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 * Grade: 7 Unit: 2 Week: 6 Dates: 11/5 – 11/7 (3 days) **
 * Content: Unit Closure **


 * __ Theme Essential Question __**** : **
 * How can you use numerical and algebraic expressions, equations and inequalities to solve real-life mathematical problems? **


 * __ Essential Questions __**** : **
 * How can you solve problems by using expressions, equations, and inequalities?
 * How do you solve equations and inequalities containing multiple operations?
 * How do use estimation strategies to assess reasonableness of solutions?
 * How can you use a graphing calculator table feature to find solutions?


 * __ Standards __**** : **
 * ** 7.EE.1 ** Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
 * ** 7.EE.3 ** Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
 * ** 7.EE.4a ** Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
 * ** 7.EE.4b ** Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.


 * __ Objectives __**** : **
 * The student will solve equations and inequalities with rational coefficients.
 * The student will write equations and inequalities to solve word problems.
 * The students will graph solutions to inequalities.

Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at@http://www.azed.gov/educator-certification/
 * __ Background Information __**


 * __ Assessment __**** : **
 * Product **
 * Students will work in groups to write problems that they can use a graphing calculator in solve. They will use the table features on the calculator to narrow down the estimate. They will be able to also look at the behavior of the function near the solution. Each group will use large chart paper and share their problem with the class.
 * Students will use their origami fortune teller to review translation of algebraic statements and simplification of algebraic expressions.
 * Students will use their “I have…who has..” cards to review solving two-step equations and inequalities.
 * Quiz (TLI Quiz Builder)


 * Key Questions **
 * How do you use a graphing calculator table feature to solve problems?
 * How do use variables in your drawing of a picture to solve word problems?
 * How do you know when to use an expression, an equation or an inequality to solve problems?
 * How do you know if you estimate makes sense?


 * Observable Student Behaviors (Performance) **
 * The student can solve and graph two-step equations and inequalities.
 * The student can apply solving techniques to word problems.

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 __**** : **

Inequality signs Inverse operations Solution set Validate ||
 * ** Math ** ||
 * Inequalities

Gizmo Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic. Measure the height and velocity of two objects connected by a mass less rope over a pulley. Observe the forces acting on each mass throughout the simulation. Calculate the acceleration of the objects, and relate these calculations to Newton's Laws of Motion. The mass of each object can be manipulated, as well as the mass and radius of the pulley. Observe light rays that pass through a convex or concave lens. Manipulate the position of an object and the focal length of the lens and measure the distance and size of the resulting image. Observe light rays that reflect from a convex or concave mirror. Manipulate the position of an object and the focal length of the mirror and measure the distance and size of the resulting image. Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. Solve a linear inequality. Graph the solution on a dynamic number line. Solve an inequality involving multiplication and division. Graph the solution on a number line. Gain an understanding of Newton's Laws by experimenting with a cart (on which up to three fans are placed) on a linear track. The cart has a mass, as does each fan. The fans exert a constant force when switched on, and the direction of the fans can be altered as the position, velocity, and acceleration of the cart are measured.
 * __ Suggested Activities __** :
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 3
 * ABC //Mastering the Common Core in Mathematics// Chapter 8 and Chapter 9
 * // See Suggested Activities recommended with this Unit 2 //
 * // Teaching the Common Core Math Standards with Hands-On Activities, //
 * **Air Track**
 * **Atwood Machine**
 * **Ray Tracing** (Lenses)
 * **Ray Tracing** (Mirrors)
 * **Solving Two-Step Equations**
 * **Solving Linear Inequalities using Addition and Subtraction**
 * **Solving Linear Inequalities using Multiplication and Division**
 * **Fan Cart Physics**

High Recommended: Illustrative Mathematics Project
 * JBHM 8th
 * Glencoe 7th Grade //Mathematics Application and Concepts Course 2//
 * Glencoe //PreAlgebra//
 * Glencoe Algebra I


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skill Tutor (teacher discretion)
 * Algebra’scool

