Title: Linear Functions               Subject/Course: Algebra Concepts

Topic: Functions                         Grade(s): ___8___ Designer(s): Benjamin Moore

Stage 1 – Desired Results

Established Goal(s)

M8A3 Students will understand relations and linear functions.

a. Recognize a relation as a correspondence between varying quantities.

b. Recognize a function as a correspondence between inputs and outputs where

the output for each input must be unique.

c. Distinguish between relations that are functions and those that are not functions.

d. Recognize functions in a variety of representations and a variety of contexts.

e. Use tables to describe sequences recursively and with a formula in closed form.

f. Understand and recognize arithmetic sequences as linear functions with

whole-number input values.

h. Interpret the constant difference in an arithmetic sequence as the slope of the

associated linear function.

i. Identify relations and functions as linear or nonlinear.

j. Translate among verbal, tabular, graphic, and algebraic representations of functions

Understanding(s) Students will understand that...

1.  There is a unique relationship between inputs and outputs of a function.

Essential Question(s)

1.      What is a function?

2.   How do you determine the relationship between a group of numbers?

3.  Why is the relationship between the inputs and outputs unique?

Q

Students will know...

1.  What a function is

2.  Defintion of range and domain

K

Students will be able to...

1.  Represent data interchangeably in the forms of equations, tables, and graphs

2. Determine the relationship between a numbers in a set

Stage 2 – Assessment Evidence

Performance Task(s) Summary in G.R.A.S.P.S. form

1. I will have each of the students to complete the following chart.  This will allow them to explore what happens when different values are put into an equation and what the relationship between them is.

 y=8.3x+11 x=5 y=52.5 y=8.3x+11 x=2 y=? y=8.3x+11 x=? y=24 y=8.3x+11 x=79 y= y=8.3x+11 x=? y=17

T

Key Criteria:

Homework and quiz

Other Evidence

Teacher observations, written explanations, class participation

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 Stage 3 – Learning Plan Learning Activities Consider the W.H.E.R.E.T.O. elements. 1.  I have a "number machine" that always affects in the same way whatever number I put in it. For example, when I put in 1, the machine gives me 6; when I put in 3, it gives me10; when I put in 6, it gives me 16; and when I put in 9, it gives me 22. What will the machine give me if I put in 100? 2.  In order to make sure that the students have a thorough understanding of what is going on, I will have each of them to get in groups of two and make their own number machine.  Their machine must use the same principles as the problem above, but they must come up with different numbers and operations.