8_1_4M


 * Grade: 8 Unit: 1 Week: 4 Dates: 9/10/12-9/14/12 **


 * Content: Analyzing Solutions **


 * Theme Essential Question: How do we use equations to model real world situations? **


 * Essential Questions: **
 * How can you give examples of equations with a given number of solutions? **

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).
 * Standards **
 * Analyze and solve linear equations. **
 * 8.EE.7 ** .**A** Solve linear equations in one variable.

The student will use their skill in solve linear equation in one variable to investigate and analyze the three possible outcome:
 * Objectives **
 * 1) One solution
 * 2) No solutions
 * 3) Infinite solutions

We had previously suggested that this lesson be introduced and/or consolidated with solving equations with variables on both sides.
 * Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team **

This lesson has strong implications for Mathematical Practice #3. Students can make supportive arguments based on prior knowledge, (make conjectures, provide counterexamples, build a logical argument), for the three possible solutions to a linear equation (one solution, no solution, infinite solution). Time has been provided to allow students to have this level of interaction.


 * Background Information **

@http://www.azed.gov/wp-content/uploads/PDF/MathGr8.pdf
 * Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials. **


 * Assessment **
 * It is recommended that students be assessed, at the end of this unit, on their ability to solving equations. **
 * Product **
 * Student groups can create an “//I have..Who has…”// game to be exchanged and shared with other groups. The following website has examples of “I have…who has…” questions: @http://www.nsa.gov/academia/_files/collected_learning/elementary/patterns/Equations_and_Expressions.pdf (page 39)


 * Key Questions **
 * When do you know an equation has infinite number of solutions?
 * When do you know an equation has no solution?


 * Observable Student Behaviors **
 * Students are able to deal with all possible solutions when solving 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 **

variables, expressions, equations, like terms, distributive property, conjecture
 * Vocabulary **

Highly Recommended
 * Suggested Activities **
 * Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 3-2
 * ABC Mastering the Common Core in Mathematics Chapter 4 Lesson 6, P. 41-42
 * Gizmo Lessons
 * Solving Equations with Decimals
 * Solve an equation involving decimals using dynamic arrows on a number line.
 * Solving Two-Step Equations
 * Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
 * __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla (page 176-177)
 * @http://illustrativemathematics.org/illustrations/583
 * 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.
 * JBHM, Unit 3, p. 133-328 and Unit 4
 * Glencoe, Algebra I, Chapter 3 Lesson 5


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Algebra’scool: Unit B Module 3

Suggested:
 * 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

What constitutes a viable argument?
 * Terminology for Teachers **

Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ||  ** Multicultural Concepts **
 * 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   ||   ||


 * 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
 * Algebra: Function Machine, Function Transformations
 * Graphing calculators


 * Games **


 * Videos **
 * Online tutorials on solving equations: [|http://www.khanacademy.org/math/algebra/#solving-linear-equations]
 * Discovery Education: Numbers: Solving Equations
 * This video introduces students to the basics of solving simple equations while practicing how to change word problems into number sentences or equations. The concept of solving equations is demonstrated using a balance scale. Always remember that the two sides of the equation must remain equal for the scale to stay balanced.
 * Discovery Education: Math Masery: Equations
 * This video includes the following chapters:* Unknowns, Reciprocals, and Signed Numbers * Absolute Value and Solving Equations * Multiplying Equations and Working with Unknowns * Working with Unknowns * Solving Word Problems with Equations * Solving Equations in Two Steps * Solving Word Problems with Equations * Working with Unknowns * Solving Two-Step Equations and Word Problems * Working with Unknowns in the Denominator * Working with Exponents * Working with Roots and Exponents (Teacher Guide Available)
 * Discovery Education: Solving Equations: Part 01
 * This video lays out the basic rules and tactics of solving for unknown variables in simple algebraic equations. Explaining important concepts like identities, inverses, and balancing the equation, this video establishes a firm ground for tackling the multiple-step problems introduced in Part Two.
 * Discovery Education: Solving Equations: Part 02
 * This video helps us solve multiple-step algebraic equations by applying the numeric operations learned in Part One and provides helpful strategies and handy shortcuts for approaching problems with fractions, negative signs, and variables with coefficients. Lastly, the video explains strategies for working with literal equations, problems containing more than one unknown variable.


 * SMART Board Lessons, Promethean Lessons **
 * SMART Board Resource Website SMART Board lesson search engine


 * Websites **
 * http://www.khanacademy.org/math/algebra/#solving-linear-equations Online tutorials on solving equations
 * @http://www.tli.net/ TLI Quiz Builder
 * @http://webmath.com/solver.html //This page will show you how to solve an equation for some unknown variable. Note: Please do not type and "=" signs. It is already put in for you. You just need to type in the expressions on the left and right side of the "=" sign.//


 * Other Activities, etc. **

Language Arts ||  ||   ||  Week 1 ||  Week 2 ||  Week 3 ||  Week 4 ||  Week 5 ||  Week 6 || Matrix ||  ||  <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 1 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 2 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 3 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 4 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 5 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 6 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Home K-2 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Home 3-6 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Home 6-8 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 1 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 2 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 3 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 4 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 5 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 6 ||
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