Smita Mittal
EDSS 511
Linear Equations Unit
Unit Context
Subject Content Area: Algebra
1
Course: Mathematics
Grade Level: 8th grade
Length of Unit: The unit will last for 15 days for 750
minutes for 15 periods (50min. each). This unit will take place in late
September-October.
Facts about
Learners
Whole Class Information
Number of Students in the Class: 28 students in the
class.
Demographic Information: 15 students are male and 13
students are female. The ethnic background of my students consists of: 21
Caucasian, 5 Hispanic, 1 Filipino, and 1 African-American student. 2 of my
students receive free or reduced lunch. 7 of my students are bilingual. 2 of my
students are early advanced and 1 intermediate ELD with Spanish as their
primary first language. 6 of my students have an IEP and perform below grade
level in reading and math.
Developmental Needs
Readiness: More
than half of the students read at or above grade level. Most students are
writing at either a 8th or 9th grade level.
Interest: This is a social group of students who are
interested in sports, drama and media arts and enjoy listening to music. 4
students enjoy surfing, 7 play soccer and 2 learn dance. Some students have their
own laptops.
Learning Profiles: Most of the students are either kinesthetic or visual learners, with some
auditory learners as well. The students like to work in pairs or small groups.
The students can follow written instructions, sometimes repeated orally. All of
them enjoy hands on activities and projects.
Individual Student
Information
1. Daisy: She is
13 year old. She is from a low income Hispanic family and has 2 younger
siblings. Her parents provide lot of support by attending all events at school,
like seminar for ELLs, conferences and asking for help from teachers and staff.
Daisy can speak fluently and read in Spanish. She is social and works well in
small groups but is shy in unfamiliar settings. The CELDT scores indicate that
she is at the Intermediate level, and is considered an English learner.
Developmental
Needs
Readiness: Daisy
can read and write and the Intermediate level. She needs to expand her vocabulary
and improve her reading and writing skills.
Interest: Family and
friends are very important to Daisy. She enjoys visiting her relatives and
grandparents in Mexico and talks fondly about the special family dinners and
occasions like anniversaries. She loves to play soccer for fun with her
friends. At school, her favorite subject is art.
Learning Profile:
Daisy likes to work in small groups. She is a visual and kinesthetic learner.
She learns best by seeing information on the board or doing things.
Differentiation
Strategies
Process/Readiness:
Teacher pairs up students to review and
discuss the vocabulary terms to support ELL.
Students identify and explain components
on the board in pairs.
Product/Learning
Profile:
Students write 1-2 sentence response on
Graphic Organizer and identify components on graph sheet.
Content/Readiness:
Students look at the visual and listen to the teacher to understand the
content.
The strategies will be assessed for
effectiveness through multiple formative assessments such as show with a finger
for understanding, discussion, show understanding on the board, graphic
organizer and graph sheet.
2. Ricky: He is a
14-year old male in 8th grade. He came from Mexico with his family
when he was 4 years old. He is fluent in speaking and reading in Spanish but
can’t write in it. He plays basketball and wants to go to college. The CELDT
scores indicate that he is at the early advanced level, and is considered an
English learner.
Developmental
Needs
Readiness: Ricky
can read and write at the early advanced level. She needs to expand her
vocabulary and sentence structure to improve his reading and writing skills.
Interest: Family
and friends are very important to Ricky. He loves to play basketball and
hangout with friends. At school, his favorite subject is math.
Learning Profile:
Ricky likes to work in groups. He is a kinesthetic learner and learns best by writing
or doing things.
Differentiation
Strategies
Process/Readiness:
Teacher pairs up students to review and
discuss terms to support ELL.
Students identify and explain components
on the board in pairs.
Product/Learning
Profile:
Students write 1-2 sentence response on
Graphic Organizer and identify components on graph sheet.
Content/Readiness:
Students look at the visual and listen to the teacher to understand the
content.
The strategies will be assessed for
effectiveness through multiple formative assessments such as show with a finger
for understanding, discussion, show understanding on the board, graphic
organizer and graph sheet.
3. Alex: He is a
14-year old male in 8th grade. Alex is considered to have a learning
disability. He had trouble developing literacy early on, and presently reads at
a 7th grade level. He struggles to decode words and has received
special education support since the 2nd grade. Alex takes daily
medication for asthma and needs to use an inhaler on occasion. He tends to keep
to himself, and does not participate in class discussions.
