Course Name: Seventh Grade Honors
Unit #
2
Unit Title: Variables and Patterns
Enduring understanding (Big Idea): Students will understand that analyzing a pattern or relationship in a graph, table or equation.
To identify variables and interpret the relationship between variables, particularly how variables change in relation to one another.
What variables are the dependent and independent variables?
Essential Questions: What are the variables in the problem? What variables are the dependent and independent variables? How
can I use a table, graph, or equation to display and analyze a relationship between quantitative variables? How can I interpret regular
change observed in a table, graph data or equation? How can I use these regular or predictable changes to make estimates or
predictions about other data values?
BY THE END OF THIS UNIT:
Students will know…
What are the variables in the problem?
How are these variables related to each other?
Which variables depend on, or change in relation to others?
How can a relationship be displayed and analyzed with
tables, graphs, and equations?
Students will be able to…





Vocabulary:
Independent variable, dependent variable, rate of change,
relationship, equation
Unit Resources
Learning Task: Mathematical Reflection
Performance Task: Check-Up(s)/Partner Quiz
Project: None
Unit Review: Looking Back and Looking Ahead
MARS: Tasks A06 Bike Ride, A08 Buses, A16 Journey
Collecting, organizing, and representing data
about the relationship between two variables
Identifying patterns and extreme values in data
organized in graphs or tables; making inferences
about situations based on such information
Analyzing a pattern or relationship in a graph or
table to identify variables and interpret the
relationship between variables, particularly how
variables change relative to one another
Extending the number line and coordinate grid to
include negative coordinates
Developing understanding of the Commutative
Property, the Distributive Property, and the order
of operations
Mathematical Practices in Focus:
1- Make sense of problems and persevere in solving
them
2- Reason abstractly and quantitatively
3- Construct viable arguments and critique the reasoning
of others
4- Model with mathematics
5- Use appropriate tools strategically
6- Attend to precision
7- Look for and make use of structure
8- Look for and express regularity in repeated reasoning
CCSS-M Included: 7.EE.2, 7.EE.3, 7.EE.4, 7.EE.4a, 7.RP.2c,
7.RP.2d, 7.RP.3, 8.EE.7
NCDPI “Unpacking” of the standards:
http://maccss.ncdpi.wikispaces.net/Seventh+Grade
Suggested Pacing: 25 Days Including Inv. 4 from Accentuate
the Negative Unit 1
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Seventh Grade Honors
Unit Plans
Standard 7.RP.2C, 7.EE.4
Investigation 1: Variables,
Tables and Coordinate Graphs
Standard 7.RP.2c; 7.RP.2d;
7.EE.3;
Investigation 2: Analyzing
Graphs and Tables
Standard 7.RP.2c; 7.EE.2; 7.EE.3;
7.EE.4; 7.EE.4a
Investigation 3: Rules and
Equations
Standard 7.RP.2c; 7.RP.3; 7.EE.3;
7.EE.4; 7.EE.4a
Investigation 4: Calculator
Tables and Graphs
Unit #
2
Unit Title: Variables and Patterns
Investigation
Problem 1.1 Preparing for a Bicycle Tour
Problem 1.2 Making Graphs
Problem 1.3 Day 1: Atlantic City to Lewes
Problem 1.4 Day 2: Lewes to Chincoteague Island
Problem 1.5 Day 3: Chincoteague Island to Norfolk
Mathematical Reflections
Problem 2.1 Renting Bicycles
Problem 2.2 Finding Customers
Problem 2.3 What’s the Story?
Mathematical Reflections
Suggested ACE Questions
1.1 ACE 13-17
1.2 ACE 1-3, 18-20
1.3 ACE 4, 5, 26
1.4 ACE 6-9, 21-24, 27, 28
1.5 ACE 10-12, 25,29, 30
Problem 3.1 Writing Equations
Problem 3.2 Writing More Equations
Problem 3.3 Paying Bills and Counting Profits
Mathematical Reflections
3.1 ACE 1-4, 21-27, 43
3.2 ACE 5-12, 28-37, 44-47
3.3 ACE 13-20, 38-42, 48,49
Problem 4.1 Making and Using Calculator Tables
Problem 4.2 Making and Using Calculator Graphs
Problem 4.3 Extending the Tour
Mathematical Reflections
Looking Back and Looking Ahead
ACE 1,7-12
ACE 2-4, 13-17
ACE 5,6,18,19
Accentuate the Negative – Investigation 4
Standard 7.NS.1, 7.NS.1.d, 7.NS.2, Problem 4.1 Order of Operations
7.NS.2.a, 7.NS.2.c, 7.NS.3, 7.EE.3
Problem 4.2 Distributing Operations
Problem 4.3 The Distributive Property and
*Investigation 4: Properties of
Subtraction
Operations
Mathematical Reflections
Looking Back and Looking Ahead
Standard 7.NS.1, 7.NS.2, 8.EE.7
Honors Section Algebra 1 Foundations Textbook
2-1
Standard 8.EE.7
2-2
Standard 8.EE.7
2-3
Standard 7.EE.3, 7.EE.4, 8.EE.7
2-4
Standard 7.EE.4
2-5
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
2.1 ACE 1-4, 15,16,20,21
2.2 ACE 5-7,17,18,22,23
2.3 ACE 8-14,19,24
4.1 ACE #1, 2, 8 - 29, 36 – 43
4.2 ACE #4-18,27-29
4.3 ACE #5 -7, 33 -35, 45, 46
Problems 1-6, Exs. 10,11-59
odd, 60-69
Problems 1-4, Exs. 11-39 odd,
40-43, 45-60
Part 1 Problems 1-3, Esz. 8-29
Part 2 Problems 4-5, exs. 7-24,
26-37
Problems 1-4, Exs. 10-18, 19-35
odd, 36-38, 40-49
Problems 1-4, Exs. 11-17 odd,
18-38 even, 39-43, 45-60
Course Name: Seventh Grade Honors
Unit #
2
Unit Title: Variables and Patterns
CORE CONTENT
Cluster Title: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard 7.RP.2: Recognize and represent proportional relationships between quantities.
Concepts and Skills to Master
 Ability to recognize in a given proportional situation that the two “between ratios” and the two “within ratios” are the same
 Ability to distinguish between additive and multiplicative situations
 Ability to recognize that two equal ratios represent a proportion
 Ability to recognize and represent the connection between equivalent ratios, values in a table, and graphed ordered pairs
 Ability to express unit rates using a variety of representations, given a contextual situation
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Conceptual
 Understand what a variable is and the importance of defining the variable in an expression or equation.
 Understand that a variable has some value and the same rules that apply to numbers also apply to variables
 Understand the concept of an independent and dependent variable
