Topic: Systems of Linear Equations
Lesson Topic: Graphing, Substitution and Elimination Comparison Chart
Grade: 11
Duration: 40 minutes x 2 classes
Summary of the Flow of Content:
In grade 9, students developed the ability to generalize a pattern generated from a problem-solving context using linear equations and verify by substitution. They should also have learnt to graph linear relations, analyze the graph, and interpolate or extrapolate to solve problems. They should have also been introduced to elimination or linear addition as another alternative method.
This lesson that might be taught at Senior 3 will take these outcomes and have the students examine what’s the best way to approach any set problem involving linear equations. They will determine if one method is better than another or if it is dependent upon the context of the problem or if it matters at all. It will develop the frame of mind of the student that each problem may have multiple solutions and methods in which to attain those solutions. It is a way for the students to develop analysis and critical assessment of the methods they have learnt previously and apply them accordingly. This decision making exercise will relate to real world challenges and applications.
Major Concepts/Generalizations/Understandings
· That graphing, substitution, and elimination are all beneficial as each question can be solved more effectively with a different method.
· That linear equations are used to solve real world problems.
Future Lesson Goals:
· SWBAT select which method is the quickest to use based on the way the question is presented, apply the method, and describe why they used this method.
· SWBAT decide whether they want to use this prediction style or favour a different method and reflect on the reasons for this decision.
Lesson Objectives/Outcomes
· Students will be able to (SWBAT) solve equations using the graphing, substitution, and elimination methods.
· SWBAT see that different questions favour different methods as one method takes less time to complete in each of the three examples.
· SWBAT make connections between the original questions and methods through reflection.
· SWBAT connect linear equations to real life problems.
· Teacher candidates will be able to (TCWBAT) see where this lesson can fit into grade 9-12 classes.
· TCWBAT see the value of this lesson as it addresses the overarching goals of using technology and making connections to real world problems.
Lesson 1:
0. Generating Interest and Getting on Topic
· As students come into class, give them the problem y= 4x/3 + 3 and y =-2x/3 -3. Ask them to solve the system of equations using the method described on the paper. (graphing, elimination or substitution: 1/3 of the class for each method) They are to show and number each step.
Introduction (10 minutes)
· Have students take out a piece of paper.
· Students are to fold their paper into three columns. At the top of each column they will write Graphing, Substitution and Elimination. This is a comparison Chart.
· Write down the following on the board: y= 4x/3 + 3 and y =-2x/3 -3 and under it make the three headings and columns.
· Work through the solutions as a class, asking students to tell you what to write step by step. Be sure to number and show all of the steps, and stress that this is important. If someone skips a step, write it down, ask if all the steps were shown. Use guiding questions if needed.
· Once all three methods are complete, ask students what discoveries they have made about each of the three methods and the connections between them. Do more examples as needed.
2. Development (30 minutes)
· Explain to students that they are going to do another example on their own. Once they are done, they will turn the page over and write a one-paragraph reflection of what discoveries they made about the three methods. (2x + y = 5, 3x + 3y = 7)
· Float and offer help where needed.
3. Closing (10 minutes)
· Ask students what they discovered in their reflections.
· Note: Students of different ability levels would receive different questions. (Differentiating Instruction)
Lesson 2:
Introduction: (10 minutes)
· Have students take out their reflections from the last class. In their home groups of four students they will discuss the discoveries they made in the reflection portion of their homework.
· Ask if there were any discoveries that students want to share. If there are none, probe students for a few examples.
Development:
A. Instruction (15 minutes)
· Put the supply and demand question on the overhead. Work through questions 1 and 2 on the board. (Link to this question at www.reachtheteach.blogspot.com)
· Guide the students through finding the equation for both lines.
· Show students the results of solving using substitution and elimination.
· Discuss discoveries and comparisons.
B. Practice: (15 minutes)
· For a group of students, the next thing would be practicing three questions using the comparison chart. Each question favours a different method. Float.
1. The data provided in the table below show the supply and demand for video games at a toy warehouse
Price $20 $30 $40
Supply 150 250 250
Demand 500 400 400
Price $20 $30 $40
Supply 150 250 250
Demand 500 400 400
2. 2x - 3y = -2 and 4x + y = 24
3. 2x - y = 9 and 3x – y = 16
Closing: (10 minutes)
· Ask students what discoveries they made. Discuss further.
Homework:
For homework, students are to complete the following 3 questions:
1. 2x + 4y = 18 and 6x – 3y = -36
2. 7x + 3y = 10 and 8x + 2y = 14
3. You are looking at buying a cell phone. There are two plans available. Plan 1 costs $60 for 200 minutes, then 10 cents a minute after that. The second plan costs $40 for 200 minutes, then 20 cents a minute. Use the following table of values to solve the problem.
Minutes 200 300 400 500 600
Plan 1 60 70 80 90 100
Plan 2 40 60 80 100 120
Resources Used for this Lesson:
A Game That You Could Use For This Lesson: (You need to subscribe to view the game.)
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