8_1_2M


 * Grade: 8 Unit: 1 Week: 2 Dates: 8/27/12 – 8/31/12 **
 * Content: Solving Equations (without rational numbers) **


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


 * Essential Questions: **
 * ** How do you apply the definition of equal to solving 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.
 * Standards **
 * Analyze and solve linear equations and pairs of simultaneous linear equations. **
 * 8.EE.7.B ** Solve linear equations in one variable.


 * Objectives **
 * The student will solve equations by combining like terms.
 * The student will solve equations by using the distributive property.
 * The student will solve equations with variables on both sides.
 * The student will use algebraic format to present their process in solving linear equations.


 * Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team **

We are moving into a new era of math education, not only in the way that we as educators approach the teaching/learning process, but also in the way our students interact with mathematics. We are being asked to help students learn the standards using the eight Mathematical Practices as appropriate. Mathematical Practice #3 wants students to construct viable arguments and critique the mathematical thinking of others. This practice will require a classroom environment where every child’s opinion/comment is accepted. Mathematical Practice #3 and the learning of how to solve equations should be merged. Remember the ‘I’ in this practice pertains to our students. Students need to learn how to critique the mathematical thinking of others. Focus on student’s ability to recognize flaws in the development of a solution, listen to others approach, asking questions for clarification, and respond and compare two logical solutions. Even though the lesson naturally applies several mathematical practices, this is a new approach both for us and our students. Let’s take it one step at a time. Let’s move together, so we as 8th grade teachers can talk and reflect on our student’s learning.


 * 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/MathGr8.pdf **


 * Assessment **
 * Product **
 * Suggested student(s) products have been listed after the development of understanding and formal algebraic process in solving equations, see Lesson


 * Key Questions **
 * How dose the algebraic solution of a linear equation relate to the manipulative and/or visual representation?
 * What properties or rules do we use to justify the steps in solving an equation?
 * What does the solution of an equation tell us about the value(s) of the variables in the equation?


 * Observable Student Behaviors **
 * The students will use proper algebraic techniques to mathematically present the development of equation solving.
 * The students will connect the model representation (use of maniupuatives and/or visual representation) to the algebraic solution.

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, constant, term, expression, equation, like terms, distributive property
 * Vocabulary: **

Highly Recommended
 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 3-1 (TG p.69, Student p.69-72)and Unit 3-2 (TG p.73, Student p.73-76)
 * ABC Mastering the Common Core in Mathematics Chapter 4, Pages 37-46
 * Gizmo Lessons
 * 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.
 * 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/550
 * 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, Pre-Algebra, Unit 3, p.326-366
 * Glencoe, Algebra I, Chapter 3
 * Index cards with equations or solutions for matching and sorting


 * 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

Properties w/ vocabulary from Table 3 in Lesson 1-1
 * Terminology for Teachers **

Students think that you always need a variable = a constant as a solution. The variable is always on the left side of the equation. ** 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)
 * Common Misconceptions **
 * || ** Multicultural Concepts **


 * Resources **


 * Professional Texts **


 * Literary Texts **


 * Resources **

@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 **
 * Graphing calculators
 * ** @http://nlvm.usu.edu/ ** National Library of Virtual Manipulatives
 * Algebra: Function Machine, Function Transformations


 * Games **
 * @http://www.sumdog.com/ Variety of games covering many math topics

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.
 * Videos **


 * 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.//


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


 * 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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