@http://www.kutasoftware.com/free.html To print assignment on a variety of topics. See appropriate Glencoe On Core, JBHM and ABC Materials under Suggested Activities Exit Slip (Question or problem to answer before leaving class that will help guide instruction for the following day.)
 * __ Homework __**** : ** (Teacher Discretion)


 * __ 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: __**

Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels. Click on the following link, __http://libguides.nl.edu/mathinchildrenslit__, then look under __Math and Literature Bibliographies__. Many books include websites with __lesson ideas__. __http://sci.tamucc.edu/~eyoung/middle_school_literature.html__ __http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html__ __http://sci.tamucc.edu/~eyoung/literature.html__
 * __ Literary Texts __**
 * ** Mathematics in Children's Literature: **
 * ** Middle & High School: Literature in Mathematics **
 * ** Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine) **
 * ** Miscellaneous Math and Children's Literature **


 * __ Informational Texts __**


 * __ Art, Music, and Media __**


 * __ Manipulatives __**
 * Graphing Calculator
 * Versa Tiles
 * Two-sided Counters
 * Hands-on equations
 * Algebra tiles

Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.
 * __ Games __**
 * @http://www.mathchimp.com/7thGrade.php
 * @http://www.sumdog.com/ A variety of games covering many math topics
 * @http://www.mathplayground.com/SMP_index.html
 * Connect Four game format:
 * ** Related Topics: ** addition, arithmetic, assessment, division, integers, multiplication, negative number, positive number, positive part of the operand, subtraction, whole numbers

** Videos ** The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams. https://www.teachingchannel.org/videos?categories=topics common-core
 * Discovery Learning []
 * The Teaching Channel