Developmental
Needs
Readiness: Alex
can read at the 5th grade level. He needs help with decoding words
and reading comprehension. He needs to build up his communication skills in
order to contribute to class discussions.
Interest: Alex
likes to be alone, and is lacking confidence to participate in group-conversations.
He does not communicate his interests, and keeps to himself.
Learning Profile:
Alex is very introverted and likes to be alone. He does not like to talk in
front of the class, but will sometimes contribute to small groups. He prefers
to stay quiet in class and is not social with his peers.
Differentiation
Strategies
Process/Readiness:
Teacher pairs up students to review and discuss terms to support
Special Ed.
Students identify and explain components on the board in pairs. Teacher
lets Alex point to/show the component while his partner explains.
Product/Learning Profile:
Students write 1-2 sentence response on Graphic Organizer and identify
components on graph sheet.
Content/Readiness: Students
look at the visual and listen to the teacher to understand the content.
The strategies will be assessed for effectiveness through multiple
formative assessments such as show with a finger for understanding, discussion,
show understanding on the board, graphic organizer and graph sheet.
4. Connor: He is
13-year old male in 8th grade. Connor has an IEP, with the
qualifying condition- Autism. He advocates for himself and seeks help whenever
needed. He is well liked by peers and works well in groups. He can read at
grade level, respond and analyze text. He struggles with organization and
keeping track of assignments and due dates. He has an iPhone and his academic
coach helps him write all the home works/assignments/due dates in it at the end
of every day. He struggles with solving multi step equations and writing
detailed responses/reports.
Developmental
Needs
Readiness: Connor
reads and responds at grade level and needs to add details in his writing. He
needs to have access to the class notes and calendar that can be used as a
backup for missed information. He also needs extended time on tests and reduced
quantity of work whenever possible without impacting the content.
Interest: Connor
likes music. He listens to music whenever he needs to focus or work
individually. His parents are professionals and very supportive of his
activities in and out of school.
Learning Profile:
Connor likes to work in small or big groups. Connor is an audio learner and
likes to dictate long assignments. He learns best by repeatedly listening to information
or doing things.
Differentiation
Strategies
Process/Readiness:
Teacher pairs up students to review and
discuss terms to support his staying on task.
Students identify and explain components
on the board in pairs.
Product/Learning
Profile:
Students write 1-2 sentence response on
Graphic Organizer and identify components on graph sheet.
Content/Readiness:
Students look at the visual and listen to the teacher to understand the
content.
The strategies will be assessed for
effectiveness through multiple formative assessments such as show with a finger
for understanding, discussion, show understanding on the board, graphic
organizer and graph sheet.
5. Nathan: He is
13-year old male in 8th grade. Nathan has an IEP, with Specific
Learning Disability. He has great ideas to
contribute to class conversation and projects and is well liked by his
classmates. He has amazing
retention of information (he hears or sees something and remembers it forever). He
struggles with reading and writing (poor motor skills).
Developmental
Needs
Readiness: Nate
has great project ideas but struggles with reading and writing. He is an audio
learner and benefits a lot from audio books. He can remember anything he hears
one time. He is extremely smart and can read at grade level if given
appropriate resources. He needs extended time to write on tests/quizzes, access
to quiet time, audio books and word processor.
Interest: Nathan
likes science and loves to develop and work on projects.
Learning Profile:
Nathan likes to work in small or big groups. He is an audio and visual learner
and remembers anything he has heard or seen once. He benefits a lot from audio
books and oral assessments.
Differentiation
Strategies
Process/Readiness:
Teacher pairs up students to review and
discuss terms to support his audio learning needs.
Students identify and explain components
on the board in pairs.
Product/Learning
Profile:
Students write short 1-2 sentence response
on Graphic Organizer and identify components on graph sheet.
Content/Readiness:
Students look at the visual and listen to the teacher to understand the
content.
The strategies will be assessed for
effectiveness through multiple formative assessments such as show with a finger
for understanding, discussion, show understanding on the board, graphic
organizer and graph sheet.
Unit Rationale
The unit of Linear Equations and
graphical representation is important because it gives students a strong
background in mathematical reasoning and problem solving that will be important
in their future. It introduces a student to many areas of mathematics and
logical thought. It allows students to better understand the language and
abstract symbols of graphical representations and how to use that language in
real-life applications.
