8_1_3M


 * Grade: 8 Unit: 1 Week: 3 Dates: 9/4/12-9/7/12 **
 * Content: Solving Equations (with 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 solve equations with rational coefficient.


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

Mathematical Practice #7 requests our children to investigate and use patterns. We need to encourage and guide this academic approach.

During the third week of solving equations, students should recognize that solving any complicated equation (for example: solving a problem with a combination of parentheses, like terms, and variables on both sides) will simplify to a two-step equation and then to a one-step equation. The last step in the process is usually to divide or multiply.

The process of solving equations has many patterns that if understood by our students would give them a better insight into the solving equations process. Take time to explore and discuss.


 * 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 **
 * The students can create a display which presents the comparison between a visual representation of a solution to an equation with its algebraic solution.
 * The students can construct a bingo game to match equations. See the following website for example: @http://www.mrbartonmaths.com/algebra.htm (See Solving Equations- bingo files.
 * The students can construct a board game such as Trouble. The popper is replaced by a deck of cards with equations. If the solution is negative, they return to start. If the solution is a fraction, they move forward the closest integer value. If they are unable to solve the equation, the next player takes a turn. Every child must solve the equation to assure the player is making the correct move.


 * Key Questions **
 * 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?
 * What patterns are recurring during the process, steps, in solving an equation?


 * Observable Student Behaviors **
 * The students will use proper algebraic techniques to mathematically present the development of solutions to 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
 * 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
 * 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/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 lesson 1-1 Addition, subtraction, multiplication, division properties of equalities Identity property Inverse operations
 * 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.
 * Common Misconceptions **

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


 * Games **


 * Videos **
 * Discovery Learning @http://www.discoveryeducation.com/


 * 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. **

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