Task Name: Objective: Save the Earth, Clean our Air!

```Task Portfolio
Task Name: Save the Earth, Clean our Air!
Objective: - Exploring the mathematics behind linear programming
- Working with multi-variable inequalities
- Optimization
- Model real-world situations with linear programming
Placement: Before and after section 3.4
Standard: 2.4b – Understand solving equations as a
process of reasoning and explain the reasoning
Indicators (bold if hit):
ME MR SP CL C
RL IL
__ __ __
Brief Description: Students are given information about two types of trees and
constraints they need to follow for planting these trees (money and area) and are
asked to find the amount of each type of tree they can plant that will maximize
carbon monoxide absorption.
Supplies:
 Handouts
 Calculator, graph paper
Implementation Plan:
Teacher
Provide students with copies of the handout
with map of possible areas to plant trees as
well as the statistics on each type of tree
that will be planted.
(Map may or may not be used
depending on time. If you don’t want
them to compute the area of 45, 000
square feet, give it to them instead)
Student


Students individually explore the
ways they could tackle this problem.
Students work with their group
members to decide how many of
each tree they need to maximize
the carbon monoxide absorption
After work time (whether or not all of the
Allow students to discuss each other’s
groups are done), strategically pick a couple strategies and whether or not they will/did
of groups to share what strategies they
work.
have decided to use.
Allow more group work time.
Let students change their approach or
refine what they’ve already started to see if
Guide share out and large group discussion Share and discuss strategies and
to lead to the amounts of each type of tree solutions.
that maximizes absorption.
Example Approaches/Solutions:
 Students may use guess and check to find their answer
 Students may create a table
 Students may create linear inequalities and either try solve them algebraically or
create a graphical representation
Evaluation / Scoring Options:
 After whole class discussion, students individually write a reflection about their
understanding of what it means to maximize a value given certain restraints.
o Proficient: concisely describes the components of the restraints of the
functions and what the solution means in terms of the problem
o Not Proficient: reflection includes the solution to the problem but limited or
no explanation about the meaning of the solution and the constraints that
were given.
 Observe group discussions and offer a participation grade based on certain
elements of discussion, such as use of mathematical vocabulary, etc.
Extending OR Supporting Options:
 Guide individual groups through questioning (support)
 Suggest strategies for groups who get stuck (support)
 Ask students to write equations for the constraints (if they haven’t already) and
graph them on a graphing calculator to see the feasible region (Extension)
 Have students work with different parameters. Brings up the discussion of having
fractional numbers and whether or not those type of numbers work with this
particular problem. Can we have fractional trees?? (Extension)
Handouts:
 Directions for activity with information about each type of tree and the constraints
they must follow
 Copy of the city map with the areas designated for tree planting (use is optional)
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