Unit Design
for
Linear Functions
Developed by
Canise Stewart-Singleton
Detroit Community Schools
UBD Unit Design Worksheet / Saginaw Valley State University
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Unit Design Worksheet
Unit Title: Functions
Subject/Course: Algebra 1
Topic: Linear Functions
Grade(s): 9
Staff Name: Canise Singleton
Stage 1 - Desired Results
Established Goals (HSCE’s, etc.):
A3.1.1 Write the symbolic forms of linear functions (standard, point slope, and slope intercept) and convert
between forms.
A3.1.2
Graph lines such as x = h and y = k given appropriate information.
A3.1.4
Find an equation of a line parallel and perpendicular to a given line.
Understandings:
Students will understand that...
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Linear functions are written in various forms.
Linear functions can be graphed using
input/output tables.
Linear functions can be graphed using x and yintercepts.
Finding the slope of an equation is determined
by the rate of change.
Lines can be horizontal or vertical.
Lines are parallel if their slopes are equal
If non-vertical lines are perpendicular, then their
slopes multiply to equal -1.
Given a line and a point, a parallel or
perpendicular equation can be found.
Students will know…
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Essential Questions:
 What forms can linear functions be written in?
 How can an input/output table be used to graph a
linear function?
 How can linear equations be graphed using the x
and y-intercept?
 How can the slope be found between two points?
 What types of equations graph horizontal or
vertical lines?
 How are lines determined to be parallel?
 What proof can be used to show that lines are
perpendicular?
 How do you write the equation of a line that is
parallel or perpendicular to a given line?
Students will be able to...
Linear equations can be converted from one
form to another.
Rise over run is another way to represent slope.
Perpendicular lines have slopes that are negative
reciprocals of each other.
Explain different methods that are useful when
graphing and writing linear functions.
Unit Enduring Understanding:
Unit Question:
Linear functions can be graphed or used to graph and
interpret real life situations.
How are linear functions graphed to interpret real life
situations?
Stage 2 - Assessment Evidence
UBD Unit Design Worksheet / Saginaw Valley State University
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Performance Tasks: (Summary in GRASPS form, end of the unit)(Summative)(After)
Goal:
Your task is to show mastery of linear functions by creating an illustrated magazine article about
functions.
Role:
You have been hired as a writer for Ebony, Jet, Sports Illustrated or a magazine name that you
choose. You have been asked to create school piece this month. You must come up with a four
page spread about linear functions. Your spread must include illustrations, and appeal to readers
who don’t know much about linear functions.
Audience: Your target is high school students, and families who do not have math backgrounds.
Situation:
The challenge involves creating a 4 page illustrated spread that is eye appealing and interesting
to the reader.
Product:
Four page article explaining linear functions.
Standards: Your work will be judged using a rubric.
Key Criteria: (Rubrics, etc.)
Rubric for GRASPS
CATEGORY
5
4
2
Diagrams and
Sketches
Diagrams and sketches
have exceptionally
attractive formatting and
well-organized
information.
Information
Gathering
At least 4 different
3 resources were used
resources were used and and cited to create the
cited to create the lesson lesson.
such as internet,
textbook etc.
2 resources were used
and cited to create the
lesson.
1 resource was used and
cited to create the
lesson.
Article Content
Accuracy/Linear
Function
Knowledge
All facts, terminology,
and notation in the
article are accurate,
indicating an accurate
understanding of linear
functions.
99-90% of the facts,
terminology, and
notation are accurate,
indicating a substantially
accurate understanding
of linear functions.
89-80% of the facts,
terminology, and
notations in the article
are accurate.
Fewer than 80% of the
facts, terminology, and
notations in the article
are accurate.
Article Writing
Mechanics
Capitalization and
punctuation are correct
throughout the article.
Writing is creative and
witty.
Capitalization and
punctuation are correct
throughout the article
after feedback from an
adult. Writing is
enjoyable.
There are 1-2
capitalization and/or
punctuation errors in the
magazine even after
feedback from an adult.
Writing is tolerable.
There are several
capitalization or
punctuation errors in the
magazine even after
feedback from an adult.
Writing is confusing and
inconsistent.
Article
Organization and
Readability
Each article in the
magazine has a clear
beginning, middle, and
end. Very enjoyable to
read.
Article has beginning,
middle, and end.
Enjoyable to read.
Article has beginning
and end. Tolerable to
read.
Article is unclear and
poorly written.
UBD Unit Design Worksheet / Saginaw Valley State University
Diagrams and sketches
have attractive
formatting and wellorganized information.
3
Diagrams and sketches The magazine's
exist, but are done with diagrams and sketches
little effort or creativity. are confusing to the
reader.
3
Holistic Rubric for
(Tests)
4
3
2
1
Student
understands the
concept, but made
minor arithmetic
errors which
affected the rest of
the work causing
the answer to be
incorrect.
Student
understands the
concept, but
missed a step
and/or is confusing
learned rules.
Student work has a
lot of errors
showing the
student has not
fully grasped the
concept. They are
mixing up
concepts or rules,
and work lacks
clarity.
Student attempted
the problem, but
clearly does not
understand the
concept.
Other Evidence: (Quizzes, Tests, Prompts, Observations, Dialogs, Work samples, etc.)(Before, During)(For
learning)
Journals, vocabulary activity, tiered assignment-(differentiation), worksheet, textbook, concept map, bingo,
classroom jeopardy set, TI-83
Before
Pre-test
During
jeopardy, double bubble maps, quizzes
Create crossword puzzles, journal prompts,
Vocabulary quiz
After
Post-test grasps
Describe the assessment/s and state the prompt
if applicable.
