes included in
the papers you give to them.
- Note that we are using the TI-Nspire instead of the
TI-83/TI-84s listed in the worksheets. Make sure to review
the procedure for graphing inequalities on the Nspire, which are
described further down this page. These instructions will
most helpful if you have chosen to focus on the second worksheet
- Review with your students the procedure for graphing
inequalities on the TI-Nspire, as the directions listed in the student
worksheets pertain to graphing inequalities on the TI-83/TI-84.
- Allow students to work in groups of 2 or 3. For
each of the activities you have chosen for your class, all you need to
do is give your students sufficient time to follow the directions
contained in the student worksheets you have passed out to them.
Make sure to walk around the classroom as your students work,
assisting them and clarifying and questions or misconceptions.
- Be aware of the following differences between the worksheet
(which is written for the TI-83/TI-84) and this lesson plan (which is
writte for the TI-Nspire):
- Page 49: the Nspire does not allow you to shade just the
region which is the intersection of all the inequalities.
Every inequality must be shaded seperately, and the region of
interest is where all of these seperate shadings overlap.
- Page 49: to find the corner points of this region of
interest, on the Nspire you will need to find the intersection of the
appropriate lines instead.
Inequalities on the TI-Nspire:
- Inequalities can only be graphed on certain kinds of pages
within your document. Either begin a new document, or insert
a new page to your current document, and choose the "Graphs and
- You will see a blank Graphs and Geometry page appear, with
a prompt at the bottom of the screen asking you to input an equation
- Delete the part of the prompt that says "f1(x)=" and
replace it with an inequality.
- Press the Enter key and your inequality will be graphed on
- To add another inequality, press the Menu button, and under
the Graph Type option, choose Function.
- The same way you entered the first inequality, delete the
part of the prompt which says "f1(x)=" and replace it with your own
inequality. To get a greater-than-or-equals or
less-than-or-equals sign, press Ctrl + > or Ctrl + <.
Then press Enter to graph your new inequality.
- Continue graphing as many inequalities as desired, using
the same steps. For this demonstration, I graphed one more
- To find points of intersection, first open the menu by
pressing the Menu button. Then move down to Points &
Lines, and choose Intersection Points.
- Move your cursor so that it is hovering over the first
inequality you want to find the intersection point for, and press the
mouse click button (in the center of the pointer wheel) or press the
Enter button. Then move your cursor so it is hovering over
the second inequality, and press Enter again. The
intersection point will automatically be labeled and displayed on the
- The more inequalities you graph, the more difficult it
becomes to tell which region of the screen is the darkest one (i.e. the
region that fulfills all of the inequalities being graphed).
To help fix this, you can change the level of shading for
each inequality. Open the menu, and under the Actions
category, choose Attributes. Then move your cursor until it
is hovering over the line you want to change properties for, and click
the center mouse button or press Enter.
- You will see three small boxes pop up. Using the
up/down/left/right buttons on the mouse wheel, you can change the
shading color and line thickness for your selected graph.
- You can view a list of all the inequalities you are
graphing, as well as edit the equations for these inequalities.
To do this, move your cursor to the bottom left corner of the
screen and click on the >> mark. This opens a
prompt at the bottom of the screen, but instead of entering anything,
press the mouse wheel right and highlight the ^ mark. Click
again and the list of all your inequalities will be displayed.
You can press the up/down buttons on the mouse wheel to
which line you are highlighting, and you can edit the line you are
currently highlighting like normal.
resources for this lesson were retrieved from our course