8_1_1M


 * Grade: 8 Unit: 1 Week: 1 Dates: 8/20/12- 8/24/12 **
 * Content: Solving Equations (manipulatives/visual) **


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


 * Essential Questions: **
 * How do you represent the process of equal solving linear with manipulatives and visual representation? **

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 convert from a //manipulative and/or visual representation// to an algebraic equation.
 * The student will convert from an algebraic equation to a //manipulative and/or visual representation.//
 * The student will solve equations //using// //manipulatives and/or visual representation// by combining like terms.
 * The student will solve equations //using// //manipulatives and/or visual representation// by applying the distributive property.
 * The student will solve equations //using// //manipulatives and/or visual representation// with variables on both sides.
 * The student will apply the properties of rational numbers to solve equations //using// //manipulatives and/or visual representation//.


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

We will use this section to share our rationale for our approach and suggested comments. We had the privilege to work extensively with the state department during the development progress. This section is intended to provide all 8th grade teachers with an insight into this curriculum.

We intentionally started with the solving equation unit. After a great deal of discussion, we decide to start with this algebraic foundational skill. Even though the analyzing solution is listed last, it needs to be blended, as appropriate, with solving equations with variables on both sides.

The solving equation unit 1-1, is launched with the **struggling learner** in mind. Allow ample time to develop a depth of understanding of the concept of equalities and the logic in solving equations. Refrain from the formal structural writing of the solution until students understand the ‘why’ of the process. Use various manipulatives and visual representations to allow students the opportunity to engage in the 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 **
 * (Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 ) **

In Grade 6, students applied the properties of operations to generate equivalent expressions, and identified when two expressions are equivalent. This cluster extends understanding to the process of solving equations and to their solutions, building on the fact that solutions maintain equality, and that equations may have only one solution, many solutions, or no solution at all. Equations with many solutions may be as simple as: 3//x// = 3//x//, 3x + 5 = x + 2 + //x// + //x// + 3, or 6//x// + 4//x// = //x//(6 + 4), where both sides of the equation are equivalent once each side is simplified. 8th graders should be able to describe these relationships with real numbers and justify their reasoning using words and with the algebraic language of Table 3. In other words, students should be able to state that 3(-5) = (-5)3 because multiplication is commutative and it can be performed in any order (it is commutative), or that 9(8) + 9(2) = 9(8 + 2) because the distributive property allows us to distribute multiplication over addition, or determine products and add them. Grade 8 is the beginning of using the generalized properties of operations, but this is not something on which students should be assessed. Pairing contextual situations with equation solving allows students to connect mathematical analysis with real-life events. Students should experience analyzing and representing contextual situations with equations, identify whether there is one, none, or many solutions, and then solve to prove conjectures about the solutions. Through multiple opportunities to analyze and solve equations, students should be able to estimate the number of solutions and possible values(s) of solutions prior to solving. Rich problems, such as computing the number of tiles needed to put a border around a rectangular space or solving proportional problems as in doubling recipes, help ground the abstract symbolism to life. Experiences should move through the stages of concrete, conceptual and algebraic/abstract. Utilize experiences with the pan balance model as a visual tool for maintaining equality (balance) first with simple numbers, then with pictures symbolizing relationships, and finally with rational numbers. This allows understanding of concepts such as the complexity of the distributive property, collecting like terms, and variables on both sides of the equation to develop.


 * Assessment **
 * Product **
 * Suggested student(s) products have been listed after the development of understanding and formal algebraic process in solving equations, see Lesson 1-3.


 * Key Questions **
 * What does it mean for two expressions to be equation?
 * What is the general strategy in solving for an unknown value?
 * How does combining like terms simplify the algebraic equations?
 * How do you represent the distributive property using manipulatives or visual representation?
 * What is the objective when solving equations with variable on both sides?

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. ||
 * Observable Student Behaviors **
 * The students will use proper algebraic techniques to mathematically present the development of equation solving.
 * ** Mathematical Practices **

Variables, expressions, equations, like terms, distributive property
 * Vocabulary: **

Gizmo Lessons
 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * Hands-on-Equation kit
 * Everyday items to represent the variables and constants (Example: marshmallow for the variable and beans for the constant)
 * **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)
 * Highly Recommended
 * @http://illustrativemathematics.org/illustrations/392
 * 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.


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

Suggested:
 * Homework **
 * Algebra’scool: Unit B Module 3 Independent Practice Activities
 * See supporting manuals with the Hands-on-Equation Kit

Properties w/ vocabulary from Table 3 above Addition, subtraction, multiplication, division properties of equalities Identity property Inverse operations
 * Terminology for Teachers **

Students think that only the letters x and y can be used for variables. The variable is always on the left side of the equation.
 * Common Misconceptions **

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 **


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


 * Art, Music, and Media **


 * Manipulatives **
 * Graphing calculators
 * ** @http://nlvm.usu.edu/ ** National Library of Virtual Manipulatives
 * Algebra: balance/scale


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


 * Videos **
 * 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.


 * 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.//


 * SMART Board, Promethean Lessons **
 * Solving Equations: @http://exchange.smarttech.com/details.html?id=733eedb0-1024-41a0-98d6-112d6d1312fc
 * Number Properties, Operations, and Solving One Step Equations: @http://exchange.smarttech.com/details.html?id=32e33839-e41e-4581-b7ed-ab5f5257535a
 * Two Step Equations: @http://exchange.smarttech.com/details.html?id=778629e4-269b-446d-bcce-c209420f9908


 * 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 ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">English
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Math || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">[[image:commoncorepcssd6/Actions-insert-table-icon.png link="@http://inst.pcssd.org/math/CCSS/8/Math8TeachingMatrix.xls"]]
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">[[image:commoncorepcssd6/PCSSDlogo.JPG link="commoncorepcssd/PCSSD"]]