Megan Murphy
EDCI 5790
Edward Janak
Unit Plan
Anything Men Can Do, Can Women Do Better?
Diagnosis of
Need/Formulation of Purpose
Topic: Solving Systems of Linear Equations.
Why Students Need to Know: They need to know this information as it is a basic concept in any algebra one course. They will be tested on the concept several times including the WyCAS, ACT and SAT. This will also prepare them for future math courses in Algebra.
Demographic Information: The students in the district are quite varied. There is a high level of lower SES students and there is significant percentage of students on IEP’s. Classes are generally made up of partially motivated kids with some “slackers”.
What Students Already Know: The students will know how to graph linear equations in a variety of forms. They will also know to solve multi-step equations.
What Students Need to Know About Topic: Students will learn 3 methods to solve Systems of Linear Equations and will then apply those skills to solve a “real-world” problem. Students will gain a deeper understanding of the concept of the different equations through the “real-world” problem.
Selection of
Content/Rationale
Goals of Unit:
1. Students will understand several methods to solve systems of equations.
2. Students will discern among methods to determine best method for a problem.
3. Students will better understand what is expected when presenting real-world data to a wide audience.
4. Students will understand how technology can aid in their productions.
5. Students will better understand how collaboration can increase proficiency in their productions.
6. Students will be able to see how slope plays a significant role in predictions.
7. Students will gain an understanding of how mathematics plays a vital role in predictions and how these predictions are best guess estimates.
8. Students will gain insights into strategies of Internet research.
How These Goals Tie Into Horizontal Articulation: This unit ties in with other concepts taught in Algebra 1. They learn about and apply linear equations before this unit. They also learn how to write and solve equations from given data. After this unit, students will use these concepts to begin linear programming with inequalities which is covered in Algebra 2.
How These Goals Tie Into Vertical Articulation: This unit will prepare them for concepts that will be revisited in greater detail in Algebra 2. The presentation and use of research will also help them with other projects in many other classes.
Fulfillment of State and National Standards: See the chart below. Standards that are met are noted with an “A”.
How These Goals Match My Philosophical Beliefs: These goals match many of my philosophical beliefs. I wrote this unit, and adapted an activity that was developed by my department. This unit is an extension of my beliefs and methods. I believe that allowing the students to learn information in a more “traditional” manner and then apply that information in a more activity-based, real-world manner allows them to learn a deeper more engaging level. I like the combination of instructional strategies because it allows for different types of learning. I believe that in our society of honoring differences it is our responsibility to teach using several methods so that their learning differences can be honored.
Organization of
content/Instructional Plan
Daily Lesson Plans: Following are the lesson plans for each day and a general description of the topics discussed. The first three days are the introduction to the content. Day four through 8 is the meat of the unit, where students are actually applying the information.
Supplemental Material: The supplemental material is found within the text book and extra resources that came with the book. The supplemental material is used for remediation and struggling students. These students are taken care of outside of class in an after school program that I am a participant.
Schultz, J., Kennedy, P., Ellis, W., Hollowell,
K. (2001) Systems of Equations and
Inequalities, Algebra 1, pp. 318-366, 756).
Linkage to Good Instructional
Strategies
Instructional Strategies Used: I used Direct Instruction, Analogies, Concept Maps, Demonstration and Discussion and twist on the CCP and Problem-Based Learning for the final activity.
Multiple Intelligences: The multiple intelligences are hit on throughout the unit. The music intelligence is used during class when students are given homework time. I generally play music for them while they work, this has a calming effect. The intrapersonal intelligence is touched when they adapt their maps to fit their understanding and when they explain their thinking and reasoning, either to me or to the class. The rest of the intelligences are utilized in the culminating activity.
Day One (90 min. Block): Graphing Systems
of Equations
Objective: The purpose of day one is to review graphing linear equations and to allow students to “see” the solution to the system. The graph is visual and can be used to easily see the trends in the data, which will be useful in the final problem.
Strategy & Explanation: Day one will be mostly direct instruction with the students. The reason for the direct instruction is because they are basically reviewing graphing lines. The new material is not conceptually difficult for most students to grasp. I use this day as a confidence builder for the students. After the direct instruction the students are given individual white boards to practice the material.
Lesson Walkthrough: I begin the lesson with a quick review/warm-up of how to graph a line. We discuss the slope and the y-intercept and how to graph from the slope-intercept form of a line. We also review how to graph a line using the x and y-intercepts if the line is not in slope intercept form. I do not dictate which method they use to graph; I allow them to use the method which they are most comfortable. I lead them through a brief understanding of systems and how if you have two variables then you need two equations and you will have two answers, the same for goes for any number of variables, you need to have the same number of equations and answers as variables in the system. This leads them to understanding that the will need to solve for two variables in order to have a complete answer.
Next are some examples that are worked out together as a class. Where the lines cross is emphasized as the solution to the system. I then ask them the coordinates of the point, and write that in point notation, (x,y). I let them know that this is how they will need to write their answers.
The “new” material for this lesson is the checking of the solution. They will then take the solution and use substitution into the original equations to see if that point lies on both lines. If it does, then they know they have worked the problem correctly.