 Understand discrete versus continuous data.
Procedural
 Plot points on a graph
 Construct graphs and tables
Academic Vocabulary
Proportional relationships; constant; unit rate; equivalent ratios
Suggested Instructional Strategies
Resources
 Introduce the lesson by allowing students to identify
patterns through the use of tables.
 Explore various ways to represent equations (describe what
made it easier for you to connect the concepts of tables and
graphs to actual equations.
Sample Assessment Tasks
Skill-based Task
The table below gives the price for different numbers of books.
Do the numbers in the table represent a proportional
relationship?
# of Books
1
3
4
7
Textbook Correlation
 Variables and Patterns
o Investigation 3
Helpful Websites / Resources
 Many links to appropriate resources connected to
7.RP.2 - http://ccssmath.org/?page_id=598
Problem Task
The price of bananas at another store can be determined by the
equation: P = $0.35n, where P is the price and n is the number of
pounds of bananas. What is the constant of proportionality (unit
rate)?
Price in Dollars
3
9
12
18
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Seventh Grade Honors
Unit #
2
Unit Title: Variables and Patterns
CORE CONTENT
Cluster Title: Analyze proportional relationships and use them to solve real-world and mathematical problems
Standard 7.RP.2c: Represent proportional relationships using equations.
Concepts and Skills to Master
• Ability to recognize that multiplicative relationships are proportional
For example, if total cost t is proportional to the number of n of items purchased at a constant price p, the relationship between the
total cost and the number of items can be expressed as t = pn.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Understand what an proportional relationship is when using graphs and tables
 Understand how to plot points on a graph
Academic Vocabulary
Proportional relationships
Suggested Instructional Strategies
 Introduce the lesson by allowing students to identify
patterns through the use of tables.
 Explore various ways to represent equations (describe
what made it easier for you to connect the concepts of
tables and graphs to actual equations.
Sample Assessment Tasks
Skill-based Task
Resources
Textbook Correlation
 Variables and Patterns
o Investigations 1, 2, 3, and 4
Helpful Websites / Resources
 Many links to appropriate resources connected to
7.RP.2c - http://ccssmath.org/?page_id=604
Problem Task
The school needs to purchase TI-84 calculators.
calculator is sells for $125.00.
Each One cellular phone carrier charges $26.50 a month plus $0.15 a
minute for local calls. Another carrier charges $14.50 a month and
$0.25 a minute for local calls.
Part A. How many calculators can be purchased with $5000?
Part A. For how many minutes is the cost of the plans the same?
calculators
minutes
Part B. Explain how you determined the number of
calculators that could be purchased. Use an
Part B. Use a table, graph and equation to justify your answer.
equation, graph and table in addition to words,
numbers, and/or symbols in your explanation.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Seventh Grade Honors
Unit #
2
Unit Title: Variables and Patterns
CORE CONTENT
Cluster Title: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Standard: 7.RP.2d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with
special attention to the points (0, 0) and (1, r) where r is the unit rate.
Concepts and Skills to Master:
• Ability to identify that a proportional relationship intersects (0,0)
• Ability to determine other points using (1, r)
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Understand what an proportional relationship is when using graphs and tables
 Understand how to plot points on a graph
Academic Vocabulary
Proportional relationships; coordinate pairs
Suggested Instructional Strategies
 Introduce the lesson by allowing students to identify
patterns through the use of tables.
 Explore various ways to represent equations
(describe what made it easier for you to connect the
concepts of tables and graphs to actual equations.
Sample Assessment Tasks
Skill-based Task
Resources
Textbook Correlation
 Variables and Patterns
o Investigations 2
Helpful Websites / Resources
 Many links to appropriate resources connected to
7.RP.2d - http://ccssmath.org/?page_id=606
Problem Task
A student is making trail mix. Create a graph to determine if the
quantities of nuts and fruit are proportional for each serving size
listed in the table. If the quantities are proportional, what is the
constant of proportionality or unit rate that defines the relationship?
Explain how the constant of proportionality was determined and how
it relates to both the table and graph.
CORE CONTENT
Cluster Title: Analyze and solve linear equations and pairs of simultaneous linear equations.
Standard 8.EE.7a- Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent
equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Concepts and Skills to Master
• Identify and provide examples of equations that have one solution, infinitely many solutions or no solutions.
• Solve multi-step linear equations with rational coefficients and variables on both sides.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
• Solve one and two-step equations (7.EE.4a); • Use properties of algebra to simplify algebraic expressions.
Academic Vocabulary
solve, variable, order of operations, solution, like terms, distributive property
Suggested Instructional Strategies
Resources
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Seventh Grade Honors
 Build on the equations solved in seventh grade and move
toward increased fluency and procedural skill in solving
more complex linear equations.
 Examine solutions in the context of the original equation.
 Consider teaching unique solutions, no solutions, and
infinitely many solutions with 8.EE.8.
Sample Formative Assessment Tasks
Skill-based Task
Solve the following equations and identify the number of
solutions:
• 3(x+7)=10
• 2(x−5)=12(4x+6)
• 2(x+3)=2x+6
Unit #
2
Unit Title: Variables and Patterns


