AUTHOR’S NAME: Lauren K. Hoegen Dijkhof TITLE OF THE ...

AUTHOR'S NAME: Lauren K. Hoegen Dijkhof TITLE OF THE LESSON: One and Two Variable Inequalities DATE OF LESSON: Fall 2009 LENGTH OF LESSON: Two 45 Minute Lessons NAME OF COURSE: Algebra I

TEKS ADDRESSED:

?111.32. Algebra I (One Credit) (a) Basic understandings. (4) Equations and inequalities arise as a way of asking and answering questions involving

functional relationships. Students work in many situations to set up equations and inequalities and use a variety of methods to solve them.

(A.8) Linear functions. (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.

CONCEPT STATEMENT: Linear Inequalities will be used to provide a basis for economic sustainability in the students' projects.

PERFORMANCE OBJECTIVES:

Students will be able to: 1. Graph one and two variable inequalities. 2. State one and two variable inequalities when given a graph. 3. Solve for variable inequalities.

SAFETY CONSIDERATIONS: None. SUPLEMENTARY MATERIALS, HANDOUTS: Handouts will be received from Instructor.

ENGAGEMENT What the Teacher Will Do

The instructor will start off with a PowerPoint slideshow of celebrities and ask the students to guess between what ages the celebrities are.

"We can write these statements mathematically by using symbols. Let X be Halle Berrys age. We dont know what it is, but you told

Probing Questions Who is this person?

She is no younger than what?

She is no older than what?

So, can she be 35 if we say X>35?

Time: 10 Minutes Student Responses Potential Misconceptions Halle Berry.

The students will give various guesses as to how young Halle Berry could possibly be. For example 35. The students will give various guesses as to how old Halle Berry could possibly be. For example 45. No.

ENGAGEMENT What the Teacher Will Do

me that it was greater than 35. A way to write this is X>35. That means she has to be older than 35." "However, we can say she is 35 if we wrote X35. This is read as ,,x is greater than or equal to 35. There are similar symbols for the concepts of ,,less than and ,,less than or equal to." "You told me Halle Berry was no older than 45." "We can also combine statements. X35 and X45 can be combined to be 35X45. Lets see if you are right. Halle Berry was born on August 14, 1966, which makes her 42." "Then you were right. Im going to show you more famous people and I want you to write down more inequalities of how old you think they are. So, take out a sheet of paper and something to write with. Try not to use numbers that are more than ten years apart. The closer your numbers are, the better you are at guessing the persons age." After each celebrity, reveal the age. "Julianne Hough was born on July 20, 1988, so she is 20. Enrique Iglesias was born on May 8, 1975, so he is 33. Vanessa Hudgens was born on December 14, 1988, so she is 19. Barack Obama was born on August 4, 1961, so he is 47. Kobe Bryant was born on August 23, 1978, so he is 30. Johnny Depp was born on June 9, 1963, so he is 45. Sean Connery was born on August 25, 1930, so he is 78." "In order for you to be able to

Probing Questions Seeing the symbols for greater than and greater than or equal to, what are the symbols for less than and less than or equal to? How would we write that? Is 42 more than or equal to 35, but less than or equal to 45?

What does mean?

Time: 10 Minutes Student Responses Potential Misconceptions < and X45 Yes.

Less than or equal to.

ENGAGEMENT What the Teacher Will Do

Probing Questions

go through todays lesson, you need to know the four inequality symbols."

What does < mean?

How is < different from ?

What does > mean? What does mean?

Time: 10 Minutes Student Responses Potential Misconceptions

Less than. With one you can be equal to something, but with the other you cant. More than. More than or equal to.

EXPLORATION AND EXPLANATION

What the Teacher Will Do

Probing Questions

The teacher will hand out the Vocab Practice Worksheet so that students can practice graphing inequalities involving one variable. Once students have completed the worksheet, the instructor will call on them to share and explain their answers. Demonstrate problem 1 by inquiry and explanation. "Let's take a look at problem one. The question is asking us to use an inequality to define the shaded region, and whether the point is in that region. We have already learned how to find the equation of a line so let's fill out the first three blanks together."

"As x increases by 1, y increases by 2, so the rate of change is 2 and m would be 2."

"B is the y-value when x is zero, and it is also the yintersect of the line. In this graph, it is -4."

What does m stand for?

What is the value of m and how did you find it? What does b stand for?

What is the value of b and how did you find it? Now that we have found m and b, what is the equation?

Time: 25 Minutes Student Responses Potential Misconceptions

Slope.

2. To get to the next point you rise two and run 1. Y intercept -4. Look at the Y-intercept or find the y value when x is zero Y=2x-4

EXPLORATION AND EXPLANATION

What the Teacher Will Do

"Because we have a dotted line instead of a solid line, were not going to use any symbols that have an ,,equal to in it. So we cant use ,,less than or equal to, or ,,more than or equal to symbols. We can use ,,less than or ,,more than symbols only." "Because the shaded area is above the line, we can assume that y2x-4. However, to make sure our inequality is correct, were going to use (0,0) as a test point. (0,0) is in the shaded region, so when we plug it in the values, the inequality should be true."

"Then we know that the inequality y2x-4 is true. Remember, when we say a point is a solution, it means it is in the shaded region. Now I want you to work on the rest of the problems. They are very similar to question 1." After students have finished working, have them share and explain their answers to the front of the class.

Probing Questions Is the shaded area above or below the line?

What is the left side of the inequality when we substitute in 0?

What is the right side of the inequality when we plug in 0? Is 0 greater than or equal to-4?

Time: 25 Minutes Student Responses Potential Misconceptions Above.

0

-4 Yes.

ELABORATION What the Teacher Will Do

"Your homework assignment for tomorrow will be used later with linear inequalities. You are going to be designing a music venue for the recreation section of your project. I want you to design a music venue however big you want it and research how much it may cost. Make sure you also report how many people can fit into this music venue." Have students fill out an exit slip

Probing Questions

Time: 10 Minutes Student Responses Potential Misconceptions

ELABORATION What the Teacher Will Do

answering the following question: Describe three real-life situations where you would need to use a two variable inequality. As a formative assessment, students will turn in the worksheets they completed in class and have them returned to them the next day.

EVALUATION What the Teacher Will Do

Students will receive a unit test on what they learned.

Probing Questions Probing Questions

Time: 10 Minutes Student Responses Potential Misconceptions

Time: 45 Minutes Student Responses Potential Misconceptions

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