 * __ SMART Board Lessons, Promethean Lessons __**

In this lesson, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls. Understanding the relationship between change and accumulation is a precursor to understanding calculus In this lesson, Constant Cost per Minute, the cost per minute for phone use remains constant over time Following a profile of fashion designer and Project Runway winner Chloe Dao, students are prompted to alter garment designs, using their sense of style combined with their math skills to hit target price points. Algebra concepts explored include: linear relationships; rates (percents), ratios, and proportions; using multiple representations; algebraic and numeric expressions, equations, and inequalities After learning how the hip-hop duo DobleFlo uses math in music production, students are challenged to match different music samples by calculating their tempos in terms of beats per minute. Algebra concepts explored include: rates, ratios, and proportions; linear relationships; algebraic and numeric expressions and equations Students explore the relationships among lines, slopes, and //y//-intercepts in the context of printing their algebra textbooks. Students use a spreadsheet to facilitate their exploration. This activity is based on an idea from Navigating Through Algebra in Grades 6-8 (NCTM, 2001) In this year-long project, students design, "build," and "sell" a house; after which they simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, and even solve simple equations. This lesson plan was adapted from an article by David B. Smith, which appeared in the September 2000 edition of Mathematics Teaching in the Middle School. Students will use vertical movement of an elevator to evaluate signed number expressions. The idea behind the method of adding and subtracting signed integers offerred in this lesson and the next is that the number of rules that students have to //memorize// and the amount of //understanding// are minimal, while the underlying concepts are not trivialized In this lesson, students will adapt expressions that add or subtract two signed integers. This lesson builds on the previous lesson in the unit, where students add/subtract just a positive integer from a signed integer. Then, students will play a game that practices adding and subtracting with signed integers. The game will enforce the skill of arithmetic with integers, but will also get students thinking about maximizing their sum, and ordering signed numbers The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School. The following lessons focus on student organization, preparation, and presentation of some simple foods as a way of applying various mathematical concepts, with problem-solving techniques being central to almost all the activities. This unit was adapted from the "Ideas" column in the February 1994 issue of [|//The Arithmetic Teacher//], Vol. 41, No. 6, pp. 309. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L263 This lesson explores magic squares from both a historical and mathematical perspective. The mathematical analysis leads into symbolic algebraic representation of the patterns. This lesson is based upon an article from the April 2001 edition of Mathematics Teaching in the Middle School. @http://www.teachersdomain.org/resource/scl10.plr.module1/ Clicking on **"View"** at the left under //"Teacher Activity"// takes you to **Teaching Module 1: Preparing To Teach Proportional Reasoning**. This interactive teaching module addresses the necessary knowledge and skills students should master in order to understand the mathematics of proportional reasoning and scaling @http://illuminations.nctm.org/LessonDetail.aspx?ID=L285 In this lesson, students experience beginning-algebra concepts through discussion, exploration, and videotaping. The concept of multiplication of integers is presented in a format which encourages understanding, not simply rote memorization of facts. This lesson plan is adapted from the article, "A Videotaping Project to Explore the Multiplication of Integers", by Marcia B. Cooke, which appeared in Arithmetic Teacher, Vol. 41, No. 3 (November 1993) pp. 170-171 @http://illuminations.nctm.org/LessonDetail.aspx?ID=L699 Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages @http://illuminations.nctm.org/LessonDetail.aspx?ID=L279 In this year-long project, students design, "build," and "sell" a house; after which they simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, and even solve simple equations. This lesson plan was adapted from an article by David B. Smith, which appeared in the September 2000 edition of Mathematics Teaching in the Middle School. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L252 In this lesson, students develop number sense through a series of three hands-on activities. Students explore the following concepts: the magnitude of a million, fractions between 0 and 1, and the effect of decimal operations @http://illuminations.nctm.org/ActivityDetail.aspx?ID=152 This applet allows you to learn about positive and negative numbers, by exploring the voltage of batteries.
 * __ Other Activities, etc. __**
 * ** Changing Cost per Minute **
 * __ @http://illuminations.nctm.org/LessonDetail.aspx?ID=L441 __**
 * ** Constant Cost per Minute **
 * __ @http://illuminations.nctm.org/LessonDetail.aspx?ID=L440 __**
 * ** Math in Fashion **
 * __ @http://www.teachersdomain.org/resource/GTM11.math.algebra.var.splmathfash/ __**
 * ** Math in Music **
 * __ @http://www.teachersdomain.org/resource/GTM11.math.algebra.var.splmathmus/ __**
 * ** Printing Books **
 * __ @http://illuminations.nctm.org/LessonDetail.aspx?ID=L271 __**
 * ** Real Estate Tycoon **
 * __ @http://illuminations.nctm.org/LessonDetail.aspx?ID=L279 __**
 * ** Elevator Arithmetic **
 * __ @http://illuminations.nctm.org/LessonDetail.aspx?ID=L733 __**
 * ** Flipping for Integers **
 * __ @http://illuminations.nctm.org/LessonDetail.aspx?ID=L734 __**
 * ** Fun with Baseball Stats **
 * __ @http://illuminations.nctm.org/LessonDetail.aspx?ID=L257 __**
 * ** Ideas with Food Unit **
 * __ @http://illuminations.nctm.org/LessonDetail.aspx?ID=U78 __**
 * ** Magic Squares **
 * ** Module 1: Preparing To Teach Proportional Reasoning **
 * ** Multiplying Integers Using Videotape **
 * ** Power Up **
 * ** Real Estate Tycoon **
 * ** Too Big or Too Small? **
 * ** Volt Meter **
 * @http://www.mathgoodies.com/lessons/vol5/division.html
 * __http://www.math.com/school/subject1/lessons/S1U1L12GL.html__
 * // Interactivate // is a set of free, online courseware for exploration in science and mathematics. It is
 * comprised of activities, lessons, and discussions. The site is structured around collections of
 * activities, lessons, and discussions.
 * __ http://www.shodor.org/interactivate/guide/ __
 * __ Activities and tools: __ __http://www.shodor.org/interactivate/activities/__
 * It’s a Party! Solving Multi-step Equations@http://alex.state.al.us/lesson_view.php?id=23865

Language Arts ||=  ||=   ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || 7 Matrix ||= Accelerated 7 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 ||
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