Textbook Correlation
Thinking With Math Models (CMP2)
 Investigations 2
 Algebra Balance Scales - Negatives
 MARS Concept Formative AssessmentLessons (MS):
Solving Linear Equations in One Variable
 MARS Assessment Task (MS):
Buying Chips and Candy MARS task
 CMP2 Resources
 Texas Instrument 8.EE.7a Lessons:
http://education.ti.com/calculators/downloads/US/Activit
ies/Search/Standards
 Coupon vs Discount Activity
 Solving Equations Activity
 The Sign of Solutions
 Boomerangs
Problem Task
Create equations that would result in one solution, no solutions,
or infinitely many solutions. What is it about the structure of the
original equation that reveals the number of solutions?
CORE CONTENT
Cluster Title: Analyze and solve linear equations and pairs of simultaneous linear equations.
Standard 8.EE.7.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding
expressions using the distributive property and collecting like terms.
Concepts and Skills to Master
 Identify and provide examples of equations that have one solution, infinitely many solutions or no solutions.
 Solve multi-step linear equations with rational coefficients and variables on both sides.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Solve one and two-step equations (7.EE.4a).
 Use properties of algebra to simplify algebraic expressions.
Academic Vocabulary
solve, variable, order of operations, solution, like terms, distributive property
Suggested Instructional Strategies
Resources
 Build on the equations solved in seventh grade and move
 Textbook Correlation
toward increased fluency and procedural skill in solving
o Thinking With Math Models (CMP2)
more complex linear equations.
 Investigations 2
 Examine solutions in the context of the original equation.
 Consider teaching unique solutions, no solutions, and
infinitely many solutions with 8.EE.8.

Texas Instrument 8.EE.7b Lessons:
http://education.ti.com/calculators/downloads/US/Activit
ies/Search/Standards

Algebra Balance Scales - Negatives

Youtube Video: Solving Equations with the Distributive
Property
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: Seventh Grade Honors
Sample Formative Assessment Tasks
Skill-based Task
Solve the following equations and identify the number of
solutions:
• 3(x+7)=10
1
• 2(x−5)=2(4x+6)
• 0.2(x+3)=0.2x+6
Unit #
2
Unit Title: Variables and Patterns
Problem Task
Create equations using the distributive property that would result in
one solution, no solutions, or infinitely many solutions. What is it
about the structure of the original equation that reveals the number
of solutions?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.