Learning Progression
The students that will be using this learning progression will be in Algebra 2 or this could be used in a college-based class. These students would have covered matrices and understand basic modeling.
The concepts that the students would need to know about matrices for this lesson would be how to create a matrix given the information provided.
The picture that the students would have to draw in the example to the right will be an example of understanding modeling and how to draw a model.
The Common Core Standards that this learning progression will be using are from the cluster Perform operations on matrices and use matrices in application. The standard is HSN-VM.C.6
This lesson will start out with a basic modeling practice problem that is written on the board. The students will be given a problem similar to the one on the right.
The teacher will talk about what stable matches are and how to find them. There is a diagram that is commonly used for showing matches. The teacher will also mention butterfly networks and Benes networks to find matches but the students will not need to work about those.
The teacher will divide the class into two different groups. One group will be companies in the form of letters and the other group will be applicants in the form of numbers.
Each student will have a slip of paper with as a company or an applicant. The companies will go to the walls and the applicants will go to their first choice and then the company will decide to keep the applicant until something better comes along or say no because they already have better. This will go on until there is a stable match and every company has an applicant. The next part of the activity is the applicants will go to the board and the companies will walk around to find a stable match.
After this activity, the teacher will ask the students to discuss what happened during the activity. The teacher will write the answers the students give on the board. After the discussion the students will work on their worksheet. The worksheet will be a formative assessment and will be the students’ admit slip to class the next day.

An example of this would be if a delivery system has three towns that they will deliver too. If a driver is in Puyallup, there is a 30% chance that they will deliver to Puyallup, 40% they will deliver to Zillah, and 30% to Milton. If the driver starts in Milton, there is a 50% chance that it will deliver to Milton, there is a 20% that they will deliver to Puyallup and 30% they will deliver Zillah. If the driver is in Zillah there is 10% chance they will deliver to Milton, 40% chance they will deliver to Zillah and 50% they will deliver to Puyallup. Draw a picture to fit this scenario and set of the M matrix.
Answer: M=■(.5&.3&.1@.2&.3&.5@.3&.4&.4) Pictures can vary

CCSS.Math.Content.HSN-VM.C.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

A modeling question can be as simple as asking the student to draw a tree diagram and correctly label the branches with titles and probabilities on the tree.

Stable match would be Justin Timberlake and Jessica Biel whereas Lady Gaga and Mick Jagger would be unstable.
The teacher would also provide other funny example of celebrity matches that did not work.

Each slip of paper will have the student’s company or applicant number then the list of their first choices for jobs or first choice of applicant and continue on until the last choice.

Questions for discussion:
Did you have the same match as the first time?
Did you have a better match?
Why do you think that happen?

Lesson Title: Good, Stable Matches
Unit Title: Networking
Teacher Candidate: Megan Turner
Subject, Grade Level, and Date: Discrete Mathematics, High School, February 28, 2014

Placement of Lesson in Sequence
This lesson is in the unit networking. This unit involves a bunch of separate lessons that could be taught in any order.
Central Focus and Essential Questions
The central focus for this lesson is to look through all the possible matches and the students will have to show and explain why certain matches work and why some do not.
Content Standards
CCSS.Math.Content.HSN-VM.C.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

Learning Outcomes Assessment
Students will be learning how to find stable matches and learn how to find non stable matches and change them to become stable. A formative assessment will be given at the end of the class and it will be an admit slip. This slip with have a few problems on it and the students will have to complete it and turn it in before entering the classroom.

Learning Targets Student Voice
I will be able to:
•Create stable matches when given two categories
•Determine if a given match is stable or unstable Students will be doing a class activity that will be having them move around the room to find a stable match given their preferences. This will lead to class discussion about matches.

Prior Content Knowledge and Pre-Assessment
The prior content knowledge that the students will have is basic matching techniques (connecting the dots) and the pre-assessment for this lesson will be a basic connect the dots and where to connect them will be written out.
Academic Language Demands
Vocabulary & Symbols Language Functions Precision, Syntax & Discourse
•Stable Match
•Unstable Match
•Define and explain what a stable math is and how to find one.
Mathematical Precision:
Finding the stable match
Syntax:
Student will be able to explain what a stable match is and how to find a stable match is.
Discourse:
Students will do a class activity and will be working together to find the stable matches given their preferences.

Language Target Language Support Assessment of Language Target
I will be able to:
•Explain what a stable match
•Explain what an unstable match The class will be doing a class discussion for the students to receive the language support they need. The students will be assess on the language targets on the admit slip.

Lesson Rationale (Connection to previous instruction and Objective Standards)
This lesson is not connected to any previous instruction in this class since this is a new concept for the students.
Differentiation, Cultural Responsiveness and/or Accommodation for Individual Differences
The students will be doing a group activity so by the end every student will be able to understand matching and finding stable matching. There will be review after the class activity to check for understanding and then the students will get their admit slip to work on for the rest of the class time.
Materials – Instructional and Technological Needs (attach worksheets used)
White board
Markers
Slips of paper for the companies
Slips of paper for the applicants

The worksheet will have 10 questions similar to the following:

Teaching & Instructional Activities
Time Teacher Activity Student Activity Purpose
10-15 minutes Explaining and describing stable matches and how to write them in matrix form. Taking notes and asking questions to understand the material To introduce the students to a new concept of matching
20-30 minutes Guiding the students through the matching activity Participating in the matching activity To give the students a concrete example of stable matching
10 minutes Assisting students with their worksheets Working on the practice problems Practice