**Written by
Title: Patterns in Algebra Subject: Algebra Concepts
Topic: Linear Functions Grade: 8^{th} 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 wholenumber
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…

Essential
Questions:


Knowledge: Students will know…

Skills: Students will be able to…
(VERBS)


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 warmup 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 WarmUp Activity using the overhead (Attachment 1) to introduce arithmetic sequences. 2. Use the results of the WarmUp 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.
***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.

ATTACHMENT 2
FUNCTION TABLE

ATTACHAMENT 3
DOMAIN
AND RANGE Determine the
domain and range for each set of ordered pairs.
