Title: An Intersection is More than Where Two Roads Meet

Subject Matter Emphasis and Level: This unit is designed for Algebra II students generally including 11^th and 12^th graders.

Instructional Designer: Cindee Evenson

Brief Description of the Unit: This is a unit on solving linear equations.

v Solve a system of linear in two variables by graphing

v Solve a system of linear equations by substitution

v Solve a system of linear equations by linear combination

v Solve and graph a linear inequality in two variables

v Use linear programming to solve real life problems

v Reflect on how solving systems can be used in real life

v Use chemical solutions as an application of systems of equations

v Use the history of WWII weapons to illustrate linear programming

v Have students write their reflections of what they learned in the unit

v Share what they learned in a class presentation

v Determine the solutions of systems in multiple ways

v Create algebraic models to represent problem situations

v Represent situations using the properties of coordinate geometry to answer pertinent questions

v Add, subtract, multiply and divide algebraic expressions

v Evaluate algebraic expressions

v Create tables or graphs to interpret relations and/or functions

v Apply appropriate mathematical techniques in evaluating experimental data

v Use correct spelling, language, punctuation, and capitalization in final copy

v Use available technology for editing and revising

v Employ precise language and technical vocabulary to communicate ideas clearly and concisely

v Use clauses, phrases and sentence structure correctly and appropriately

v Demonstrate proficient use of grammar, diction syntax, and paragraph structure

v Articulate strengths and weaknesses as a writer through personal reflection and /or conferencing

v Use topics, concepts and knowledge form other content areas as an arena and focus for writing

v Work effectively in group setting to solve specific problems

v Use technical terms and notations accurately in oral presentation

v Use visual aids and/or technology to support presentation

 

Prior Learning, Interests, Misconceptions and Conceptual Difficulties: Students will have trouble with this unit if they have not mastered the concepts of graphing lines and adding, subtracting, multiplying and dividing algebraic equations.

This unit is designed to take about two weeks.

Day One

Introduce systems of equations using power point presentation.

Distribute and discuss vocabulary words.

Solve equations using graphing and substitution.

Day Two

Introduce linear combination.

Have chemistry teacher come to class and discuss solutions.

Work story problems dealing with chemical solutions.

Day Three

Internet connect activity where students solve a system of linear equations to find the number of two point and three point goals made by leading scorers in Division I. Go to www.go.hrw.com .

Use keyword: MB1 WBB

Students will work on this project in pairs and also do review problems from the chapter. They will be reminded to review vocabulary words.

Day Four

Short vocabulary quiz will be given.

Introduce linear inequalities in two variables using the overhead projector.

Students will graph using colored pencils.

Students will also graph using the graphing calculator.

Day Five

Students will be in groups of four. Each group member will be assigned either > , < , ³ , or £ . They will be given the equation

y = 2x +1. Each student independently puts in their symbol and graphs their equation . When they are done they will compare results and discuss. They need to decide if all the graphs were done correctly as a group. They will be given three more equations and each person in the group will graph a different symbol each time. After they have finished they will write a reflection on what they learned.

Day Six

The teacher will present an introduction to linear programming using the graph board, and work several examples.

Teacher and students will discuss how linear programming can be used in real life situations.

Students will work problems independently and as a homework assignment.

Day Seven

Linear Programming in World War II Project will be presented. During WWII, the need for efficient transportation of supplies inspired mathematician George Dantzig to develop linear programming. The LST was a ship used during WWII that carried 3 ton trucks and 25 ton tanks. The upper deck could carry 27 trucks but no tanks. The tank deck could carry 500 tons, but no more than 33 trucks. Students will find the maximum number of tanks and the maximum number of trucks a LST could hold. More about this problem and history on the web site

www.mcdougallittel.com  .

Day Seven

Students will be given three story problems and be divided into groups of three. Each person is assigned a role: The constrainer identifies the constraints and writes the inequalities. The grapher graphs the feasible region and identifies its corner points. The maximizer or (minimizer) writes an equation for the objective function and then maximizes or minimizes it. All members of the group work together to solve all three problems with each member taking on a different role with each problem.

Day Eight

Students will work on chapter project. They will be maximizing profits and minimizing costs. Students will solve two business problems by using linear programming techniques that they learned in this unit. One problem deals with a floral shop trying to minimize labor costs and the other with a construction firm maximizing profits. Activities today are done independently.

Day Nine

Students continue to work on projects and may work with a partner to compare results and resolve any discrepancies. Students independently will write a summary of what they learned and how linear programming can be used in real life. Projects will be due the next day.

Day Ten

Students will share the results of what they learned while working on their projects with the rest of the class. They may use a power point or any other visual aid to show their results.

There will be a short paper and pencil test including several story problems.

Assessment: Vocabulary Quiz, Rubric created by students to evaluate work in groups, Rubric for classroom presentation, and paper and pencil test at the end of the unit.

Materials and Resources: Holt, Rinehart and Wilson Algebra II Textbook

McDougal Littell Algebra II Textbook

Community Resources: Chemistry Teacher

v Internet sites

o www.mcdougallettell.com 

o www.go.hrw.com  Keywords: MB1 WBB

v Graphing Calculators

v Power Point program and equipment