Justin Sealand

Algebra I

6/20/08

Period 3

50 minutes

A. OBJECTIVE

1.    TSW be able to identify the domain and range of a function. (DOK 1, Algebra I – 2.c)

2.    The student will distinguish between functions and non-functions. (DOK 2, Algebra I – 2.c)

B. MATERIALS

Transparencies; Algebra I (1995), Foster et al.; overhead projector; note cards; graph paper

Do Now: [2 minutes]

Graph the following points:

(3,4),(5,6),(3,9),(5,8),(4,2)

C. SET

Any time you are working with numbers in the real world, you are working with data. Data is almost always something that can be put on a coordinate grid like we have done for our Do Now. Many of the things we have already done have been functions, and you might not have even known it; for example, the problem we used for buying a car was a function, and you all used it without even knowing that word. By the end of today, you will be able to tell me what the domain and range are for a function, and you will be able to distinguish between what is a function and what is not. [5 minutes]

D. PROCEDURE

1.    Let’s start with the definition of a relations and then build our way up to functions: a relation is any set of ordered pairs. So, that means that the ordered pairs you all graphed first thing this period were all a relation because they were a set of ordered pairs. Another way to look at this set of ordered pairs—AKA relation—is in a chart format. You can draw a chart with your x-values on the left-hand side and your y-values on the right. [5 minutes]

2.    This chart is already broken into two components, but they have other names than just “x” and “y.” When someone says, “this is my domain,” what are they talking about? What do they mean? Someone’s domain is his or her home. In the case of ordered pairs, the “x” value is the domain, because it is where they start; it is the pair’s home. In a relation, the domain is each x value. It’s the first thing you find when you plot points. The second number on the right, the “y” value is called the range. The range is like a firing range. It is where things land when they leave the home point, or domain. In a relation, the range is each y value. TTW quickly verbally assess whether the students understand the difference between domain and range. [10 minutes]

3.    Using this chart is one of the easiest ways to distinguish between which set of ordered pairs is a relation and which are a function. A function is a relation (set of ordered pairs) in which each element of the domain is paired with exactly one element of the range. So in the example we used earlier, was that a function? The values in the domain will not be used more than once in a function. Values in the range may occur more than once, though. [3 minutes]

4.    TSW randomly choose note cards from the teacher with ordered pairs on them. The students are to get up in front of the room and order themselves from least to greatest by range first. Then least to greatest by domain. Once they have done so by domain, they are to tell the teacher whether they are a function or not. Then they will re-draw for more ordered pairs and replay the game. [15 minutes]

5.    The last thing I want you to learn before practicing out of the book is what it means to state the inverse of a relation. What is a relation again? How is that different from a function? To state the inverse, you literally switch the domain and range of each ordered pair. It means that within each set of parentheses, you switch the x-value with the y-value. TTW model the inverse of a relation.

6.    Practice. P. 377 # 19-24.

E. CLOSURE

Today I wanted you not only to be introduced to the idea of relations and functions, but to distinguish between the two and be able to tell me what the domain and range are. What is the domain? What is the range? What is a relation? How is that different from a function?

F. ASSESSMENT

- TSW be able to identify the domain and range of a function. (DOK 1, Algebra I – 2.c)

Informal: TTW monitor student progress by verbally checking (M) for understanding (C).

Formal: Students will take a test (M) for a grade (C) that will be recorded in the grade book (D).

- The student will distinguish between functions and non-functions. (DOK 2, Algebra I – 2.c)

Informal: TTW monitor student progress by verbally checking (M) for understanding (C).

Formal: Students will take a test (M) for a grade (C) that will be recorded in the grade book (D).

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