Constructing and Analyzing Function Tables: CC Math 6 Expressions and Equations Unit 3
This instructional material provides resources for teachers to help students understand how to represent real-world problems using variables, write equations, analyze relationships between variables, and use graphs and tables. The content covers Common Core Standards 6.EE.9, focusing on using variables in a real-world context and analyzing dependent and independent variables. The material also emphasizes mathematical practices such as problem-solving and pattern recognition. Prerequisite skills, grade level progressions, and a pathway to high school algebra are included for a comprehensive learning progression. Source: [Link](https://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf)
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CC Math 6: Expressions and Equations Unit 3
Purpose Provided is a lesson for teachers to use to help students understand how to construct and analyze function tables. Included are the following resources: Expressions and Equations Learning Progression Standards Lesson Agenda Getting Ready for the Lesson (Resources and Tips) Lesson (Presentation and Video) Vocabulary Activities Textbook Connections Additional Resources
Common Core Standards 6.EE.9 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (Understand, 3) (Understand, 3) (Apply, 3) (Apply, 3) (Analyze, 3) (Analyze, 3)
Math Practices MP1 Make sense of problems and persevere in solving them. MP8 Look for and express regularity in repeated reasoning.
Expressions & Equat Prerequisite Skills: CC Math 6 https://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf
Progressions in Grade Level Standards 6th Grade Applying and extending previous understandings of arithmetic to algebraic expressions. Reason about and solve one- variable equations and inequalities. Represent and analyze quantitative relationships between dependent and independent variables. 7th Grade Use properties of operations to generate equivalent expressions. Solve multi-step and real-life mathematical problems posed with positive and negative rational numbers in any form. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 8th Grade **New Course Work with radicals and integer exponents. Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous equations. Grades K 5 Connecting standards Writing numerical expressions Interpreting numerical expressions without evaluating them. Source: https://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf-
Learning Progression: Road to HS Algebra http://commoncoretools.me/wp-content/uploads/2012/12/ccss_progression_algebra_2012_12_04.pdf
Lesson Agenda O Vocabulary O Video: Recognize how an equation relates independent and dependent variables O Lesson: Pancake Mix O Textbook Connections
Core Lesson Recognize how an equation relates independent and dependent variables
Getting Ready O Pre-assessment- used to determine understanding of prerequisite skills O Prerequisite skills include O 6 6 EE.1 EE.1 O Write and evaluate numerical expressions involving whole number exponents. O 6 EE.2A 6 EE.2A O Write expressions that record operations with numbers and letters standing for numbers. O 6 EE.6 6 EE.6 O Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Source: http://curtismapper.pic.ucla.edu/MapApp/app/#/map
Misconceptions and Anticipated Issues Common Issues Common Issues Suggested Strategies/Resources Suggested Strategies/Resources Use a whole-class discussion to review order of plotting points. Use a whole-class discussion to analyze and interpret the relationship shown within several sample equations. Teacher models how to identify independent and dependent variables using think-aloud strategy during whole-class discussion. a. Plotting points (y,x) instead of (x,y). Viewing the relationship shown in an equation backwards. For example, y = 6x, students may think this means that x is 6 times larger than y. Not being able to identify the independent and dependent variables in a written context. a. b. b. c. c.
Required Resources Materials Materials Required Special Materials: O Graph paper for each student Required Handouts: O LearnZillion presentation handouts O LearnZillion additional worksheets O https://learnzillion.com/lesson_plans/681-recognize-how-an- equation-relates-independent-and-dependent-variables
Needed Vocabulary O Equation Frayer Model Example Alternative tools: Word Map, Layered Book, etc.
Learnzillion For this lesson you need to create an account to access the handouts from Learnzillion. This is a free account and you will have access to many more lessons.
Understand and solve unit rate problems by using graphs of equivalent ratios https://learnzillion.com/lesson_plans/681-recognize-how-an- equation-relates-independent-and-dependent-variables
Planning and Time Activities Activities Time Time Notes Notes Preparation 2 hours Includes creating a pre- assessment, making copies, obtaining materials Pre-lessons 2 hours Review of 6th grade EE standards Vocabulary 1 hour Defining equation, dependent and independent variables Pancake Task-Lesson 2 hours Explanation and completion of work Practice and Additional Tasks 3 hours Additional worksheets from LearnZillion, Textbook practice, Illustrative Mathematics Tasks Total Time Total Time 10 hours 10 hours
Textbook Connection: California Math Textbook Course 1 Section 8.1 O Problem Problem- -Solving Investigation: Making a Table, Pages 611 Solving Investigation: Making a Table, Pages 611- -612 O Classwork: Page 582 Classwork: Page 582- -584, problems 1 584, problems 1 7 7 O Homework: Page 584, problems 8 Homework: Page 584, problems 8- -13 O Extra Practice: Course 1 Resources by Chapter Section 8.1 Extra Practice: Course 1 Resources by Chapter Section 8.1 O Lesson 8.1 HW Practice Lesson 8.1 HW Practice O Lesson 8.1 Extra Practice: Completing Function Tables Lesson 8.1 Extra Practice: Completing Function Tables O Student Re Student Re- -teaching Section 8.1 teaching Section 8.1 O Re-teaching: Function Tale O Assessment Book Course 1 Section 8.1 Assessment Book Course 1 Section 8.1 O Self Self- -Check Quick 8.1 Check Quick 8.1 O Textbook Course 1 Section 8.1 612 13
Additional Resources O Illustrative Illustrative Mathematics Mathematics - - www.illustrativemathematics.com www.illustrativemathematics.com O Chocolate Bar Sales O https://www.illustrativemathematics.org/content- standards/tasks/806 O Khan Khan Academy Academy - - www.khanacademy.org www.khanacademy.org O Inside Mathematics Inside Mathematics O Gym Task Gym Task O http:// http://www.insidemathematics.org/assets/common www.insidemathematics.org/assets/common- -core math math- -tasks/gym.pdf tasks/gym.pdf O Mathematics Assessment Project Mathematics Assessment Project O Modeling: Car Skid Marks O http://map.mathshell.org/lessons.php?collection=8&unit =6210#task588 core- -
Textbook Connection: Go Math O Lesson 12.2: Independent and Dependent Variables in Lesson 12.2: Independent and Dependent Variables in Tables and Graphs Tables and Graphs O Classwork Page 344, Problems 1 Classwork Page 344, Problems 1 5 5 O Homework Page 345 Homework Page 345- -346, Problems 6 346, Problems 6- -10 O Lesson 12.3: Writing Equations From Tables Lesson 12.3: Writing Equations From Tables O Classwork Page Classwork Page 350, 350, Problems 1 Problems 1 6 6 O Homework Page Homework Page 351 351- -352, 352, Problems O Lesson Lesson 12.4: Representing Algebraic Relationships in 12.4: Representing Algebraic Relationships in Tables and Graphs Tables and Graphs O Classwork Page Classwork Page 356, 356, Problems 1 Problems 1 4 4 O Homework Page Homework Page 357 357- -358, 358, Problems 10 Problems 7 7- -15 15 Problems 5 5- -14 14
Textbook Connection CPM O 8.1.2 What is Typical Value? O Classwork, Pages 382-383 O Homework, Pages 384-388 O 8.1.3 How else can I describe the data ? O Classwork, Pages 389-392 O Homework, Page 393
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