We will then as a class work through two to three other systems on the whiteboards. The students are given the problem and I will walk around and help where needed. Students are allowed and encouraged to discuss the problem and help each other where needed. I monitor their progress throughout the practice. Once they have successfully completed enough problems for them to fill comfortable, I will give them their homework assignment over the section. There are only a few problems for two reasons. The first so they have time to get it mostly completed in class. The second is to keep them doing the homework in this lesson, with out the extra work outside of class they will struggle with the content.
Below is the homework assignment. The class problems are of the same type as the homework. Some examples are below. I make certain that the answers today will come out “nice” so the lines will cross at integer values.
1. 
Answer: (-1,0)
2. 
Answer: (2, -2)
3. 
Answer: (2,1)
4. 
Answer: (-1,-3)
Name: ____________________
Algebra One Homework 7.1
Solve each of the following systems by Graphing. Check your solution in both equations.
1. 
2. 
3.
Day Two (90 min. Block): Solving Systems of
Equations by Substitution
Objective: Day two will assess the work from the previous day. Day two also introduces a new twist on a concept that begins in elementary school, substitution. Students will be solving systems equations using substitution as an alternate method to graphing.
Strategy & Explanation: Graphing is good for some of my more visual students and substitution works better for some more mathematical students. Though I try to connect to my linguistic students in the beginning explanation, it is a simplistic analogy in the English language but as soon as words are replaced with numbers and symbols there is often a mental block and many struggle with the concept.
Lesson Walkthrough: To begin the day I will answer any questions they have on the homework from the previous day. After that, I will give them a small quiz over the material. I will keep this quiz to about 1/3 of the length of their homework and usually takes at most 10 minutes at the beginning of the hour. The quiz given is below, before the homework.
After the quiz, I begin the lesson with an analogy to the concept being taught. I start with a simple example:
Suzan is the same age as Joe. Betsy is also the same age as Joe. What conclusion can you make about Suzan and Betsy?
Students immediately come to the answer that Suzan and Betsy are the same age. Then I do a second example to illustrate the analogy to the concept. In the second example I will throw in a little math.
Fred has half as many siblings as Gina. Abby also has half as many siblings as Gina. What conclusion can be made about Fred and Abby?
Again, they get this example, and come to the conclusion that Fred and Abby have the same number of siblings. At this point I transition to a more “mathematical” example.
I say “y is the same as two times x plus one” and write y = 2x + 1 simultaneously. Then I say “y is also the same as negative x plus four” and write y = -x + 4. Then I ask what conclusion can be made about these equations.
I give them lots of time to process, and they will generally come to the conclusion that 2x+1 is equal to –x+4. We don’t solve this, I just let in marinate for a small time. I go next to an example from elementary school, something like: If a = 2 and b = 4 find 3a+2b. The students will substitute and simplify this, and then get excited thinking that today is going to be really easy. I tell them that they will be using the English analogies and the elementary school substitution together to solve their systems.
I then give an example for them to try. I do not give them direct instruction on the method, they will need to apply the analogies first and struggle with the problem. Most of the time many of them will be able to apply the information. I give them the system from the third example from the beginning of class, but I write it as a system.
(1,3) Other Examples: 
(3, -4) 
(1,3) 
(4,2)
I will have them write it on paper and try to solve it. They will talk and discuss, when they mostly have the first part of the solution I will have a student write it on the board. There is usually a discussion as to “how many answers do you need” and “how many do you have”.
Collaboratively as a class the entire solution will end up on the board. We will then discuss how we can check the solution…the same way they checked their answers from Day One. I also let them know that they need to express their answers in point notation. We will practice with other systems where they will have to solve for a variable before they substitute, but the general process is the same.
Below is the homework assignment that they would be expected to complete and the quiz they take at the beginning of the hour.
Name: ____________________
Algebra One
Quiz 7.1
Graph the following system. Check you solution in both equations.
1. 
Name: ____________________
Algebra One
Quiz 7.1
Graph the following system. Check you solution in both equations.
1.
Name: ___________________
Algebra
One Homework 7.2
Solve the following systems by Substitution and Graphing. Check your solutions.
Substitute and Graph.
1.
Substitute.
2. 
3. 
4. 
Substitute and Graph.
5. 
Day Three (90 min. Block): Solving Systems
of Equations by Elimination
Objective: Day three will assess the work from the previous day. Day three introduces a new concept that will be presented using a concept map.
Strategy & Explanation: The concept map is used here as an organizational tool to help students maneuver through the elimination method. There are more mental steps to solving a system in this manner, but after they steps are mastered, it is a highly effective method.
Lesson Walkthrough: Questions are answered about the previous homework assignment and the Quiz 7.2 is given. Next, the students are given an example problem and the concept map to help them solve the problem. They will work with a partner on the problem to see if they can get to a solution following the concept map algorithm. Groups are given ample time to work through the problem and map. When groups begin to finish, I will have one group do a “mini presentation” and discuss how they solved the problem. If others did the problem a different way, those ideas will also be shared. I choose the groups to present as I look at what each is doing. I do this so that I don’t have several groups echoing each other and differing methods are presented. Students continue working in groups until they are more comfortable with the process. Students are then encouraged to look at which method is best to use when. Students will generally gravitate towards a method they are comfortable with using. They will then have a homework assignment over the concept. Students are encouraged to adapt their maps to fit their language. If they add to it, they will understand it better.
Sample problems to be used:
1. 
2. 
3. 
4. 