Enduring Understanding: Most 'real world' functions are approximations,
as the world usually contains too many variables to be modeled exactly by
mathematical functions. Linear
equations are helpful in first approximations and promoting logical thought
process. Linear functions are easy to solve, easy to plot, and easy to
understand. The two-variable linear-function is the most significant concept
for the students to understand before they can move on to model and solve more
complex, real-life problems.
Essential Questions:
1. Why is it important to learn mathematical models of two-variable
linear functions? (Explanation)
2. How can you use this knowledge to
explain the relationship between the variables? (Application)
3. What can you learn about the relationships between different
quantities in the world around you from linear functions? (Perspective)
Standards
CA Content Standards:
·
4.0 Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
·
4.0 Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
·
5.0 Students graph a linear equation and compute the x- and y-intercepts
(e.g., graph 2x + 6y = 4).
·
6.0 Students verify that a point lies on a line, given an equation of
the line. Students are able to derive linear equations by using the point-slope
formula.
·
7.0 Students understand the concepts of parallel lines and
perpendicular lines and how those slopes are related. Students are able to find
the equation of a line perpendicular to a given line that passes through a
given point.
CA ELD Standards:
·
Listening/Speaking: Cluster 5, EA – Participate
in and initiate more extended conversations with peers and adults on unfamiliar
topics by asking and answering questions and restating and soliciting
information.
·
Listening/Speaking: Cluster 5, A – Negotiate and initiate social
conversations by questioning, restating, soliciting information, and
paraphrasing the communication of others.
·
Writing: Cluster 1, EA – Use appropriate language variations and
genres in writing for language arts and other content areas.
·
Writing: Cluster 1, A – Produce writing by using various
elements of disclosure (e.g., Purpose, speaker, audience, form).
Unit Objectives (according to the
day)
1. After
reviewing the basic components of graphs on the white board, the students will
draw and label all the graph components using the key terms like quadrants,
x-axis, y-axis, perpendicular, number line, origin and coordinates on the
graphic organizer.
2. After
reviewing the given graph, students will identify the variables represented on
the graph, and write a short paragraph to describe the graph and the
relationship between variables, using the key terms like quadrants, x-axis,
y-axis, coordinates, variables, direct and indirect relationship on the graphic
organizer.
3. After reviewing coordinate graphing system and guided
practice, students graph linear equations and compute
the x- and y-intercepts, using appropriate components of
graphing system and mathematical notations.
4. After guided practice, students are able to verify that a point lies on a line, given an equation of
the line and derive linear equations, using the point-slope formula.
5. After reviewing and understanding the concepts of parallel lines and perpendicular lines and how
those slopes are related, students are able to find the equation of a line perpendicular
to a given line that passes through a given point, using the point-slope
formula.
Student Activities
(according to the day)
1. Work with a partner to answer questions on the board and
complete the graphic organizer.
2. Work with a partner to interpret a given graph, complete the
graphic organizer with a short paragraph to describe it.
3. Work in groups to practice graphing
linear equations and compute the x- and y-intercepts and sketch
the region defined by linear inequality on graph paper.
4. Work in groups to practice verifying
that given points lie on a line, given the equations of the lines and derive
linear equations on graphic organizer.
5. Work with a partner to identify
parallel and perpendicular lines. Work independently on graphic organizer.
Instruction Strategies
(according to the day)
1. Students think-pair-share to review what they
have already learned/know. Project a graph with various components and ask the
students to come in pairs. Have one student identify a component and the other
explains what it is. They work with partners to complete the graphic organizer.
2. Students work with a partner to interpret a
given graph, complete the graphic organizer. Have the students discuss their
responses in small groups and then and write a short paragraph. The key words
to be used in the write up are projected on the board along with their
definitions to support the ELLs and Special Ed students. After writing, the
students pair up with a partner to review each other’s written response and
then edit their own write-ups before turning it in.
3. Demonstrate how to compute the x- and y-intercepts
and sketch the region defined by linear equations on graph using 2 different
examples. Students work in small
groups of 3-4 to practice graphing linear equations on graph sheets.
4.
Demonstrate how
to verify that given points lie on a line, given the equations of the lines
and derive linear equations when two points are known. Students work in groups
on the problems given on graphic organizer.
5.
Demonstrate how to identify parallel and
perpendicular lines from given equations using few different examples. Students
work independently on their graphic organizers.
Assessments (according to the
day)
1. Diagnostic: Informal check with show of 1 finger for
understanding and 0 for review. Call students in pairs to identify and explain
components on the board. Formative: Evaluation of graphic organizer.
