Rachel+Unit+Plan

Unit Introduction  Understanding inequalities is very important in the real world. It is vital that students learn not only how to work with inequalities, but also the why behind them. With an understanding of inequalities a student could budget money better or, for example, a group of students could figure out how many t-shirts they would need to sell for their club to make a profit. For example, a student organization is selling t-shirts to make money. They can sell long sleeve or short sleeve. They know that it will cost a certain amount to make all the t-shirts; therefore they need to figure out how much they should sell each shirt for so that they can come out on top. Similarly, they could have already figured out how much they want to sell each shirt for, but now need to figure out how many of each type of shirt they would have to sell to see if they will come out ahead. The students would have to understand and know how to compute inequalities to solve these problems. Another example is that a person has a certain amount of money to spend on groceries or clothes. Using inequalities, the person could figure out how many of each food items or how many clothes they could purchase. Inequalities are very helpful when it comes to using money, which would be a good thing to mention to students while teaching this unit. Personally, I chose this topic, because I enjoy algebra and enjoy working with inequalities. Inequalities always make me think, because I always have to check to make sure that the inequality sign is facing the correct way. EA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.  EA-1.3 Apply algebraic methods to solve problems in real-world contexts. EA-1.4 Judge the reasonableness of mathematical solutions. EA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic). EA-2.5 Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions. EA-2.6 Carry out a procedure to evaluate an expression by substituting a value for the variable. EA-4.8 Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution. EA-5.12 Analyze given information to write a linear inequality in one variable that models a given problem situation. Represent and analyze mathematical situations and structures using algebraic symbols. · Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations  · Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency-mentally or with paper and pencil in simple cases and using technology in all cases  · <span style="font-family: 'Times New Roman','serif'; mso-fareast-font-family: Calibri;">Use symbolic algebra to represent and explain mathematical relationships <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;"> <span style="font-family: Symbol; font-size: 12pt; mso-bidi-font-family: Symbol; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Symbol; msobidifontfamily: Symbol; msobidifontsize: 11.0pt; msofareastfontfamily: Symbol; msolist: Ignore;">· <span style="font-family: 'Times New Roman','serif'; mso-fareast-font-family: Calibri;">Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;"> <span style="font-family: 'Times New Roman','serif'; font-size: 14pt; mso-bidi-font-size: 11.0pt;"> <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: 'Times New Roman'; msobidifontsize: 11.0pt; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">1.) <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">Students will be able to solve inequalities by using addition and subtraction. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: 'Times New Roman'; msobidifontsize: 11.0pt; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">2.)  <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">Students will be able to solve inequalities by using multiplication and division. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: 'Times New Roman'; msobidifontsize: 11.0pt; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">3.) <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">Students will be able to solve linear inequalities involving more than one operation. They will also be able to find the solution set for a linear inequality when replacement values are given for the variables. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: 'Times New Roman'; msobidifontsize: 11.0pt; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">4.)  <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">Students will be able to solve problems by making a diagram, solve compound inequalities and graph their solution sets, and solve problems that involve compound inequalities. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: 'Times New Roman'; msobidifontsize: 11.0pt; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">5.) <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">Students will be able to use a graphing calculator to graph inequalities in two variables. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: 'Times New Roman'; msobidifontsize: 11.0pt; msofareastfontfamily: 'Times New Roman'; msolist: Ignore;">6.)  <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">Students will be able to graph inequalities in the coordinate plane.
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">State Standards __**
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;">Standard EA-1: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;">The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;">Standard EA-2: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;"> The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions. <span style="font-family: 'Times New Roman','serif';">
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;">Standard EA-4: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;">The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;">Standard EA-5: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;"> The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: Calibri;">National Standards __**
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">Objectives __**<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-bidi-font-size: 11.0pt;">:

Some instructional strategies that I would employ during this unit would include direct, indirect, and student led. I would start out by explaining inequalities. Then I would have the students think of all the ways that they use inequalities throughout their day. We would discuss these as a class and any that they left out. I would demonstrate to them how to solve the inequalities, using the different methods. I could also let them work on their own “inequality situation”. It would be a mini-project done in a half or full class period, depending on how long it takes. Their inequalities must be complex, having addition, subtraction, and multiplication involved. They will see how useful inequalities are in their everyday life.

Informal assessment could take place with the mini-project. Instead of taking it up for an actual grade, I could make sure that everyone understands inequalities and is grasping what they can be used for. Another way to have informal assessment could include having discussions. Instead of just teaching the material, I could teach a little bit and inquire the students to think about what is going on. From there, I would call on as many students as possible to help everyone understand the concept. After finishing “teaching” the lesson, we could have a class or group discussion about inequalities. I would either take notes during the class discussion or walk around and take notes while listening to the group discussions. From the discussions, I will see who grasp the subject and who needs more help. A more formal assessment could take place with homework or a quiz. This I could grade for accuracy to make sure that they are correctly working through the problems. A test I could give at the end of the unit could include just solving for x. It could also include having to plug numbers in other variables to solve for x. Lastly, I could include word problems. These could test whether or not the students understand inequalities, i.e. how to set them up, how to solve for the correct value(s), and how to perform solving the inequalities. The summative assessment can be done during the informal assessments that I suggested above. The informal setting of the assessments should evaluate the students’ attainment of the information but showing me who really understands. My formative assessment would take place after I see how well the students do during the formal and informal assessment. If students seem to grasp the subject both informally and on a test, then formatively, things should be fine. However, if one or both are off, then I would know that I need to change how I am presenting the topic and if I am presenting the right content.

Rachel Curry