6.2.1Ma

** Grade: 6 Unit: 2 Week: 1 Dates: 10/1-10/5 ** ** Content: The Number System: Decimals-adding, subtracting, multiplying and dividing ** ** Theme Essential Question: ** 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 apply to the rational number system?

** Essential Questions: **
 * Can students add and subtract multi-digit decimals?
 * Can students multiply multi-digit decimals?
 * Can students divide decimals by whole numbers?
 * Can students divide whole numbers and decimals by decimals?

** Standards ** ** Compute fluently with multi-digit numbers and find common factors and multiples. ** 
 * ** 6.NS.3: ** Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

**Objectives**  ** Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team ** In Mathematical Practice #2, we look at two skills reasoning abstractly and quantitatively.
 * Students will fluently add and subtract multi-digit decimals.
 * Students will fluently multiply multi-digit decimals.
 * Students will fluently divide decimals by whole numbers.
 * Students will fluently divide whole numbers and decimals by decimals.

(Taken from Ohio Department of Education Teaching) As students study whole numbers in the elementary grades, a foundation is laid in the conceptual understanding of each operation. Discovering and applying multiple strategies for computing creates connections which evolve into the proficient use of standard algorithms. Fluency with an algorithm denotes an ability that is efficient, accurate, appropriate and flexible. Division was introduced in Grade 3 conceptually, as the inverse of multiplication. In Grade 4, division continues using place-value strategies, the properties of operations, the relationship with multiplication, area models, and rectangular arrays to solve problems with one digit divisors. In Grade 6, fluency with the algorithms for division and all operations with decimals is developed. Fluency is something that develops over time; practice should be given over the course of the year as students solve problems related to other mathematical studies. Opportunities to determine when to use paper pencil algorithms, mental math or a computing tool is also a necessary skill and should be provided in problem solving situations. ** Background Information ** ** Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials. ** <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;">** Assessment ** <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">**Product** <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">**Key Questions** <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">**Observable Student Behavior** 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. || <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;">** Vocabulary ** Estimate Place value Expressions Sum Differences || <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;">** Suggested Activities ** <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">On Core Mathematics <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">Mastering the Common Core ABC <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">Gizmos <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">JBHM <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">Glencoe <span style="color: windowtext; display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="color: windowtext; display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">Tasks that illustrate content standard 6.NS.3: <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;">** Diverse Learners ** <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;">** Homework ** <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;">** 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 ||   || <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 14px; text-align: left;">Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ** http://www.azed.gov/wp-content/uploads/PDF/MathGr6.pdf (page 11) Includes mathematical practices and specific examples of the standards. **
 * ** @http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/6th.pdf (page 19) **
 * Create a foldable Glencoe 6th p99
 * Create a number map-Glencoe 6th pg 120
 * Have students bring examples of decimals from their lives and post around the room.
 * Create, from the examples brought, two examples of decimal addition, subtraction, multiplication and division application problems.
 * Can students explain in their own words or draw a diagram that explains the steps for adding decimals?
 * Can students explain in their own words or draw a diagram that explains the steps for subtracting decimals?
 * Can students explain in their own words or draw a diagram that explains the steps for multiplying decimals?
 * Can students explain in their own words or draw a diagram that explains the steps for dividing decimals?
 * Students use the similarities between whole number and decimal addition, subtraction, multiplication and division.
 * ** Mathematical Practices **
 * ** Math ** ||
 * Order of operations
 * Add and Subtract Decimals Lesson 27 p53-54
 * Multiply Decimals Lesson 28 p55-56
 * Divide Decimals by Whole Numbers Lesson 29 p57-58
 * Divide with Decimals Lesson 30 p59-60
 * Chapter 2 pgs 15-25
 * Decimal Operation Tournament p15
 * Sums and Differences with Decimals
 * Multiplying Decimals (Area Model)
 * Find the sum or difference of two decimal numbers using area models. Find the decimals and their sum or difference on a number line.
 * Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product).
 * GP1-Unit 1, SBIL 3 Operations on Decimals
 * Workbook lesson 27 pg53-54-Ensure students are using order of operations accurately
 * Book p121-128: Smart essentials, study guide
 * Buying Gas @http://illustrativemathematics.org/illustrations/274
 * Gifts from Grandma, Variation 3 @http://illustrativemathematics.org/illustrations/374
 * Jayden’s Snacks @http://illustrativemathematics.org/illustrations/273
 * Reasoning About Multiplication and Division and Place Value, Part 1 @http://illustrativemathematics.org/illustrations/272
 * Reasoning About Multiplication and Division and Place Value, Part 2 @http://illustrativemathematics.org/illustrations/275
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool 5.3, 5.4, 5.5
 * Math.com ( @http://www.math.com/school/subject1/lessons/S1U1L4GL.html, @http://www.math.com/school/subject1/lessons/S1U1L5GL.html , @http://www.math.com/school/subject1/lessons/S1U1L6GL.html )
 * ** @http://www.kutasoftware.com/free.html ** to print assignments on variety of topics
 * See appropriate Glencoe, OnCore, JBHM, and ABC materials under suggested activities
 * || ** Multicultural Concepts **

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Resources **
 * Professional Texts **


 * Literary Texts **


 * Informational Texts **
 * See New York Common Core Aligned Task (other resources)
 * @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


 * 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
 * @http://www.tli.net/ TLI Quiz Builder
 * @http://webmath.com //.//


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

@http://illuminations.nctm.org/LessonDetail.aspx?ID=L257 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.//
 * Other Activities, etc. **
 * ** Fun with Baseball Stats **

@http://www.nctm.org/standards/content.aspx?id=25090 Students can learn to visualize the effects of multiplying a fixed positive number by positive numbers greater than 1 and less than 1 with this tool. Using interactive figures, students can investigate how changing the height of a rectangle with a fixed width changes its area. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations. @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.
 * ** Learning about Multiplication Using Dynamic Sketches of an Area Model **
 * ** Too Big or Too Small? **

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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