OBJECTIVE
SWBAT use systems of linear equations to solve real-world problems
C.C.S. Expressions and Equations: 8.EE.8b, 8.EE.8.c
KEY POINTS
1) WHAT:
systems of equations: a set of two or more equations that have the same variable
linear equations: an equation between two variables that gives a straight line when plotted on a graph
2) HOW:
· Graphing Method
· Substitution Method
· Elimination Method
3) WHY: You can use a system of equations to model real life data. This is important because it can help us solve problems in our community.
OPENING (5 min.)
Teacher Actions:
Students will silently copy down notes in notebook as follows:
Vocabulary Review:
systems of equations: a set of two or more equations that have the same variable
linear equations: an equation between two variables that gives a straight line when plotted on a graph
Reminder!
- To solve a system of equations using the elimination method, you eliminate one variable and solve for the remaining variable.
- To solve a system of equations using the substitution method, you one of the equations for one of the variables and then plug that into the other equation.
- To solve a system of linear equations by graphing, we find the points of intersection.
Student Actions:
Students will copy notes silently and independently.
INTRODUCTION OF NEW MATERIAL (10 min.)
Teacher Actions:
“The past few days we have learned all of the different ways that we can solve systems of two linear equations with two variables. Today we are going to be using what we have learned to help us analyze these systems, so we can understand real life problems. This is important to practice because it can help us to solve problems in our community that we otherwise did not know were there. Practicing to analyze these types of problems will also help us improve our math literacy and helps us to understand how what we’re learning fits into our every day life.
Consider the following question:
Taxi company A charges a flat fee of $8.50 plus $2.00 per mile traveled. Taxi Company B charges a flat fee of $5.50 plus $4.00 per mile traveled. When would it be better to hire Company A? Company B? Explain.
--The first step is to write a system of equations to represent the situation. Let x= the number of miles traveled, and let y= the total charge, in dollars.
Y= 8.50 + 2.00x
Y= 5.50 + 4.00x
--The second step is to graph both equations in the same coordinate plane. The lines intersect at (1.5,11.5)
--The third step is to analyze the graph. For a ride that is less than 1.5 miles, Company B is less expensive. For a ride that is greater than 1.5 miles, Company A is less expensive. The cost is the same for a ride of 1.5 miles.
Working with the people at your table, turn to pages 50 and 51 in your workbook and try more problems like this one.
Student Actions:
Students will be taking notes in their workbooks. Students will be silent and raise their hand for clarifying questions.
GUIDED PRACTICE (25 min.)
Teacher Actions:
I will use this time to help students who may require more explanation as to how they can analyze the equations using the methods we have previously learned. This will allow me to check for understanding and allow the high-fliers to move at their own pace.
Student Actions:
Students will be actively engaged during the guided practice. This means that they will be working with their peers to solve the problems in the book, not just copying down one student’s work.
INDEPENDENT PRACTICE (50 min.)
Teacher Actions:
Each student will be given the following problem:
Globalization and Labor Problem
Nike Corporation currently pays workers in China $0.44 per hour to work at their factory. After their shoes are made, it costs Nike $750 dollar to ship them to the United States to be sold.
A local shoe company pays workers in the United States, $7.50 per hour to work at their factory. After their shoes are made it costs them $500 to ship them to various parts of the country to be sold.
--What linear equations can represent the amount of money being spent per hour by both companies?
-- Use both the substitution method and the elimination to demonstrate how to solve system of linear equations.
--Graph both equations to visually represent each company’s cost of manufacturing.
--Write a one page reflection based on an analysis of these graphs.
--Some things to think about while reflecting:
How would you feel if you were a worker in China? In the United States? Why might Nike choose to hire workers in China instead of in the United States? Do you think ethicality is important when doing business? What other questions does this data make you think about?
Student Actions:
Students will be actively participating in this assignment and using what math skills they know to interpret the data. They will think critically and reflect upon the data, helping to form their own opinions on fair wages overseas.
LESSON ASSESSMENT: (5 mins)
Once students have had an opportunity to practice independently, how will they attempt to demonstrate mastery of the knowledge/skills required of the objective?
Teacher Actions:
Since this is the end of the chapter, INM reflection paper will be used as their assessment. This will help me to see whether or not they understand how to analyze and compare linear equations.
Student Actions:
Students will silently be work on their INM activity.
CLOSING (2 min.)
Teacher Actions:
I will hand out an article about fair wages and sweat shops. I will summarize what the article is about and tell them to read and highlight important parts for homework. We will have a brief discussion about the article in the Do-Now of the next day’s lesson.
Student Actions:
Students will listen silently as I briefly talk about what the article is about. They will be asked to talk to their table partner to debrief how this information made them feel.
HOMEWORK
Read/highlight/take notes on article about sweat shops.