Task Portfolio Task Template 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 problem and think about possible 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 they get the final answer 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. Task Portfolio Task Template 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)