6.4.3Ma


 * Grade:6 Unit:4 Week:3** **Content: Independent and Dependent Variables Dates: 2/4-2/8**

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


 * Essential Questions: **
 * Can students write an equation to represent the relationship between an independent and a dependent variable?


 * Standards **
 * 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, write the equation d=65t to represent the relationship between distance and time.


 * Objectives **
 * Students will write an equation to represent the relationship between an independent and dependent variable.


 * Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team **

(Taken from Ohio Department of Education Teaching) The goal is to help students connect the pieces together. This can be done by having students use multiple representations for the mathematical relationship. Students need to be able to translate freely among the story, words (mathematical phrases), models, tables, graphs and equations. They also need to be able to start with any of the representations and develop the others. Provide multiple situations for the student to analyze and determine what unknown is dependent on the other components. For example, how far I travel is dependent on the time and rate that I am traveling. Throughout the expressions and equations domain in Grade 6, students need to have an understanding of how the expressions or equations relate to situations presented, as well as the process of solving them.

Common Misconceptions: Students may misunderstand what the graph represents in context. For example, that moving up or down on a graph does not necessarily mean that a person is moving up or down.


 * 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 **


 * Observable Student Behaviors **

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 **

Dependent Variable Function Function table Function rule ||  ||   ||
 * Vocabulary **
 * ** Math ** ||  ||   ||
 * Independent Variable

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:
 * Suggested Activities **
 * Independent and Dependent Variables Lesson 68 p135-136
 * 10.2 p128
 * Examining Relationships p51-Extend by having the students write their own situation
 * Comparing Heart Ratesp52
 * Distance-Time and Velocity-Time Graphs
 * Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. (Student Exploration Sheet & Teacher Guide Available.)
 * 6th GP4, Unit 2 SBIL – 1 Linear Functions
 * 6th GP4, Unit 2 Game Dissection Lesson
 * 7th GP2, Unit 2 SBIL – 2 Function Tables
 * 7th GP2, Unit 2 SBIL – 3 Function Tables and the Real World
 * 6th 9-6a, 9-6, 9-7-Be sure to emphasize independent and dependent for input ant output.
 * 7th 4-6a, 4-6, 4-7
 * None currently
 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool: None
 * Math.com: None


 * Homework **
 * @http://www.kutasoftware.com/free.html to print assignments on variety of topics
 * See appropriate Glencoe, OnCore, JBHM, and ABC materials under suggested activities


 * 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//.//
 * Pedal Power @http://illuminations.nctm.org/LessonDetail.aspx?id=L586


 * Sight Words **

The learning objectives are to identify, describe, extend, and create linear patterns and functions.
 * SMART Board Lessons, Promethean Lessons **
 * [|Smartboard Resource Website] Smartboard lesson search engine
 * 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"]]