6.3.4Ma

 ** Grade: 6 Unit: 3 Week: 4 Dates: 12/3-12/7 **
 * Content: Prime factors, LCM, GCF; Multiplying and Simplifying Fractions **

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

** Essential Questions: **
 * Can students write the prime factorization of a number?
 * Can students find the least common multiple of two numbers?
 * Can students find the greatest common factor of two whole numbers?
 * Can students use the strategy //draw a diagram// to help them solve problems involving the GCF and Distributive Property?
 * Can students multiply fractions?
 * Can students simplify fractional factors by using the GCF?

** Standards **   ** Objectives **
 * Compute fluently with multi-digit numbers and find common factors and multiples. **
 * 6.NS.4: ** Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
 * Students will write the prime factorization of numbers.
 * Students will find the least common multiple of two whole numbers.
 * Students will find the greatest common factor of two whole numbers.
 * Students will solve problems involving greatest common factor by using the strategy //draw a diagram//.
 * Students will multiply fractions.
 * Students will simplify fractional factors by using the greatest common factor.

** Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team ** We are returning to this standard because it is such an important piece in the learning progression for students. This is not a repeat of what you did in the second unit. Take what you have been doing and include fractions in the combining of like terms, writing equivalent expressions, evaluating algebraic expressions. You must take the students deeper into the understanding of fractions. Mathematical Practice #7 requests our children to investigate and use patterns. We need to encourage and guide this academic approach. (Taken from Ohio Department of Education Teaching) // Greatest common factor // and //least common multiple// are usually taught as a means of combining fractions with unlike denominators. This cluster builds upon the previous learning of the multiplicative structure of whole numbers, as well as prime and composite numbers in Grade 4. Although the process is the same, the point is to become aware of the relationships between numbers and their multiples. For example, consider answering the question: “If two numbers are multiples of four, will the sum of the two numbers also be a multiple of four?” Being able to see and write the relationships between numbers will be beneficial as further algebraic understandings are developed. Another focus is to be able to see how the GCF is useful in expressing the numbers using the distributive property, (36 + 24) = 12(3+2), where 12 is the GCF of 36 and 24. This concept will be extended in Expressions and Equations as work progresses from understanding the number system and solving equations to simplifying and solving algebraic equations in Grade 7.

** 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 **
 * ** [] **

** 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. || ** Vocabulary ** Properties Venn Diagram Greatest Common factor Equivalent fractions Simplest form Mixed number Improper fraction Multiple Common multiple Least common multiple ||
 * ** Mathematical Practices **
 * ** Math ** ||
 * Equivalent expressions

** Suggested Activities-Remember Deepen the Understanding ** On Core Mathematics Mastering the Common Core ABC Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8 Gizmos JBHM Glenco 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.4:
 * Prime factorization Lesson 31 p61-62
 * Least Common Multiple Lesson 32 p63-64
 * Greatest Common Factor Lesson 33 p65-66
 * Problem Solving-Applying the GCF Lesson 34 p 67-68
 * Multiplying Fractions Lesson 34 p69-70
 * Simplifying Factors Lesson 36 p71-72
 * Chapter 1 pgs 1-14
 * The Numbers Game p17
 * Pattern Flip (Patterns)
 * In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck!
 * 6th GP1-Unit 1, SBIL 6 Factorization
 * 7th GP1-Unit 1, SBIL 4 LCM, GCF, and Prime Factorization
 * 6th grade 1-3, p176, 5-1, 5-2, 5-4, 7-2a,
 * 7th grade 5-1a, 5-1, 5-2, 5-3, 5-7, 6-4
 * Adding Multiples @http://illustrativemathematics.org/illustrations/257
 * Bake Sale @http://illustrativemathematics.org/illustrations/258
 * Factors and Common Factors @http://illustrativemathematics.org/illustrations/255
 * Multiples and Common Multiples @http://illustrativemathematics.org/illustrations/256
 * The Florist Shop @http://illustrativemathematics.org/illustrations/259

** Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool 4.3, 4.4, 6.5
 * Math.com (@http://www.math.com/school/subject1/lessons/S1U3L1GL.html, @http://www.math.com/school/subject1/lessons/S1U3L2GL.html, @http://www.math.com/school/subject1/lessons/S1U3L3GL.html )

** Homework **   ** 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)
 * ** @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 **

** Resources **   ** Literary Texts **   ** Informational Texts **   ** Art, Music, and Media **   ** Manipulatives **
 * Professional Texts **
 * See New York Common Core Aligned Task (other resources) @http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm
 * www.nlvm.usu.edu
 * @http://jeopardylabs.com/play/expressions24
 * @http://jeopardylabs.com/play/expressions21
 * Graphing calculators

** Games **
 * www.mathplayground.com
 * @http://www.sumdog.com/ Variety of games covering many math topics
 * @http://www.nctm.org/resources/middle.aspx

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

** Websites **   ** Sight Words **  <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> ** SMART Board Lessons, Promethean Lessons ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> ** Other Activities, etc. **
 * @http://www.khanacademy.org/math
 * @http://www.tli.net/ TLI Quiz Builder
 * @http://webmath.com//.//
 * Smartboard Resource Website Smartboard lesson search engine

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