7_2_2Ma


 * Grade: 7 Unit: 2 Weeks: 2 Dates: 10/8 -10/12 **
 * Content: Solving Equations with Multi-Steps **


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


 * __ Essential Questions __**** : **
 * How do you solve equations that contain multiple operations?
 * What are some characteristic found in word problems that denote the usage of two-step equations?


 * __ Standards __**** : **
 * ** 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?


 * __ Objectives __**** : **
 * The student will translate world problems into algebraic equations.
 * The student will model the solution of a two-step equation w/wo the distributive property.
 * The student will solve algebraically a two-step equation w/wo signed rational coefficients.
 * The student will solve multi-step real-world and mathematical problems posed w/wo signed rational coefficients.


 * __ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team: __** In order to establish a solid foundation in solving equations, students need the experience of using a concrete model, such as Hands-On-Equations, a pictorially representation of their work, a verbal explanation of their logic, and the algebraic solution. This is supported by Mathematical Practice #4, model with mathematics:
 * __ Background Information __**

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/

To assist students’ assessment of the reasonableness of answers, especially problem situations involving fractional or decimal numbers, use whole-number approximations for the computation and then compare this value to the actual computation.
 * Taken from __Ohio Dept of Education Mathematics Model Curriculum 6-28-2022__ **

Connections between performing the inverse operation and undoing the operations are appropriate here. It is appropriate to expect students to show the steps in their work. Students should be able to explain their thinking using the correct terminology for the properties and operations.


 * __ Assessment __**** : **
 * Products **
 * The students will be designing two separate “I have… who has...” card game that will include problems from unit-lesson 2-2 to unit-lesson 2-4 with supporting word problems. The first game will deal with equalities and the second will deal with inequalities.
 * Students should be placed into small groups.
 * Each group is to design several cards representing the work addressed during each lesson 2-2 to 2-4.
 * The games are exchanged between groups and played.


 * Key Questions **
 * How would you summarize the process of solving a two-step equation?
 * What are the similarities and differences between solving two-step equations with integers compared to solving two-step equations with signed rational numbers?
 * What patterns or conclusions can be drawn with regards to solving two-step word problems?


 * Observable Student Behaviors **
 * The student can algebraically solve two-step equations with sign rational coefficients.
 * The student can identity when a word problem can be appropriately represented by a two-step equation.

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 __**** : **

Constant Variables Algebraic expressions Coefficient Like terms Combining like terms Factors Common factor Factoring expressions Simplified expressions Distributive properties Communitive properties Associative properties Identity properties Equivalent ||
 * ** Math ** ||
 * Numerical expressions

Gizmo Correlation 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. 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.
 * __ Suggested Activities __** :
 * Model concretely solving two-step equations, example Hands-On-Equations.
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 3-3, p. 65-68
 * ABC //Mastering the Common Core in Mathematics//
 * Word Problems, Chapter 8-4 and 8-5, p.95-96
 * Two-step Equations Chapter 9.1, 99-100
 * Two-step Equations with rational numbers Chapter 9-2, p.100-101
 * Teaching the Common Core Math Standards with Hands-On Activities
 * 7.EE.4, Activity 1: Writing Equations, p.110
 * ** Air Track **
 * ** Atwood Machine **
 * ** Ray Tracing (Lenses) **
 * ** Ray Tracing (Mirrors) **
 * ** Solving Two-Step Equations **
 * ** Highly Recommended **** – ** None available at this time
 * JBHM 8th, GP 2, p. 133-176
 * Glencoe 7th Grade //Mathematics Application and Concepts Course 2//, Chapter 1-5, p. 24-27, Chapter and 4-1through 4-3, 150-165
 * Glencoe 7th Grade //PreAlgebra//, Chapter 3-3, p. 110-130
 * Glencoe Algebra I, Chapter 3-2, p.128-148


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skill Tutor (teacher discretion)
 * Algebra’scool: Unit B, Mod 5


 * __ 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 Document (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 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 __**
 * Versa Tiles
 * Two-sided Counters
 * Hands-on equations
 * Algebra tiles
 * Geoboard

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
 * __@http://www.shodor.org/interactivate/activities/AlgebraFour/__

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
 * __ Videos __**
 * Discovery Learning @http://www.discoveryeducation.com/
 * The Teaching Channel

http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-millionaire.html This Algebraic Expressions Millionaire Game can be played online alone or in two teams. For each question you have to identify the correct mathematical expression that models a given word expression. You could also use it as classroom challenge and have students write their answers on white board and check.
 * __ SMART Board Lesson, Promethean Lessons __**
 * ** ALGEBRAIC EXPRESSIONS MILLIONAIRE **

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.
 * __ 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 __**
 * @http://www.mathgoodies.com/lessons/vol5/division.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.

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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