**Written by Lisa Parsons Rockdale County

Title:  Patterns in Algebra                    Subject:  Algebra Concepts

Topic:  Linear Functions                       Grade:  8th      Designer(s):  Lisa Parsons

Algebra Concepts (Variables - Grade 5)

 

Stage 1 – Desired Results

Established Goals:

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.

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.

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

 

Understandings:

Students will understand that…

  • A unique relationship exists between the inputs and outputs of a function.
  • An arithmetic sequence is a linear function.
  • A constant difference in an arithmetic sequence is associated with the slope of a linear function.

 

Essential Questions:

 

  • What is a function?
  • Why is the relationship between the inputs and outputs of a function unique?
  • How can a function be represented in tabular and graphic form?

Knowledge:

Students will know…

  • The definitions of:  function, input, output, domain, range, arithmetic sequence, and slope.
  • Arithmetic sequences are linear functions.
  • That linear functions can be represented in verbal, tabular, graphic and algebraic forms.

 

Skills:

Students will be able to…   (VERBS)

  • Represent data interchangeably in the forms of equations, tables, and graphs.
  • Translate among verbal, tabular, graphic and algebraic representations of functions.
  • How to translate among verbal, tabular, graphic and algebraic representations of functions.

 

Stage 2 – Assessment Evidence

Performance Tasks:

 

1.  Students will be able to define arithmetic sequence and function.

 

2.  Students will be able to complete a table of values using function rules.

 

3.  Students will be able to formulate ordered pairs from the input/output values in a table and graph the ordered pairs on a coordinate plane.

 

4.  Students will recognize arithmetic sequences as linear functions.

 

Other Evidence:

 

·   Students will complete warm-up activity.

·   Students will complete various tasks related to the objectives.

·   Teacher observation of students working on tasks.

·   Assessment of student work.

·   Orally review vocabulary words.

·   Oral discussion and written response to Essential Questions. 

 

Stage 3 – Learning Plan

1.  Begin with the Warm-Up Activity using the overhead (Attachment 1) to introduce arithmetic sequences.

 

2.  Use the results of the Warm-Up Activity to define:  arithmetic sequence, input, output, domain, range and function.

 

3.  Construct a table of values with input and output values using the sequences.  Allow students to discover patterns or rules.  (Attachment 2)

 

4.  Use the Function Tables to create ordered pairs.

 

5.  Graph the ordered pairs on a coordinate plane.  Have students discover that each of the tables produces a straight line that has a continuous slant.

 

6. Define slope as the steepness of a line or as the ratio of vertical rise to horizontal run.  Discuss the concepts of positive slope, negative slope, zero slope and no slope.  (Slope aerobics activity.)

 

7.  Have students discover that arithmetic sequences produce linear functions using the concept of constant differences.

 

8.  Given the following ordered pairs of functions.  Have students determine the domain and range of each.  (Attachment 3)

 

9.  Have students create a table of values for the following functions, formulate ordered pairs using input and output values, and graph each linear function on a coordinated plane. 

FUNCTIONS:

y =  10x + 25 

 

y  =  8x + 35 

 

y = 5x – 1

 

y = 2x + 1

 

y = 3x

 

y = x

 

 

***EXTENSION:

Intermath connection:

Intersecting Lines:

Two lines in the same plane can have zero points of intersection (if parallel) or one point of intersection (if they cross). Three lines in the same plane can have zero (if all three lines are parallel), one (if all three lines intersect at the same point), two (if two lines are parallel and the third is a transversal that crosses both of them), or three (if the lines form the sides of a triangle) points of intersection. Suppose a total of nineteen different lines are arranged in the same plane. Determine how many different possibilities exist for the number of points of intersection of the nineteen lines.

 

 

ATTACHMENT 1

 

PATTERNS IN ALGEBRA                                                        

Directions:  Find the next 3 terms in each sequence.                               

 

    1. 1, 3, 5, 7, ______, _______, _______
    2. 52, 59, 66, 73, 80, _______, ______, _______
    3. 18, 32, 46, 60, 74, _____, _____, _____
    4. 26, 24, 22, 20, _____, _____, _____
    5. a, c, e, g, _____, _____, _____

 

 

 

ATTACHMENT 2

                                                                                                                    

FUNCTION TABLE

 

INPUT

FUNCTION

 

OUTPUT

1

 

 

2

 

 

3

 

 

4

 

 

5

 

 

6

 

 

7

 

 

8

 

 

9

 

 

 

 

 

 

ATTACHAMENT 3

                                      DOMAIN AND RANGE

 

Determine the domain and range for each set of ordered pairs.

  1. {(4,12), (5,13), (7,15), (8,16)}
  2. {(1,18.5), (2,22), (3,25.5),(4,29), (5,32.5)}
  3. {(0,0), (1,150), (2,300), (3, 450)}
  4. {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}