2. Formative: Informal monitoring the discussions with partners
and evaluation of graphic organizer.
3. Formative: Informal monitoring practice on graph paper and
evaluation of homework.
4. Formative: Evaluation of graphic organizer.
5. Summative: Evaluation of graphic organizer.
Unit Calendar: (Algebra 1: Linear equations)
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Day
1
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Day
2
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Day
3
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Day
4
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Day
5
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Content
Standards
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4.0 Students understand that the slope (m) of a line is a
constant rate of change, so that if the input or x-coordinate changes
by an amount A, the output or y-coordinate changes by the
amount m·A
|
4.0 Students understand that the slope (m) of a line is a
constant rate of change, so that if the input or x-coordinate changes
by an amount A, the output or y-coordinate changes by the
amount m·A
|
5.0 Students graph a linear equation and compute
the x- and y-intercepts (e.g., graph 2x + 6y =
4).
|
6.0 Students verify that a point lies on a line,
given an equation of the line. Students are able to derive linear equations
by using the point-slope formula.
|
7.0 Students understand the concepts of parallel
lines and perpendicular lines and how those slopes are related. Students are
able to find the equation of a line perpendicular to a given line that passes
through a given point.
|
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Learning
Objectives
|
Cognitive: After
reviewing single variable expressions and equations, students are able to
solve single variable equations for the value of variable using appropriate
notations and order of operations.
|
Cognitive: After
reviewing the given graph, students will identify the variables represented
on the graph, and write a short paragraph to describe the graph and the
relationship between variables, using the key terms like quadrants, x-axis,
y-axis, coordinates, variables, direct and indirect relationship on the
graphic organizer.
|
Cognitive: After
reviewing coordinate graphing system and guided practice, students graph linear equations and compute the x- and y-intercepts,
using appropriate components of graphing system and slope-intercept equation.
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Cognitive:
After guided practice,
students are able to verify that a point lies on a
line, given an equation of the line and derive linear equations, using the
point-slope formula.
|
Cognitive:
After reviewing and
understanding the concepts of parallel lines and
perpendicular lines and how those slopes are related, students identify from
a set of linear equations if the two lines are perpendicular or parallel,
using the slope-intercept equation.
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Student
Activity
|
Work with a partner to
answer questions on the board and complete the graphic organizer.
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Work with a partner to
interpret a given graph, complete the graphic organizer with a short
paragraph to describe it.
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Work in groups to practice
graphing linear equations and compute the x-
and y-intercepts on graph paper.
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Work in groups to practice
verifying that given points lie on a line, given
the equations of the lines and derive linear equations on graphic organizer.
|
Work with a partner to identify parallel and perpendicular lines. Work independently
on graphic organizer.
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Assessment
|
Diagnostic: Informal
check with show of 1 finger for understanding and 0 for review. Call students
in pairs to identify and explain components on the board.
Evaluation of graphic
organizer.
|
Formative: Informal monitoring
the discussions with partners.
Evaluation of graphic
organizer.
|
Formative:
Monitoring group
discussions.
Monitoring practice on
graph paper and evaluation of homework.
|
Formative:
Monitor group
discussions.
Evaluation of graphic
organizer.
|
Formative:
Evaluation of graphic
organizer.
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Closure/Beyond:
Closure: Students will work independently
on a graphic organizer, which will be used for summative assessment of this
part of the unit.
Beyond: Students will identify some
quantities in the real world that have linear relationship with each other.
They will share their findings with the class and explain which of the
variables is dependent or independent, if the relationship is direct or
indirect and what are the applications of this relationship.
Assessment Evaluation
1. Strength: My assessment plan for
the unit is using multiple types of assessments, varying from informal check with show of 1 finger
for understanding and 0 for review, call students in pairs to identify and
explain components on the board, group discussions, graphic organizers, graph sheets, homework and
unit test.
2. Weakness: one weakness in my
assessment for the unit is that most of the graphic organizers include short
direct problems that assess the students’ computational skills.
3. Additional assessment: an
additional assessment that I could include in my unit plan is an open ended or
descriptive problem.
a. When: Given on day 6, and
addressed throughout the next week.
b. Goal/Objective/Standards: to
assess the students’ conceptual understanding.
c. Purpose: To determine if students understand
the material well enough to proceed with the next part of the unit (linear
inequalities), which requires the understanding of linear functions and slope.
d. Implementation method:
pre-printed problem to hand out on day 6.
e. Feedback: feedback will be by
answering student questions about the confusions they have about the topics
covered.
f. Inform instruction: I will be
able to note what concepts need additional review on day 7 and review them
during the next week before moving on to the next topic.
