7.3.6Ma


 * Grade: 7 Unit: 3 Week: 6 Dates: 12/17 – 12/21 **
 * Content: Solving Problems with Expressions, Equations, and Inequalities with percentages **


 * Theme Essential Question: **
 * How can you analyze proportional relationships and use them to solve real-world and mathematical problems? **

How can you solve problems with expressions, equations, and inequalities with **percentages**?
 * Essential Questions: **


 * 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.

Review concepts:
 * Objectives: **
 * The student will solve a variety of problems with expressions, equations, and inequalities involving positive and negative rational numbers with **percentages**.
 * The student will use estimation strategies in assessing reasonableness of solutions to problems.
 * The student will use tools strategically in solving problems.

During this unit, we will be returning to Unit 2. Word problems in Unit 2 excluded percentage problems; they have been re introduced during this lesson.
 * __ 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 __**


 * Assessment: **
 * Product **
 * Students will work in small groups to create a variety of problems that they have worked on in Unit 2 and 3 with percentages. Each group will use large chart paper to display their problem, strategy they would used to solve it. Students will move on a rotation basic around the room (4 min per station) and someone from each group will stay with their problem and explain what the group did and why.
 * Journal entry- describing what they have learned; what they still need to work on; and anything they still have questions about from their portfolio and/or the group problem solving experience.
 * The study of ratio, rates, and proportions
 * The study of percentages


 * Key Questions **
 * How do you use the graphing calculator table feature to help solve problems?
 * How does drawing a picture help you solve 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?
 * What strategies are most helpful when working through word problems?


 * Observable Student Behaviors (Performance) **
 * The student can solve real-world and mathematical problems dealing with ratios, rates, proportions, and percents.

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 Correlation 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 ** :
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 3-6, p. 77-80
 * ABC //Mastering the Common Core in Mathematics//
 * Solving Proportions, Chapter 6.5, p. 66
 * Ratio and Proportion Word Problems, Chapter 6.6, p. 67-68
 * Mixture Problems, Chapter 6.7, p. 69
 * Chapter 6 Review and Test, p. 70-72
 * Glencoe 7th Grade //Mathematics Application and Concepts Course 2//, Chapter 8.2, p. 340-343
 * Air Track
 * 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.
 * Fan Cart Physics
 * 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.
 * Ray Tracing (Lenses)
 * 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.
 * Ray Tracing (Mirrors)
 * 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.
 * // Teaching the Common Core Math Standards with Hands-On Activities, //
 * // 7.EE.2 – Activity p. 106 //
 * // 7.EE.3 – Activity p. 108 //
 * ** Highly Recommended **
 * [] (7.EE.3) **
 * [] (7.EE.3) **
 * Glencoe 7th Grade //Mathematics Application and Concepts Course 2//, Chapter 8.2, p. 340-343


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skill Tutor (teacher discretion)


 * Homework: ** (Teacher Discretion)
 * [] 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 annotated Lists of Children's Literature including the math concepts and grade levels. Click on the following link, __ http://libguides.nl.edu/mathinchildrenslit __, and 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 **
 * Discovery Learning @http://www.discoveryeducation.com/
 * The Teaching Channel
 * 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]


 * SMART Board Lessons, Promethean Lessons **
 * __ Smartboard Resource Website __ Smartboard lesson search engine.


 * Other Activities, etc. **
 * @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.
 * 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 || Week 7 || Week 8 || 7 Matrix ||= Accelerated 7 Matrix ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || Week 7 || Week 8 || 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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