5E Lesson Design Template – Tracene Nechamkin – Systems of Equations Expected Student Outcome(s): Students will analyze situations and formulate systems of linear equations in two unknowns. Student will solve systems of linear equations. Students will interpret and determine the reasonableness of solutions. Mathematics TEKS: Target Grade Level/Course: Algebra I Materials/Equipment Needed: projector, screen, computer, video link, copies of break-even worksheet, copies of graphs worksheet, copies of homework problems, paper bowls, pretzels. Engagement (A.8) Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (A) analyze situations and formulate systems of linear equations in two unknowns to solve problems; (B) solve systems of linear equations using concrete models, graphs, tables, and algebraic methods; and (C) interpret and determine the reasonableness of solutions to systems of linear equations. Exploration Explanation Elaboration Describe how you will capture student interest. What kinds of questions should the students ask themselves after the engagement? Describe what hands-on/mindson activities students will be doing. List at least 2 questions you may use to encourage and/or focus students’ exploration. Students are put into groups based on level from previous learning (high with medium, medium with low). Students will view Discovery Education video on break-even/systems of equations to understand real world examples where systems are used. Can you think of other types of applications for systems? What other examples in your daily lives might you find a “break-even”? Why would it be important to know? This is a review/application lesson. Students will be in groups of 3-4. Each student will have a role: time-keeper, facilitator, artist, and scribe. Teacher will explain the activity. Students will work in groups to solve each analysis (2). Scribe will complete table. Artist will graph the equations using two different colors, one for each graph. When groups are complete, teacher will present the solutions on excel spreadsheet and www.mathcracker.com to show the use of technology and how spreadsheets can graph the equations. What information is needed to determine the fixed expenses? What information is needed to determine the variable expenses? List at least 2 higher order thinking questions you may use to solicit student explanations and help students justify them. What questions or techniques will you use to help students connect their exploration to the concept under study? Teacher will ask the questions below. After each question is answered, teacher will show results on the excel spreadsheet. Describe how students will develop a more sophisticated understanding of the concept. What terminology will be introduced and how will it connect to students’ observations? How is this knowledge applied in science or in our daily lives? Break-even point Fixed Expenses Variable Expenses Describe what would happen to the break-even point if Priscilla had to hire a second manager with a salary of $1375? Compare the changes in the graphs from the new hire. The cost of hamburger has increased by $0.05 each. Modify the expense equation and explain the changes in the graph. Students will be able to see a connection of Algebra to realworld application such as finding how many boxes of cookie dough need to be sold for a club to break-even, finding out how many shirts might need to be sold for the FCA to make a profit, and devising a business plan for a summer job. Evaluation How will students demonstrate that they have achieved the lesson objective? This may be done throughout the lesson as well as at the end of the lesson. Students will write a ticket to leave: Develop a situation where you might use a system of equation. Prepare two equations: one that represents possible expenses and one that represents possible income. Day 2: Students will meet in Computer Lab to represent their equations graphically, either using www.mathway.com, www.mathcracker.com or Microsoft Excel.