8.6.5Ma


 * Grade: 8 Unit: 6Week: 5 **
 * Content: Problem Solving Connections **
 * Dates: 5/6-5/10 **

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 do you solve equations by combining like terms and multiplying expressions?
 * How can you give examples of equations with a given number of solutions?
 * How can you solve a system of equations by graphing?
 * How can you solve a system of equations algebraically?


 * Standards **
 * Analyze and solve linear equations and pairs of simultaneous linear equations. **
 * ** 8. EE.7a ** Solve linear equations in one variable.
 * Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
 * ** 8. EE.7b ** Solve linear equations in one variable.
 * Solve linear equations with rational number coefficients, including
 * equations whose solutions require expanding expressions using
 * the distributive property and collecting like terms.
 * ** 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.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 a graphical representation and technology to solve and interpret the solution to a system of linear equations.
 * The students will investigate the outcome of linear equations that intersect, coincide, or are parallel.
 * The student will use algebraic methods 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 **
 * Product **
 * @http://mwstrange.com/Systems%20of%20Linear%20Equations%20Group%20Project.pdf **

Additional Option Supply and Demand Activity from NCTM __ @http://inside.mines.edu/~preitz/SupplyDemand-AS-Applications_OLD.pdf __ (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.//


 * Key Questions **
 * What is the process to graphically represent a solution to a system of linear equations?
 * What conclusion can be made when the system of linear equation intersect, coincide, or are parallel?
 * Using technology, what is the process to represent and interpret a solution to a system of linear equations?
 * What is the process to algebraically solve a system of equations by substitution or elimination method?
 * What algebraic solution indicates the outcomes are parallel lines, intersecting lines, or lines that coincide?


 * Observable Student Behaviors **
 * The student can graph and interpret a solution to a system of linear equations.
 * Students can use technology to graph and interpret a solution to a system of linear equations.
 * The student can solve and interpret a solution to a system of linear equations by the substitution or elimination method.

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 **


 * Vocabulary **

Problem Solving Connections, p. 83-86 Gizmo Lessons __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla Glencoe Algebra 1- p.380 @http://illustrativemathematics.org/illustrations/583 (G.7) @http://illustrativemathematics.org/illustrations/392 (G.7) @http://illustrativemathematics.org/illustrations/550 (G.7) @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.
 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * Houghton Mifflin OnCore Mathematics Middle School Grade 8
 * ABC Mastering the Common Core in Mathematics Chapter 6.5-6.6, p. 83-87
 * 8.EE.7b
 * Modeling and Solving Two-Step Equations
 * Solve a two ‑ step equation using a cup ‑ and ‑ counter model. Use step ‑ by ‑ step feedback to diagnose and correct incorrect steps.
 * Solving Equations with Decimals
 * Solve an equation involving decimals using dynamic arrows on a number line.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Solving Two-Step Equations
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">8.EE.8a
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Solving Linear Systems by Graphing
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Compare a system of equations in standard form or in slope <span style="font-family: 'MS UI Gothic','sans-serif'; font-size: 15px;">‑ <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Special Types of Solutions to Linear Systems
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Compare a system of equations in standard form to its graph. Examine the graph and table of values. Determine the solutions to the system.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">8.EE.8b
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Solving Linear Systems by Graphing
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Compare a system of equations in standard form or in slope <span style="font-family: 'MS UI Gothic','sans-serif'; font-size: 15px;">‑ <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 15px;">Systems of Linear Equations - Activity A
 * <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','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.
 * 8.EE.7 p. 177
 * 8.EE.8 Activity 1 p. 180, Activity 2 p. 181
 * Highly Recommended:


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Algebra’scool: Unit C Module 10

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/

Revies of Number Properties, Operations, and Solving One Step Equations. Students will use algebra tiles as a manipulative in learning how to solve for a variable when given an equation with the variable on both sides. Introduction to solving two step equations in pre-algebra. includes guided and independent practice Uses algebra tiles and whole to part diagrams to model, and introduces traditional paper pencil recording. Use the game press your luck to solve simple equations. The objective is to solve multi-step equations.
 * SMART Board Lessons, Promethean Lessons **
 * [|Smartboard Resource Website] Smartboard lesson search engine
 * 8. EE.7 Number Properties, Operations, and Solving One Step Equations
 * 8. EE.7 Solving Multi-step Equations
 * 8. EE.7 Two Step Equations
 * 8. EE.7a Press Your Luck Revised…Solving Equations
 * 8. EE.7b Solving Equations


 * 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"]]
 * = [[image:commoncorepcssd6/PCSSDlogo.JPG link="commoncorepcssd/PCSSD"]]