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.