8.6.2Ma


 * Grade: 8 Unit: 6Week: 2 **
 * Content: Solving Systems Graphically (Technology) **
 * Dates:4/15-4/19 **

How do we use a system of equations to model real world situations that have multi-constraints to simulate relationships?
 * Theme Essential Question **** : **

How systems of equations are represented and interpreted using technology?
 * Essential Questions: **


 * Standards **
 * Analyze and solve pairs of simultaneous linear equations. **
 * ** 8. EE.8a ** Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
 * ** 8. EE.8c ** Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.


 * Objectives **
 * The student will use technology to prepare a graphical representation to interpret the solution to a system of linear equations.
 * The students will investigate the outcome of linear equations that intersect, coincide, or are parallel.

In this project the students will be choosing between two real life situations and then using systems of linear equations to decide what to buy. Please be advised computer access will be advantageous. Week 1: Teacher introduction to the project and rubric. Week 2: Students thoroughly exploring and selecting their project. Option: Cell Phone Plans Encourage students to explore and compare other company plans and vary the options available. Option: Car Comparisons Encourage students to explore and compare other cars. Week 3: Students will conduct research and apply a graphical solution to their project (manually or using technology). Week 4: Students will support their solution by using the substitution method and/or the elimination method to their project. Week 5: Students will analyze their solution, complete their project, and conduct presentations.
 * Assessment **
 * Product **
 * @http://mwstrange.com/Systems%20of%20Linear%20Equations%20Group%20Project.pdf **


 * Key Questions **
 * Using technology, what is the process to represent and interpret a solution to a system of linear equations?
 * What conclusions can be made when the system of linear equations intersect, coincide, or are parallel?


 * Observable Student Behaviors **
 * Students can use technology to graph and interpret a solution to a system of linear equations.

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 **

System of equations, coordinate plane, slope, y intercept, slope-intercept form
 * Vocabulary **

Unit 3.3, p. 75-78 Gizmo Lessons __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla Glencoe Pre-Algebra – p. 414-418, p. 428
 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * Houghton Mifflin OnCore Mathematics Middle School Grade 8
 * ABC Mastering the Common Core in Mathematics 6.1- p. 76-78
 * 8.EE.8a
 * Solving Linear Systems by Graphing
 * Compare a system of equations in standard form or in slope ‑ intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
 * Special Types of Solutions to Linear Systems
 * Compare a system of equations in standard form to its graph. Examine the graph and table of values. Determine the solutions to the system.
 * 8.EE.8 Activity 1 p. 180, Activity 2 p. 181

Glencoe Algebra 1- p. 369-375 @http://illustrativemathematics.org/illustrations/469 (G.8) @http://illustrativemathematics.org/illustrations/472 (G.8) @http://illustrativemathematics.org/illustrations/554 (G.8) @http://illustrativemathematics.org/illustrations/73 (G.8)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.
 * Highly Recommended:
 * Highly Recommended:


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Algebra’scool: Unit C Module 10.1

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

** 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)
 * Terminology for Teachers **
 * ** Multicultural Concepts **


 * Resources **


 * Professional Texts **


 * Literary Texts **

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


 * Art, Music, and Media **


 * Manipulatives **
 * http://nlvm.usu.edu/ National Library of Virtual Manipulatives
 * Graphing calculators


 * Games **


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

Solve systems of two linear equations in two variables by graphing. Interpret solutions of two linear equations. Solving Problems Involving Algebraic Techniques (Question set)
 * SMART Board Lessons, Promethean Lessons **
 * [|Smartboard Resource Website] Smartboard lesson search engine
 * 8. EE.8a Solving Systems of Equations through Graphing
 * 8. EE.8c Solving Problems Involving Algebraic Techniques (Question Set)


 * Websites **
 * @http://illustrativemathematics.org/standards/k8 PARCC Online (released items)
 * http://www.khanacademy.org Online tutorials
 * @http://www.tli.net/ TLI Quiz Builder


 * Other Activities, etc. **

Language Arts ||=  ||=   ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || 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/8/Math8TeachingMatrix.xls"]]
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