□F XS
What type of scoring tools will be used for
evaluation?
□ Analytic rubric
X Holistic rubric
X Criterion rubric
□ Checklist
□ Answer Key
□ Other
Student Self-Assessment and Reflection:
Students can write journals explaining what they understood specifically about that day’s concept or what
they are having trouble with. They may be asked to describe what they found to be the best part of the unit.
Students may also be given a questionnaire at the end of the unit.
UBD Unit Design Worksheet / Saginaw Valley State University
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Unit Design Worksheet
Stage 3 - Learning Plan
Differentiated Instruction (Layers, Tiered, etc.):
Level C- 45 pts. (Choose 3 of the following)
1. Use the calculator to graph equations in slope intercept form in order to identify their x and yintercepts. (15 pts)
2. Create 10 equations to be graphed using x and y-intercepts, and then pass them to another group to
graph them. (15 pts.)
3. Create a matching game to identify different forms of linear equations. (15 pts.)
4. Create vocabulary words using the bubble maps. (15pts.)
Level B- 30 pts. (Both activities are required)
1. Use the graphics calculator to discover slope-intercept form on the graphing linear equations activity
sheet. (20 pts.)
2. Draw 5 linear equations using the slope triangle method to identify the slope and identify the yintercepts. (10 pts.)
Level A- 25 pts. (Choose 1 of the following).
1. Create equations of parallel and perpendicular lines. (25 pts.)
2. Create an original 20 question test for the unit. Give to a class-member and grade. Turn in blank
copy, key copy, and student copy. (25 pts.)
3. Create a poster on linear functions using the poster rubric as a guide. (25 pts.)
UBD Unit Design Worksheet / Saginaw Valley State University
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Learning Activities: (consider the WHERE TO elements)
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The end of the unit project asks students to answer the question of (W) where are we going. They
will have to (R) rethink and (O) organize what they have learned into information to create a
magazine on linear functions.
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Students will use technology to understand slope intercept form. Students will be given Texas
Instruments guided practice in order to discover what happens when m and b change. This will (T)
tailor learning to varied needs, interests, and styles.
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Ring toss—Comparing negative slopes. Students will work in groups tossing pennies into rings with
various diameters. They will then graph the results of the number of times the six pennies fell into
each of the circles based on the distance away from the circle. The data will be collected and graphed
in order to determine the slope and make predictions. This will (H) hook and hold students’ interest.
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Vocabulary activity- students are given a choice of six activities to choose from to show mastery of
the unit vocabulary.
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At the end of the unit students will reflect on what they learned using a survey or a questionnaire.
This is the (E) evaluation.
Students will be (E) equipped with materials and supplies to complete each learning activity.
Unit Design Worksheet
Essential Vocabulary
(Identify and define)
Standard form: a linear equation of the form Ax + By = C where A, B, and C are real numbers and A and B
are not both zero.
Slope intercept form: A linear equation of the form y = mx + b where m is the slope and b is the y-intercept.
Point-slope form: A linear equation of the form y –y = m(x –x)
X-intercept: The x-coordinate of a point where the graph crosses the x-axis.
Y-intercept: The y-coordinate of a point where the graph crosses the y-axis.
Slope: The ratio of the vertical change to the horizontal change between any two points on the line.
(m = rise/run)
Parallel lines: Two non-vertical lines in the same plane with the same slope.
Perpendicular lines: Two non-vertical lines in the same plane whose slopes are negative reciprocals of each
other.
UBD Unit Design Worksheet / Saginaw Valley State University
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Sequencing the Learning
Monday
(pre-test)
Identify different
forms or linear
equations in their
various forms.
Tuesday
Wednesday
Graph lines using
input/output tables.
Graph lines using x
and y-intercepts.
(group activity)
Group C work day
Thursday
Slope formula song
and activity (kuta
worksheet)
Friday
Ring toss activity
(slope activity)
Slope quiz
Write equations in
their different forms
such as slope
intercept form, pointslope form.
Monday
Layer B work day
Tuesday
Layer B work day
Wednesday
Parallel lines
(textbook)
Thursday
Perpendicular lines
Friday
Vocabulary activity
workday
Graph lines using
y = mx + b
(TI calculator activity
slope-intercept form).
Monday
Jeopardy game
Tuesday
Layer A workday
Wednesday
GRASPS
Thursday
GRASPS
Friday
Linear functions test
(post test)
(double bubble map)
UBD Unit Design Worksheet / Saginaw Valley State University
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Linear Functions Test
Name
Date
Section
(Show all work)
1. Draw and label the coordinate plane including the quadrants.
Convert the following linear equations into slope intercept form.
2.
3x + 4y = 12
3.
–9x + y = 5
4.
x – 6y = 10
5.
5x + 3y = –15
Graph the following linear equations by creating an input/output table.
6.
y = 7x – 3
7.
y = 3/4x
8.
y = –x + 4
9.
y=x
UBD Unit Design Worksheet / Saginaw Valley State University
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10. Write an equation parallel to y = 4x + 7 passing through the point (–1, 5)
11. Write an equation perpendicular to y = –2x passing through the point (4, –3).
12. Write an equation of the line passing through the given points. (1, 4), (6, –1)
Find the x and y-intercepts.
13. –5x + y = 20
UBD Unit Design Worksheet / Saginaw Valley State University
14. –4x + 5y = 30
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