Lesson -1
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TITLE OF THE LESSON: Introduction
to Graphing
Introductory
lesson on the first day of the unit
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CURRICULUM AREA & GRADE LEVEL:
Math/Science 8th Grade
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RATIONALE
A.
Enduring Understanding:
Students need
to understand the basic components of graphing system. Their ability to understand
the graphs and identify the variables and relationship between them helps the
students to interpret the data and graphs they come across in their
day-to-day lives. With this knowledge, they are better equipped with skills
to derive useful information from graphs and make informed decisions in life.
B.
Essential Questions:
How are graphical concepts and
language used in our day-to-day lives?
How can we use and interpret
graphical data representations to solve real life problems?
C. Reason
for Instructional Strategies and Student Activities: Lesson will introduce the coordinate
graphing system to the students. It will also incorporate all three major
learning preferences to address different learning needs.
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CONTENT
STANDARD(S)
Grade
8 Standard 1:
Students understand that the slope (m) of
a line is a constant rate of change, so that if the input or x-coordinate
changes by an amount A, the output or y-coordinate changes by
the amount m·A
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ELD STANDARDS
Standard 5-EA (Listening and Speaking: Participate in and initiate more extended
social conversations with peers and adults on unfamiliar topics by asking and
answering questions and restating and soliciting information.
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LEARNING GOALS - OBJECTIVES
A.
Cognitive
After reviewing the basic components
of graphs on the white board, the students will draw and label all the graph
components using the key terms like quadrants, x-axis, y-axis, perpendicular,
number line, origin and coordinates on the graphic organizer.
B.
Affective
After completing
this activity, the students will be able to describe how a coordinate graphing
system is arranged, and identify its parts using the correct mathematical
terminology
C.
Language Development
After
completing this lesson, the students will be able to identify correct
mathematical terminology related to coordinate graphing system and use these
terms in appropriate context.
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ASSESSMENTS
A.
Diagnostic/Entry Level
I will ask
the students specific questions about number line, horizontal and
perpendicular lines. I
will ask the students to raise their hands and show me with 1 finger if the
understand what the terms are and a zero if they are not sure. I will review
these if more than 4 students are not sure. I will be able to assess Daisy’s
previous knowledge along with other students.
B.
Formative-Progress Monitoring
The
students will participate in discussion with their partner. I will monitor the discussions to
check that Daisy is participating by asking and answering questions to learn
about the words/terms she doesn’t know. I will ask her question to make sure
that she can restate the information.
C.
Summative
The
students will draw and label different graph components and write their
definitions on activity sheet.
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EXPLANATION OF DIFFERENTIATION FOR
ENGLISH LANGUAGE LEARNERS
1.) Content/Based on Readiness, Learning Profile or Interest
Content of the assignment is aligned
with Daisy’s and Ricky’s readiness. It includes simple terminology explained
with visual and working with a partner.
2.) Process/Based on Readiness, Learning Profile or Interest
This is a small lesson including lot
of visual aid, drawing activity and some writing. The instructions on the
worksheet are simple and small and will be read aloud in the class to make
the task simpler for Daisy.
3.) Product/Based on Readiness, Learning Profile or
Interest
A drawing of simple graph and
labeling its components are tangible products, which are based on Daisy’s and
Ricky’s readiness, interest and learning profile.
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EXPLANATION OF DIFFERENTIATION FOR
STUDENTS WITH SPECIAL NEEDS
1.) Content/Based on Readiness, Learning Profile or Interest
Content of the assignment is aligned
with the readiness and interests of all Alex, Connor and Nathan.
It includes working with a partner
and simple terminology explained with visual. Alex can choose to work alone
or with his coach.
The discussion with partner, oral
instructions and repeated explanation by students will cater to Connor’s
audio learning style.
There is minimal writing in single
sentences on the graphic organizer, which is manageable for Nathan.
2.) Process/Based on Readiness, Learning Profile or Interest
This is a small lesson including lot
of visual aid, drawing activity and minimal writing. The instructions on the
worksheet are simple and small. It is based on the readiness of all students.
3.) Product/Based on Readiness, Learning Profile or Interest
A drawing of simple graph and
labeling its components are tangible products which are based on readiness
and learning profiles of all students.
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INSTRUCTIONAL STRATEGIES
A. Anticipatory Set/Into
I will ask the students to
review/recall number line, horizontal and perpendicular lines. I will walk
around the room while they think-pair-share for a quick check that all of
them understand these terms. After 2 min. I will ask the students to raise
their hands and show me with 1 finger if the understand what the terms are
and a zero if they are not sure. I will review these if more than 4 students
are not sure. 5 min
B. Instruction/Through
I will explain the components of coordinate graphing system one at a
time one at a time and show the definition on the projector simultaneously. I will have the students take notes. 10 min.
C. Guided Practice/Through
I will project all components of graph on
the board and call on a pair of students, one at a time to come on board –
one of them will label the correct component and the other will explain what
it is. I will guide them at any step they are struggling. 10 min
D. Independent
Practice/Through
I will pass an activity sheet/Graphic organizer to the students and
ask them to work on it independently. I will display all the definitions on
the projector. I will walk around the room, monitoring the students’ work and
check on Daisy and Connor if they need extra help with instructions or
content. 10 min
E. Closure
I will ask the students to finish
their Graphic organizer as homework. 2 min
F. Beyond
I will show a couple of graphs from newspaper
or article and ask the students to relate them to the basic coordinate
graphing system, identify all the components they learned today and interpret
the graph using these terms. I will encourage them to interpret any graph
they come across in their lives in these terms. 7 min.
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STUDENT ACTIVITIES
A. Anticipatory Set/Into
The students will review number
line, horizontal and perpendicular lines through think-pair-share. 5 min.
B. Instruction/Through
The students will look at the board
and take notes on definitions in their own words. 10 min.
C. Guided Practice/Through
The students will come to the white board
and work in pairs to identify and label a component of graph and explain what
it is. 10 min.
D. Independent
Practice/Through
Each student will work quietly and
independently on the graphic organizer/activity sheet to identify, label and
define the components of graphing system taking help from the display of
definitions on the board. 10 min
E. Closure
The students note the homework and wrap up
their activity sheets. 2 min.
F. Beyond
The students will familiarize with
the basic coordinate graphing system and whenever they see a graph, they
should be able to identify all the components they learned today and
interpret the graph using these terms.
7 min.
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RESOURCES
Graphic Organizers, visual and
vocabulary list used in this lesson are attached as separate files.
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Reflection
I have
learned, through my experience with students, that it is very important and
helpful to know the students, their backgrounds, interests, learning styles and
needs. This information goes a long way in supporting the content,
instructional strategies and assessments aligned with the different learning
styles, interests and needs. This single strategy not only makes all aspects of
the lesson more meaningful and effective but also makes the students feel
included, engaged and motivated in learning process. Differentiating the lesson
by including strategies like work with a partner, graphic organizer, visual aid
and sharing on the board offers several benefits.
·
It
caters to all the learning styles and needs of ELLs and Special Ed students by
making the content accessible to them in different ways.
·
It
draws all the other students into whole brain learning by – listening, saying,
seeing and writing.
·
It
allows the teacher to assess the students’ work and progress in different ways,
both formally and informally, like, monitoring the discussions, checking for understanding
by show of fingers and calling to show and explain on the board, and evaluating
the graphic organizers.
·
It
keeps the students engaged and motivated and hence, makes classroom management
easier. It creates an inclusive and low-risk environment for the students.
Words to Learn
1.
The coordinate
graphing system is formed by a pair of perpendicular number
lines.
2. The
intersection point at zero of both number lines is called the Origin
3. Each
of the two number lines is called an axis
4. The
horizontal axis, the one that goes across from side to side, is called the X-axis.
5. The
vertical axis, the one that goes across from side to side, is called the Y-axis.
6. The independent
variable represents the input or cause.
7. The dependent
variable represents the output or effect.
8. The direct
relationship means that both the variables are either increasing
or decreasing together.
9. The indirect
relationship means that one variable is increasing then the
other is decreasing and vice versa.
Name
___________________________________________________ Date _________________________
Define the following terms in your own words.
1. Origin
2. X-axis
3. Y-axis
4. Coordinates
5. Quadrants
On the graph provided, identify and label
the following-
·
Origin
·
x-axis – number the axis
·
y-axis – number the axis
·
Quadrants I, II, III, and IV
·
coordinates (4,5), (0,6),
(1,-5), (-4,-7), (6,-6)
