7_2_5Ma


 * Grade: 7 Unit: 2 Week: 5 Dates: 10/29 – 11/2 **
 * Content: Solving Problems with Expressions, Equations, and Inequalities (w/o percentages) **


 * __ 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?


 * __ Standards __**** : **
 * ** 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.


 * __ Objectives __**** : **
 * The student will use a bar model to solve problems.
 * The student will draw pictures and label them to help write equations to solve problems.
 * The student will write equations and inequalities to solve word problems.
 * The student will use estimation strategies in assessing reasonableness of solutions to problems.

The percentage problems associated with expression, equations, and inequalities have been moved to Unit 3 on Ratios and Proprotions. The problems omitted in this unit will be re-introduced in lesson 3-5.
 * __ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team __**

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 __**

// Problem solving using equations // OR // Struggling Students //
 * __ Assessment __**** : **
 * Product **
 * Students will work with a partner to design a problem that uses a bar model.
 * They will solve for an appropimate solution.
 * They will find the actual solution and compare the two solutions.
 * They will prepare a display of their work.
 * Students will work with a partner to design two problems similar to the ABC //Mastering the Common Core in Mathematics// Chapter 9.10, p. 111.
 * They will solve the problems
 * They will prepare a display that provides clarity to the solution.
 * A visual sketch depicting the word problem
 * Identify the variable
 * Detail the approached used to solve the problem


 * Key Questions **
 * What is a bar model?
 * How do you use a bar model to help solve a problem?
 * How do you use variables in your drawing of a problem to help solve it?
 * How do you know when to use an equation or an inequality?
 * How do you know if you answer makes sense?


 * Observable Student Behaviors **
 * The student can develop solutions, while provided written and/or verbal justifications, to support their approach to word problems (equations and inequality).

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 __**** : **

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

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. 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. 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.
 * __ Suggested Activities __** :
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 3-6, p. 77-80
 * ABC //Mastering the Common Core in Mathematics// Chapter 9.10, p. 111
 * Teaching the Common Core Math Standards with Hands-On Activities
 * 7.EE.3, Activity, Estimation Game, p. 108
 * ** Air Track **
 * ** Fan Cart Physics **
 * ** Ray Tracing (Lenses) **
 * ** Ray Tracing (Mirrors) **
 * JBHM 8th, GP 2, p. 133-176
 * Glencoe 7th Grade //Mathematics Application and Concepts Course 2//, Chapter 4, p. 172-175
 * Glencoe //PreAlgebra//, Chapter 7-3, p. 339-354
 * Glencoe Algebra I, Chapter 6-1 to 6-2, p. 318-331


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skill Tutor (teacher discretion)
 * Algebra’scool Unit B, Mod 3


 * __ Homework __**** : ** (Teacher Discretion)
 * @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.)


 * __ Terminology for Teachers __**** : **

** 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: __**

Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated 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 __**
 * Versa Tiles
 * Pictures
 * Hands-on equations
 * Algebra tiles
 * Chart Paper and Markers

Connect Four game format: 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. negative number, positive number, positive part of the operand, subtraction, whole numbers __@http://www.shodor.org/interactivate/activities/AlgebraFour/__
 * __ 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
 * ** Related Topics: ** addition, arithmetic, assessment, division, integers, multiplication,

** 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 @http://www.discoveryeducation.com/
 * The Teaching Channel


 * __ Smartboard Lessons, Promethean Lessons __**

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. __**
 * ** 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 **

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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