8.6.4Ma


 *  Grade: 8 Unit: 6Week: 4 **
 *  Content: Solving Systems Algebraically (Elimination) **
 *  Dates: 4/29-5/3 **

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


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


 *  Standards **
 *  Analyze and solve pairs of simultaneous linear equations. **
 * ** 8. EE.8b ** Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
 * ** 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 the elimination method to solve and interpret the solution to a system of linear equations.

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. 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 **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Product **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> @http://mwstrange.com/Systems%20of%20Linear%20Equations%20Group%20Project.pdf **

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">Additional Option Supply and Demand Activity from NCTM __<span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> @http://inside.mines.edu/~preitz/SupplyDemand-AS-Applications_OLD.pdf __<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">(Student Worksheet) @http://illuminations.nctm.org/lessons/9-12/Supply/SupplyDemand-AS-ApplicationsKEY_OLD.pdf (Solution) This activity focuses on having students create and solve a system of linear equations in a real-world setting. By solving the system, students will find the equilibrium point for supply and demand. Students should be familiar with finding linear equations from two points or slope and //y//-intercept. This lesson was adapted from the October 1991 edition of //Mathematics Teacher.//


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Key Questions **
 * <span style="font-family: arial,helvetica,sans-serif;">What is the process to algebraically solve a system of equations by the elimination method?
 * <span style="font-family: arial,helvetica,sans-serif;">What algebraic solution indicates the outcomes are parallel lines, intersecting lines, or lines that coincide?

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">Students can solve and interpret a solution of a system of linear equations using the elimination method.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> 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. ||
 * **<span style="font-family: 'Gotham-Medium','sans-serif'; font-size: 15px;">Mathematical Practices **


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Vocabulary **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Slope-intercept form, solution, outcome **

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">Unit 3.4, p. 79-82 <span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">Gizmo Lessons <span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">@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.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Suggested Activities **<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;"> [see Legend to highlight MCO and HYS]
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Houghton Mifflin OnCore Mathematics Middle School Grade 8
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> ABC Mastering the Common Core in Mathematics Chapter 6.3, p. 79-80
 * <span style="font-family: Arial,sans-serif; font-size: 15px;">8.EE.8b
 * <span style="font-family: Arial,sans-serif; font-size: 15px;">Systems of Linear Equations - Activity A
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"><span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Solve a system of linear equations by graphing and finding the intersection of the lines of the equations. Create a system of equations, examine its graph, matrix, and table of values, and determine the solution of the system.
 * <span style="font-family: Arial,sans-serif; font-size: 15px;">8.EE.8c
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"><span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Modeling Linear Systems - Activity A
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Experiment with a system of two lines representing a cat <span style="font-family: 'MS UI Gothic','sans-serif'; font-size: 15px;">‑ <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">and <span style="font-family: 'MS UI Gothic','sans-serif'; font-size: 15px;">‑ <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real <span style="font-family: 'MS UI Gothic','sans-serif'; font-size: 15px;">‑ <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">world meaning to slope, y <span style="font-family: 'MS UI Gothic','sans-serif'; font-size: 15px;">‑ <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">intercept, and the intersection of lines.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">__ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla
 * 8.EE.8 Activity 1 p. 180, Activity 2 p. 181
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Glencoe Pre-Algebra- p. 414-418, p. 428
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Glencoe Algebra 1- p. 382-386
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Highly Recommended:


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Diverse Learners **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Odyssey (teacher discretion)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Skills Tutor (teacher discretion)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Algebra’scool: Unit C Module 10.2

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">Suggested:
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Homework **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">** @http://www.kutasoftware.com/free.html ** to print assignments on variety of topics
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> 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)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Terminology for Teachers **
 * ** Multicultural Concepts **


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Resources **


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Professional Texts **

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 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Literary Texts **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">

<span style="font-family: arial,helvetica,sans-serif; font-size: 15px;">@http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Informational Texts **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> See New York Common Core Aligned Task (other resources)

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 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Art, Music, and Media **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Manipulatives **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> http://nlvm.usu.edu/ National Library of Virtual Manipulatives
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Graphing calculators

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 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Games **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;">


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Videos **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Discovery Learning @http://www.discoveryeducation.com/

A real life problem is used for a cue set and a backdrop for teaching how to solve a system of equations graphically. These questions test the ability to understand and solve linear equations and linear inequalities. Solving Problems Involving Algebraic Techniques (Question set)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> SMART Board Lessons, Promethean Lessons  **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> [|Smartboard Resource Website] Smartboard lesson search engine
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> 8. EE.8bSystem of Equations
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> 8. EE.8bSystem of Linear Equations and Linear Inequalities (Question Set)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> 8. EE.8cSolving Problems Involving Algebraic Techniques (Question Set)


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Websites **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> [] PARCC Online (released items)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> [|http://www.khanacademy.org] Online tutorials
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> @http://www.tli.net/ TLI Quiz Builder


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14px;"> Other Activities, etc. **

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