I. Curricular Framework

Concept:

Correspondence

Essential Question:

What role does the concept of Correspondence play in relation to algebraic functions?

Bridge:

Ranking Exercise

Content:

Functions in Algebra II

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To create student curiosity about the process of random matching function in a way that directly affects students' lives.

Activity: Draft Lottery: Have two bowls in the room, one bowl with numbers 1 to 365, another with dates January 1 to December 31. Have ten students pick a date from the first bowl and then pick a number from the second. Then in the interest of time, have the students whose birthdates have not been picked, call out their birthdates, and have a student pick from the number bowl (1 to 365) until all students' birthdates have been matched with a number from 1 to 365. (Teacher must write down birthdates of each students as s/he will need them later in the unit.) Briefly discuss how the students feel about a random lottery deciding whether or not they are drafted for military service. What is the purpose of a draft lottery? Why do you need to draw birthdates as well as lottery numbers? What do students know about the draft lottery? In what sense is this kind of lottery fair/unfair?

Assessment: Quality of discussion.

2. Attend: Attending to the Connection

Objective: To allow students to analyze the lottery activity as an example of a random function.

Activity: Discussion pertaining to the technical aspects of the lottery activity: How many sets of elements were used? What were the elements of each set? What do the elements in each set mean? What do they stand for or represent? Is it possible that one birthdate could be assigned to two lottery numbers? What would that do to the whole process if this were so? Have the students write brief statements about the discussion for homework.

Assessment: Discussion pertaining to the technical aspects of the lottery activity: How many sets of elements were used? What were the elements of each set? What do the elements in each set mean? What do they stand for or represent? Is it possible that one birthdate could be assigned to two lottery numbers? What would that do to the whole process if this were so? Have the students write brief statements about the discussion for homework.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To create matching based on a rule.

Activity: Teacher lines up the students in rank order by birthdate. First student closest to January 1, etc. The students do not know the rankings or why. Teacher assigns the number 1 to the student whose birthday is closest to January 1 and so on. The class is asked to figure out what system the teacher used to give each of them a number. Note: If two or more students have the same birthdate, they must share the same ranking number. After the students have figured out the why of the rankings, explain the pattern used. Ask how it is different from the ranking according to their lottery numbers. If it's possible for one birthdate to be assigned more than one ranking number? End by identifying the concepts they have experienced by their mathematical names: topics, domain, range, rule of correspondence, unique pairing or matching.

Assessment: Quality of discussion and understanding of the concepts.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To teach the concepts they need to understand functions.

Activity: Teach the following concepts: Domain; Range; Cartesian Product and Graphing; Relation; Rule of Correspondence; Function: Definition of, Notation, How to Recognize from a Graph, Ordered Pair, Preimage (input), Image (output).

Assessment: Objective quiz.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To allow students to practice concepts and reinforce learning.

Activity: Workbooks, questions at end of chapters, teacher worksheet based on lottery experience and birthdate ranking experience, graphing plotting points, etc.

Assessment: Quality and accuracy of worksheets.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To allow students to personalize the material.

Activity: Students make up their own rule of correspondence. From that rule they must generate five ordered pairs. The students can either hand their worksheets to a partner or the teacher can collect them and make one large worksheet for the next class.

Assessment: Accuracy of ordered pairs based on student's chosen rules.

7. Refine: Refining the Extension

Objective: Students increase their ability to choose from options based on curiosity and interest. Students increase their ability to write a personalized plan for learning. To apply the concepts they have learned.

Activity: Present the class four options. Ask them to choose one. Have them write a short essay telling why they have chosen a particular one. The Four Options: 1. Compare statistics of accidents with the ages of people who have the most accidents. Is there a relationship? What do you conclude from this? Do you think accident statistics affect insurance rates? Is age related? Is sex related? 2. Do a survey of possible relationships between number of hours students sleep and grades, number of hours students work outside school and grades, number of hours students watch TV and grades. Note: Teacher must have this data available ñ a simple questionnaire without student names could be given to the class. 3. Scientific experiment: Obtain a lab stand and spring apparatus from your school's physical science lab. You will also need a meter stick and a set of weights of various sizes. Hang the spring with no weight attached from the lab stand, then measure the length of the unstretched spring. Attach various weights to the spring, and take a measurement of the length of the spring for each different weight. Record your data in a table in two columns, weight and length of spring. Be sure to record the first trial ñ zero weight, and the unstretched length of the spring. Make a graph of the results in your table. Explain how this experiment is related to the concept of a function: (domain, range, ordered pairs, etc.) Consult a physics teacher for alternative experiments. 4. Do a study of the following: the cost of your home, the mortgage interest rate, the number of years until it is paid. Compute the total amount your parents will have paid for your house if they live there for the length of the mortgage. Find out how the interest rate is computed. What is the rule of correspondence? Research this, use other texts, interview your parents and/or your banker.

Assessment: Quality of essay telling why they choose one of the above.

8. Perform: Creative Manifestation of Material Learned

Objective: Quality of essay telling why they choose one of the above.

Activity: Complete one of the four options and share with other students.

Assessment: Quality of project and sharing.

Assessment, Phase Five,Performance, Creative Use of Material Learned: