Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Formative Assessment Lesson: Modeling Situations with Linear Equations
Source: Balanced Assessment Materials from Mathematics Assessment Project
http://map.mathshell.org/materials/download.php?fileid=673
In this FAL, students will explore relationships between variables in everyday situations,
find unknown values from known values, find relationships between pairs of unknowns, and
express these as tables and graphs, find general relationships between several variables, and
express these in different ways by rearranging formulae.
STANDARDS ADDRESSED IN THIS TASK:
Define, evaluate, and compare functions.
•
MCC8.F.1 Understand that a function is a rule that assigns to each input exactly one
output. The graph of a function is the set of ordered pairs consisting of an input and the
corresponding output.
•
MCC8.F.2 Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). For example,
given a linear function represented by a table of values and a linear function represented
by an algebraic expression, determine which function has the greater rate of change.
STANDARDS FOR MATHEMATICAL PRACTICE:
This task uses all of the practices with emphasis on:
2. Reason abstractly and quantitatively.
4. Model with mathematics.
BACKGROUND KNOWLEDGE:
•
MCC5.G.1,
MCC5.G.2, MCC6.EE.2, MCC6.EE.3, MCC6.EE.4, MCC6.EE.6, MCC7.EE.2, MCC7.E
E.4
COMMON MISCONCEPTIONS:
•
•
Students may mix up the input and output values/variables. This could result in the
inverse of the function.
Students will have trouble writing a general rule for these situations. They tend to mix up
the dependent and independent variable.
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 70 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
•
•
Some student will mix up the x- and y- axes on the coordinate plane. Emphasizing that
the first value is plotted on the horizontal axes (usually x, with positive to the right) and
the second is the vertical axis (usually called y, with positive up) point out that this is
merely a convention. It could have been otherwise, but it is very useful for people to
agree on a standard customary practice.
Additional misconceptions can be found within the FAL Teacher Guide.
ESSENTIAL QUESTIONS:
•
•
How do you represent relations and functions using tables, graphs, words, and algebraic
equations?
How can graphs and equations of functions help us to interpret real-world problems?
MATERIALS:
•
See FAL
GROUPING:
•
Partner/Small Group
TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION:
Tasks and lessons from the Mathematics Assessment Project are specifically designed to
teachers effectively formatively assess their students. The way the tasks and lessons are designed
gives the teacher a clear understanding of what the students are able to do and not do. Within the
lesson, teachers will find suggestions and question prompts that will help guide students towards
understanding. For more information access the MAP website:
http://www.map.mathshell.org/materials/background.php?subpage=summative
The task, “Modeling Situations with Linear Equations,” is a Mathematics Assessment Project
Assessment Task that can be found at the website:
http://www.map.mathshell.org/materials/tasks.php?taskid=278&subpage=expert
The PDF version of the task can be found at the link below:
http://map.mathshell.org/materials/download.php?fileid=673
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 71 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
*Create Matching Function Cards
INTRODUCTION TO THIS FORMATIVE ASSESSMENT LESSON
MATHEMATICAL GOALS
This lesson unit is intended to help you assess how well students are able to create functions and change the form of
how a function is represented
COMMON CORE STATE STANDARDS
This lesson involves mathematical content in the standards from across the grades, with emphasis on::
• MCC8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The
graph of a function is the set of ordered pairs consisting of an input and the corresponding
output.
• MCC8.F.2 Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a
linear function represented by a table of values and a linear function represented by an algebraic
expression, determine which function has the greater rate of change.
• MP.1 Make sense of problems and persevere in solving them.
• MP.7 Look for and make use of structure.
INTRODUCTION
This lesson is structured in the following way:
Before the Lesson, students will perform a pre-assessment to demonstrate their understanding of the basics related to
defining linear functions. This will give the teacher some alerts as to student misconceptions and also provide
information to aid in forming small groups for the activity.
At the Start of the Lesson, students will divide into groups of 2 or 3 and will prepare to create cards that represent
certain functions, but in different forms than the completed card(s) of the set given to them. They will be given
enough blank cards of each of five different representations so that they can create functions for the given data.
During the Lesson, students will determine the representation of mappings, charts, ordered pairs, and graphs for
certain linear equations. The groups will complete blank cards so that they create a complete set of five cards that
represent the same data. Differentiation by the teacher can have groups creating 1,2,3,or 4 cards to complete the sets
of five.
After the Whole-Group Class Discussion, students should be able to identify the graph of a function given any of the
other four parts of the set, or identify the linear equation given one of the other four parts
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 72 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
MATERIALS REQUIRED
Each individual student will need 1, 2, or 3 of the preprinted cards for several sets of five different sets of data
representations provided. The number of completed cards for each set and the number of different sets given to each
group will be determined by the level of differentiation needed based on the pre-assessment.
•
Sets provided are labeled with both letter and number. Match alpha representations for numeric sets.
TEACHER PREP REQUIRED
Teacher, be advised that prior to the lesson, the following preparations/copies will need to be made:
• Copies of completed cards separated into sets with blank cards for the alpha representations to be made.
• Sufficient numbers of sets so that students will have enough practice based on ability levels.
• Pencils are recommended for initial construction, but markers may be used for final form.
TIME NEEDED:
For Pre-Assessment:
15 minutes
For Lesson:
30 minutes
For Post:
15 minutes
Other:
Special Note(s) about timing:
FRAMING FOR THE TEACHER:
After students understand that functions have unique domain elements, they should be ready to identify the different
representations of the data for a function. This FAL is designed to assess their abilities to connect representations of
similar data in different formats (mappings, charts/tables, ordered pairs, as well as equations and graphs).
FRAMING FOR THE KIDS:
Say to the students:
This activity will take about a day for us to complete.
The reason we are doing this is to be sure that you understand the different representations of data for a function
before we move on to a new idea.
You will have a chance to work with a partner to correct any misconceptions that you may have regarding the
different forms of function representation. After the partner work, you will be able to show me what you have
learned!
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 73 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
PRE-ASSESSMENT BEFORE THE LESSON
ASSESSMENT TASK: Function Cards
Name of Assessment Task:
Time This Should Take: 15 minutes
Have the students do this task in class or for homework, a day or more before the formative assessment lesson. This
will give you an opportunity to assess the work, and to find out the kinds of difficulties students have with it. You
will them be able to target your help more effectively in the
follow-up lesson.
Give each student a copy of the Pre-Assessment:
Briefly introduce the task and help the class to understand the
problem and its context.
Spend 15 minutes working individually on this task.
Read through the task and try to answer it as carefully
as you can. Show all your work so that I can
understand your reasoning. Don’t worry if you can’t
complete everything. There will be a lesson that should
help you understand these concepts better. Your goal is
to be able to confidently answer questions similar to
these by the end of the next lesson.
Students should do their best to answer these questions, without
teacher assistance. It is important that students are allowed to
answer the questions on their own so that the results show what
students truly do not understand.
Students should not worry too much if they cannot understand or
do everything on the pre-assessment, because in the next lesson
they will engage in a task which is designed to help them..
Explain to students that by the end of the next lesson, they should
expect to be able to answer questions such as these confidently.
This is their goal.
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 74 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
COLLABORATION TIME/READING STUDENTS RESPONSES
You Will Not “Grade” These!
Collect students’ :responses to the task. It is helpful to read students’ responses with colleagues who are also
analyzing student work. Make notes (on your own paper, not on their pre-assessment) about what their work reveals
about their current levels of understanding, and their approaches to the task. You will find that the misconceptions
reveal themselves and often take similar paths from one student to another, and even from one teacher to another.
Some misconceptions seem to arise very organically in students’ thinking. Pair students in the same classes with
other students who have similar misconceptions. This will help you to address the issues in fewer steps, since they’ll
be together. (Note: pairs are better than larger groups for FAL’s because both must participate in order to discuss!)
You will begin to construct Socrates-style questions to try and elicit understanding from students. We suggest you
write a list of your own questions, however some guiding questions and prompts are also listed below as a jumpingoff point.
GUIDING QUESTIONS
COMMON ISSUES
SUGGESTED QUESTIONS AND PROMPTS
Student does not use a straightedge to create
graph of the linear equation.
Student has difficulty developing the value of the
y-intercept.
Student chooses a domain scale that is too small
to aid in determining the slope.
How accurate is you line? Would a ruler have
helped?
What happens if you extend the pattern left and
right? Where will the next points be located?
Will using a different scale change your ability to
see the direction the line takes? Can you count
the boxes to determine slope?
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 75 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
LESSON DAY
SUGGESTED LESSON OUTLINE:
Part 1: Whole-Class Introduction:
Time to Allot: ( 5 minutes)
Today you will be working in small groups to create various representations of linear relationships.
You will be given one or more completed cards, and your team’s responsibility will be to create the missing cards.
Who can describe how to identify these relationships?
Display the “Warm Up” slide provided.
Suggested Prompts:.
What are the differences in how these items are represented?
How would you create one if you had to?
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 76 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Part 2: Collaborative Activity::
Time to Allot: ( 20 minutes)
Put students into their pairs according to your analysis of student errors.
Do/Say the Following:
• I will be giving you [X] completed cards for a certain mathematical relationship. Your job is to figure out
how to create the other representations without changing the data relationship.
• You will have blank cards to create the parts needed to complete your set. I may be wise to use scratch paper
to plan what will go on your cards BEFORE actually writing on them.
• Be ready to present your set of cards and to justify what you did if someone disagrees with your final product.
During the Collaborative Activity, the Teacher has 3 tasks:
• Circulate to students’ whose errors you noted from the pre-assessment and support their reasoning with your
guiding questions.
• Circulate to other students also to support their reason in the same way.
• Make a note of student approaches for the summary (plenary discussion). Some students have interesting and
novel solutions!
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 77 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Part 4: Improving Solutions to the Assessment Time to Allot: ( 10 minutes)
Task
The Shell MAP Centre advises handing students their original assessment tasks back to guide their responses to their
new Post-Assessment (which is sometimes the exact same as the Pre-Assessment). In practice, some teachers find
that students mindlessly transfer incorrect answers from their Pre- to their Post-Assessment, assuming that no “X”
mark means that it must have been right. . Until students become accustomed to UNGRADED FORMATIVE
assessments, they may naturally do this. Teachers often report success by handing students a list of the guiding
questions to keep in mind while they improve their solutions.
Practice will make perfect, and teachers should do what makes them most comfortable with their students to find skill
misconceptions!
Have students critique their own pre-assessment and write out an explanation for any mistakes they find.
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 78 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Part 3: Plenary (Summary) Discussion:
Time to Allot: ( 15 minutes)
Gather students together, share solutions. Discussion prompts should be made up of your original guiding questions
and notes about student approaches. Some other discussion prompts are listed below:
NOTE: “Scribing” helps to increase student buy-in and participation. When a student answers your question, write
the student’s name on the board and scribe his/her response quickly. You will find that students volunteer more often
when they know you will scribe their responses – this practice will keep the discussions lively and active!
•
•
•
Student should be able to create ordered pairs as long as they identify the domain and range correctly.
The constant rate of change is the X coefficient. They are all whole numbers for this exercise.
Graphs should have lines extended beyond the “points”. We are assuming continuous graphs.
Slide text for discussion:
•
GIVEN THE GRAPH, HOW DID YOU CREATE THE
MAPPING OR THE CHART?
•
GIVEN THE EQUATION, HOW DID YOU CREATE THE
CHART OR THE GRAPH?
•
GIVEN THE CHART, HOW DID YOU FIND THE RATE OF
CHANGE OR THE SLOPE OF THE LINE?
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 79 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
PRE-ASSESSMENT (Answer Key)
ASSESSMENT TASK: Function Cards
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 80 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Collaborative Activity (Answer Key)
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 81 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 82 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
PRE-ASSESSMENT
Name of Assessment Task: Functions
1] Shawn mowed lawns during the summer. He charged each customer a fixed amount for gasoline for the mower
and an hourly rate for the actual mowing. The chart below shows data for his charges for various hours of work. Is
there an equation that would represent this data? If you graph the data and assume it is linear, what does the Yintercept represent?
Hours
1
2
3
4
5
70--------------------------------------------------------------------------Mowing
-----Total
17.00 29.50 42.00 54.50 67.00
------------------------------------------------------------------------------Charged
60------------------------------------------------------------------------------------------------------------------------------------------------------------50-------------------------------------------------------------------------------
-----------------------------------------------------------------------40--------------------------------------------------------------------------------
---------------------------------------------------------------30---------------------------------------------------------------------------
2] The cost for buying 3, 4, 6 and 8 T-shirts at a local sports store is shown in the chart. Do you think that this data
represents a linear relationship? If you graph the data what does the Y-intercept appear to be and what does it
represent?
No.
of
Shirts
Total
Cost
3
4
6
8
12
$19 $22 $28 $34 $46
50-45-40-35-30-25-20-15-10-5-0
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 83 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
COLLABORATIVE ACTIVITY (Answer Key)
A]Equations
B]Mappings
C] Tables/T-charts
D] Ordered Pairs
1A)
1B List inputs & outputs
1C
1D
1
4
2
3
Y = 2X – 3
(Minimum of 3)
X
1
2
3
4
–1
5
1
3
Y
–1
1
3
5
E] Graphs
( 1 , –1)
( 2, 1 )
( 3, 3 )
( 4, 5)
( –2 , –7)
1E
2A)
Y = 3X + 2
2B
2C (Minimum of 3)
1
2
3
4
5
8
11
14
x
y
1 2
4
5 8
14
3
11
2D
(1 , 5)
(2 , 8)
( 3 , 11)
( 4 , 14)
(–1 , –1)
2E
3A)
Y= X+1
3B List domains &
ranges
–1
1
2
3
4
3C (Minimum of 3)
X
0
4
3
2
5
1 2
2 3
3 4
4 5
–1 0
Y
3D
( 1,2)
( 2,3)
( 3,4)
( 4,5)
( –1 , 0 )
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 84 of 101
All Rights Reserved
3E
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
A]Equations
B] Mappings
C] Tables/T-charts
D] Ordered Pairs
E] Graphs
4A)
4B List inputs &
outputs
4C (Minimum of 3)
4D
4E
Y = –2x + 1
5A)
Y = –3X +2
–1
0
1
2
3
3
–3
1
–1
–5
5B
–1
1
2
3
X
3
2
1
0
–1
5C
–7
5
–1
–4
x
y
Y
–5
–3
–1
1
3
(Minimum of 3)
–1 1 2
3
5 –1 –4 –
7
( 3 , –5)
( 2 , –3)
( 1 , –1)
( 0 , 1)
( –1 , 3 )
5D
( –1 , 5 )
( 1 , –1)
( 2 , –4)
( 3 , –7)
5E
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 85 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
6A)
6B List domains &
ranges
6C
(Minimum of 3)
6D
(
(
(
(
(
6E
,
,
,
,
,
)
)
)
)
)
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 86 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Collaborative Activity (Blank “E” Cards #1)
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 87 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Collaborative Activity (Blank “B” Cards #2)
MAPPING
MAPPING
MAPPING
MAPPING
MAPPING
MAPPING
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 88 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Collaborative Activity (Blank “D” Cards #3)
ORDERED
(
(
(
(
(
,
,
,
,
,
ORDERED
(
(
(
(
(
,
,
,
,
,
PAIRS
)
)
)
)
)
PAIRS
)
)
)
)
)
ORDERED
(
(
(
(
(
,
,
,
,
,
ORDERED
(
(
(
(
(
,
,
,
,
,
PAIRS
)
)
)
)
)
PAIRS
)
)
)
)
)
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 89 of 101
All Rights Reserved
ORDERED
(
(
(
(
(
,
,
,
,
,
ORDERED
(
(
(
(
(
,
,
,
,
,
PAIRS
)
)
)
)
)
PAIRS
)
)
)
)
)
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Collaborative Activity (Blank “C” Cards #4)
T-CHART
X
T-CHART
Y
X
BOX-CHART
T-CHART
Y
X
BOX-CHART
BOX-CHART
X
X
X
Y
Y
Y
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 90 of 101
All Rights Reserved
Y
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Collaborative Activity (Blank “A” Cards #5)
EQUATION
EQUATION
EQUATION
EQUATION
EQUATION
EQUATION
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 91 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Card Set ONE
EQUATION SET #A1
Y = 2X – 3
ORDERED PAIRS SET#D4
MAPPING SET #B2
1
2
3
4
GRAPH
T–CHART SET #C3
5
8
11
14
SET #E5
( 3 , –5)
( 2 , –3)
( 1 , –1)
(0,1 )
(–1, 3 )
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 92 of 101
All Rights Reserved
X
1
2
3
4
–1
Y
2
3
4
5
0
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Card Set TWO
EQUATION SET #A2
Y = 3X + 2
MAPPING SET #B3
–1
1
2
3
4
T–CHART SET #C4
0
4
3
2
5
ORDERED PAIRS SET#D5
X Y
3 –5
2 –3
1 –1
0
1
–1 3
GRAPH #E1
(–1 , 5 )
( 1 , –1)
( 2 , –4)
( 3 , –7)
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 93 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Card Set Three
EQUATION SET #A3
Y = X+1
ORDERED PAIRS SET#D1
( 1 , –1)
(2, 1)
(3, 3)
(4, 5)
(–2, –7)
MAPPING SET #B4
–1
0
1
2
3
3
–3
1
–1
–5
BOX CHART SET #C5
X –1
Y 5
1
–1
2
–4
GRAPH #E2
3
–7
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 94 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Card Set Four
EQUATION SET #A4
Y = –2X + 1
MAPPING SET #B5
–1
1
2
3
T–CHART SET #C1
–7
5
–1
–4
ORDERED PAIRS SET#D2
X Y
1 –1
2 1
3 3
4 5
GRAPH #E3
(1, 5)
(2, 8)
( 3 , 11)
( 4 , 14)
(–1, –1)
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 95 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Card Set Five
EQUATION SET #A5
MAPPING SET #B1
1
4
2
3
Y = –3X + 2
ORDERED PAIRS SET#D3
(1,
(2,
(3,
(4,
(–1,
2)
3)
4)
5)
0)
–1
5
1
3
BOX CHART SET #C2
1
2
3
4 –1
5
8 11 14 –1
X
Y
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 96 of 101
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GRAPH #E4
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Lesson Day Warm-Up
Name of Assessment Task:
•
•
•
•
•
•
Equations
Mappings
Tables
T-charts
Ordered Pairs
Graphs
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 97 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Collaborative Activity Instructions:
• Create the full set of representations without changing the data relationship.
• Use blank cards to create the parts needed to complete your set.
• Be ready to present your set of cards and to justify what you did.
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 98 of 101
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework
Eighth Grade Mathematics • Unit 4
Collaborative Plenary Discussion Questions:
GIVEN THE GRAPH, HOW DID YOU CREATE THE
MAPPING OR THE CHART?
GIVEN THE EQUATION, HOW DID YOU CREATE THE
CHART OR THE GRAPH?
GIVEN THE CHART, HOW DID YOU FIND THE RATE OF
CHANGE OR THE SLOPE OF THE LINE?
MATHEMATICS  GRADE 8  UNIT 4: Functions
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
July 2014 • Page 99 of 101
All Rights Reserved