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 * Grade:6 Unit:4 Week:5** **Content: Problem Solving and Graph Relationships Dates: 2/19-2/22**

How can you use numerical and algebraic expressions, equations, and inequalities to solve real life mathematical problems?
 * Theme Essential Question **** : **


 * Essential Questions: **
 * Can students use the strategy //find a pattern// to solve problems involving relationships between quantities?
 * Can students graph the relationship between two quantities?


 * Standard **
 * 6.EE.9 Represent and analyze quantitative relationships between dependent and independent variables. 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. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d=65t to represent the relationship between distance and time.


 * Objectives **
 * Students will solve problems involving relationships between quantities by using the strategy //find a pattern.//
 * Students will graph the relationship between two quantities.

(Taken from Arizona Department of Education) Students can use many forms to represent relationships between quantities. Multiple representations include describing the relationship using language, a table, an equation, or a graph. Translating between multiple representations helps students understand that each form represents the same relationship and provides a different perspective on the function.
 * Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team **


 * Background Information **


 * Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials. **
 * @http://www.azed.gov/wp-content/uploads/PDF/MathGr6.pdf
 * @http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/6th.pdf


 * Assessment **
 * Product **


 * Key Questions **
 * What is a linear equation?
 * What is an ordered pair?


 * Observable Student Behaviors**
 * Have students model the graphing of the ordered pairs.
 * Have students identify relationships by observing their characteristics.

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. ||
 * **Mathematical Practices **

On Core Mathematics Mastering the Common Core ABC Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8 Gizmos JBHM Glenco Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions. Tasks that illustrate content standard 6.EE.9:
 * Vocabulary **
 * ** Math ** ||  ||   ||
 * Suggested Activities-Find as many real-world examples as possible. **
 * Suggested Activities-Find as many real-world examples as possible. **
 * Problem Solving-Analyze Relationships Lesson 70 pg139-140
 * Graph Relationships Lesson 71 p141-142
 * p78 extend tables and graphs
 * Same as week 3 extended
 * Same as week 3 extended
 * Same as week 3 extended
 * Same as week 3 extended
 * None currently
 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool: None
 * Math.com: None

See appropriate Glencoe, OnCore, JBHM, and ABC materials under suggested activities
 * Homework **
 * []to print assignments on variety of topics


 * Terminology for Teachers **

** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers  || Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ** Multicultural Concepts **


 * Resources **
 * Professional Texts **


 * Literary Texts **


 * Informational Texts **
 * See New York Common Core Aligned Task (other resources) @http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm


 * Art, Music, and Media **


 * Manipulatives **
 * www.nlvm.usu.edu
 * @http://jeopardylabs.com/play/expressions24
 * @http://jeopardylabs.com/play/expressions21
 * Graphing calculators


 * Games **
 * www.mathplayground.com
 * @http://www.sumdog.com/ Variety of games covering many math topics
 * @http://www.nctm.org/resources/middle.aspx


 * Videos **
 * Discovery Learning @http://www.discoveryeducation.com/


 * Websites **
 * @http://www.khanacademy.org/math
 * @http://www.tli.net/ TLI Quiz Builder
 * http://webmath.com//.//


 * Sight Words **


 * SMART Board Lessons, Promethean Lessons **
 * [|Smartboard Resource Website] Smartboard lesson search engine

The learning objectives are to identify, describe, extend, and create linear patterns and functions.
 * CC.6.EE.9 Patterns in Math

Reinforces the meaning of a variable.
 * CC.6.EE.9 Letters in Math

The objective is to find the equation of a line from a table of values.
 * CC.6.EE.9 Finding the Equation of a Line


 * Other Activities, etc. **

Language Arts ||=  ||=   ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || 6 Matrix ||= 6 PAP Matrix ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || Home K-2 ||= Home 3-6 ||= Home 6-8 ||= Unit 1 ||= Unit 2 ||= Unit 3 ||= Unit 4 ||= Unit 5 ||= Unit 6 ||
 * = English
 * = Math ||= [[image:commoncorepcssd6/Actions-insert-table-icon.png link="@http://inst.pcssd.org/math/CCSS/6/Math6TeachingMatrix.xls"]]
 * = [[image:commoncorepcssd6/PCSSDlogo.JPG link="commoncorepcssd/PCSSD"]]