6.2.4Ma


 * Grade:6 Unit:2 Week:4 Dates: 10/22-10/26**
 * Content: Positive and Negative Numbers, Points on a Coordinate Plane**

Can students apply and extend previous understandings of multiplication/division and the number system to divide a fraction by a fraction, find common factors/ multiples and extend to the rational number system?
 * Theme Essential Question:**


 * Essential Questions:**
 * Can students use positive and negative numbers to represent real-world quantities?
 * Can students plot rational numbers on a number line?
 * Can students identify the relationship between points on a coordinate plane?


 * Standards**
 * Apply and extend previous understandings of numbers to the system of rational numbers.**
 * **6.NS.5** Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
 * **6.NS.6** Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
 * Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
 * Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.


 * Objectives**
 * Students will use positive and negative numbers to represent real-world quantities.
 * Students will plot rational numbers on a number line, and use a number line to identify opposites.
 * Students will identify the relationship between points on a coordinate plane.

Integers, positive and negative numbers, are a perfect place to use Mathematical Practice #4-Model with mathematics. This week focuses on the introduction to and the graphing of integers and rational numbers. This is not the time to work on any operations with them.
 * Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team**

(Taken from Ohio Department of Education Teaching) The purpose of this cluster is to begin study of the existence of negative numbers, their relationship to positive numbers. Starting with examples of having/owing and above/below zero sets the stage for understanding that there is a mathematical way to describe opposites. Students should already be familiar with the counting numbers (positive whole numbers and zero), as well as with fractions and decimals (also positive). They are now ready to understand that all numbers have an opposite. These special numbers can be shown on vertical or horizontal number lines, which then can be used to solve simple problems. Demonstration of understanding of positives and negatives involves translating among words, numbers and models: given the words “7 degrees below zero,” showing it on a thermometer and writing -7; given -4 on a number line, writing a real-life example and mathematically -4.


 * 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/MathGr6.pdf
 * **Includes mathematical practices and specific examples of the standards.**
 * @http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/6th.pdf


 * Assessment**
 * Product**


 * Key Questions**


 * Observable Student Behaviors**

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**

Negative Number line Opposites Coordinate plane ||
 * Vocabulary**
 * **Math** ||
 * Positive

On Core Mathematics Mastering the Common Core ABC Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8 Gizmos JBHM Glencoe Highly Recommended: 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. Tasks that illustrate content standard 6.NS.5, 6.NS.6a,b:
 * Suggested Activities**
 * Understanding Positive and Negative Numbers Lesson 37 p73-74
 * Rational Numbers and the Number Line Lesson 38 p75-76
 * Ordered Pair Relationship Lesson 39 p77-78
 * Chapter 3 p26-30
 * Chapter 4 p36-41
 * Chapter 5 p54-59
 * Finding the Opposite p19 (@http://www.dltk-kids.com/world/japan/mfortune-teller.htm )
 * Comparing and Ordering Integers
 * Compare and order integers using moveable points on a number line. Also explore the opposites of numbers on the number line.
 * Real Number Line - Activity A
 * Use a number line to compare numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers.
 * Real Number Line - Activity A
 * Identify the coordinates of points in the coordinate plane. Drag the points in the plane and investigate how the coordinates change in response.
 * 6th GP2, Unit 2 SBL-6: Coordinate Geometry
 * 7th GP1, Unit 2 SBL-1: Comparing and Ordering Integers
 * 6th 8-1, 8-6
 * 7th 3-3, p117,
 * It’s Warmer in Miami @http://illustrativemathematics.org/illustrations/277
 * Mile High @http://illustrativemathematics.org/illustrations/278
 * Diverse Learners**
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool 3.1 (omit absolute value for now),
 * Math.com (@http://www.math.com/school/subject2/lessons/S2U4L1GL.html )


 * 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

Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * Terminology for Teachers**


 * Resources**
 * Professional Texts**


 * Literary Texts**


 * Informational Texts**
 * @http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm This site gives detailed tasks and assessments for each standard. You can search by subject, grade, or standard.


 * Art, Music, and Media**


 * Manipulatives**
 * The National Library of Virtual Manipulatives: __@http://nlvm.usu.edu__
 * Calculators
 * Number line with positive and negative integers @http://www.helpingwithmath.com/printables/others/lin0301number03a.htm


 * Games**
 * www.mathplayground.com
 * @http://www.sumdog.com/ Variety of games covering many math topics


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


 * Websites**
 * @http://www.khanacademy.org/math Online math tutorials on a variety of topics
 * @http://www.tli.net/ TLI Quiz Builder
 * @http://webmath.com


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


 * Other Activities, etc.**

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