First lesson

Subject: Mathematics
Date: September 29, 2014
Topic: Inequations
Subtopics: Introduction to Linear Programming
Level: Fourth Form
Time: 40 minutes (9:30-10:10)
References:
Toolsie Raymond (2004) : “Mathematics A Complete Course with CXC Questions” Volume 1.
Pgs. 301-304
Greer A. & Layne C. E. (1994): Certificate Mathematics-A Revision Course for the Caribbean,
Pg. 77-83
Previous Knowledge: Students know deduce inequality provided with graphical representation
and number line illustration. In addition, they know the four inequalities signs and when to use
each depending on the key word used in verbal sentences. Furthermore, they know to construct
simple linear inequality graph.
Objectives: Through guided practice and cooperative learning, students will be able to:
1. Model real-life situation using a linear inequality in two variables (C-A,S)
2. Appreciate the importance of linear programming in solving real-life situation (A)
Concepts: Linear programming is the process of taking various linear inequalities relating to
some situation, and finding the "best" value obtainable under those conditions. A typical
example would be taking the limitations of materials and labor, and then determining the "best"
production levels for maximal profits under those conditions.
In "real life", linear programming is part of a very important area of mathematics called
"optimization techniques". This field of study (or at least the applied results of it) is used every
day in the organization and allocation of resources. These "real life" systems can have dozens or
hundreds of variables, or more. In algebra, though, you'll only work with the simple (and
graphable) two-variable linear case.
The general process for solving linear-programming exercises is to graph the inequalities (called
the "constraints") to form a walled-off area on the x,y-plane (called the "feasibility region").
Then you figure out the coordinates of the corners of this feasibility region (that is, you find the
intersection points of the various pairs of lines), and test these corner points in the formula
(called the "optimization equation") for which you're trying to find the highest or lowest value.
Skills:




Identify which inequality signs to use
Derive and graph the inequality
Identify the feasible region
Deduce the ordered pairs that satisfies the inequality
Attitudes:
 Willingness to participate in class activity
 Work cooperatively to reach a common goal
Materials: worksheet (application problem)
Introduction:
1. Teacher will provide students a brain teaser on inequalities:
2. Students will be given one minute to think about it on their own and then one minute to
discuss with a shoulder partner.
3. Students will then share their solutions with the rest of the class and their approach to
finding the only ordered pairs.
4. Students will be randomly chosen to provide the inequality from the assignment given
and teacher will randomly select students to agree or disagree with the result giving a
logical justification.
Development:
1. In pairs, teacher will provide each student with an example of a question modeling linear
inequality.
2. Through questioning, the teacher will guide students to deriving the appropriate
inequality.
3. Using a scale of 1cm to represent 400 coins on each axis, students will construct an
appropriate graph to model the inequality.
4. Students will then identify the feasible region and shade it. Then they will identify the
ordered pairs of integers in the graph that are possible solutions.
5. Teacher will clarify any misconceptions.
Closure: Teacher will ask students, what the objectives for the day’s lesson were.
Conclusion:
Extended Activity: Students will research other applications of linear programming in real life.
Evaluation:
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________