6.2.2Ma

 ** Grade: 6 Unit: 2 Week: 2 Dates: 10/8-10/12 ** ** Content: Fractions and Mixed Numbers ** ** 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 extend to the rational number system? ** Essential Questions: ** ** Standards ** ** Apply and extend previous understandings of multiplication and division to divide fractions by fractions. ** ** Objectives ** ** Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team ** This unit is an excellent representation of Mathematical Practices #4. Students will be required to look at fractions from concrete models or pictures to mathematical representations. The students will need to move from one representation to another. They will need to compare different situations from different perspectives. Mathematical Practice #1 will be a perfect companion to Mathematical Practice #4. Students will analyze problems with various representations, and develop a plan to obtain the solution. (Taken from Ohio Department of Education Teaching) Teaching “invert and multiply” without developing an understanding of why it works first leads to confusion as to when to apply the shortcut. Learning how to compute fraction division problems is one part, being able to relate the problems to real-world situations is important. Providing opportunities to create stories for fraction problems or writing equations for situations is needed. Computation with fractions is best understood when it builds upon the familiar Understandings of whole numbers and is paired with visual representations. Solve a simpler problem with whole numbers, and then use the same steps to solve a fraction divided by a fraction. Looking at the problem through the lens of “How many groups?” or “How many in each group?” helps visualize what is being sought. For example: 12÷3 means; how many groups of three would make 12? Or how many in each of 3 groups would make 12? Thus can be solved the same way. How many groups of ? Or, how many objects in a group when fills one fourth? Creating the picture that represents this problem makes seeing and proving the solutions easier.
 * Can students use a model to show division of fractions?
 * Can students use compaitable numbers to estimate quotients of fractions and mixed numbers?
 * Can students divide fractions?
 * Can students use a model to show division of mixed numbers?
 * Can students divide mixed numbers?
 * Can students use the strategy //use a model// to help them solve a division problem?
 * ** 6.NS.1: ** Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. //For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?//
 * Students will use a model to show division of fractions.
 * Students will use compatible numbers to estimate quotients of fractions and mixed numbers.
 * Students will divide fractions.
 * Students will use a model to show division of mixed numbers.
 * Students will divide mixed numbers.
 * Students will solve problems with fractions and mixed numbers by applying the strategy //use a model//.

** Background Information ** ** Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials. ** ** 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 ** Divisor Reciprocal Pattern Blocks Fraction Strips || ** Suggested Activities ** 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.3: ** Diverse Learners ** ** 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.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
 * Foldable Glencoe p255
 * ** Mathematical Practices **
 * ** Math ** ||
 * Dividend
 * Investigate-Model Fraction Division Lesson 20, pages 39-40
 * Estimate Quotients Lesson 21, pg 41-42
 * Divide Fractions Lesson 22, pg 43-44
 * Investigate-Model mixed Number Division Lesson 23, pg 45-46
 * Divide Mixed Numbers Lesson 24, pg 47-48
 * Problem Solving-Fraction Operations Lesson 25,pg 49-50
 * Chapter 1 pgs 6-11
 * Modeling Division of Fractions p9
 * Dividing Fractions
 * Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change.
 * GP1-Unit 2, SBIL 5 Fractional Operations (Multiply/Divide)
 * Glencoe: Study and Intervention, page 342-344
 * Activity 1, Glencoe, page 270
 * Mini Lab,Glencoe, page 372
 * Find The Error, Glenco page 274
 * Open-Ended Assessment, Glenco, page 275
 * Baking Cookies @http://illustrativemathematics.org/illustrations/50
 * Drinking Juice, Variation 2 @http://illustrativemathematics.org/illustrations/412
 * Drinking Juice, Variation 3 @http://illustrativemathematics.org/illustrations/413
 * How Masny Containers in One Cup / Cups in One Container @http://illustrativemathematics.org/illustrations/408
 * Making Hot Cocoa, Variation 1 @http://illustrativemathematics.org/illustrations/407
 * Making Hot Cocoa, Variation 2 @http://illustrativemathematics.org/illustrations/411
 * Running to School, Variation 2 @http://illustrativemathematics.org/illustrations/410
 * Traffic Jam @http://illustrativemathematics.org/illustrations/464
 * Video Game Credits @http://illustrativemathematics.org/illustrations/267
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool 6.6
 * Math.com (@http://math.com/school/subject1/lessons/S1U4L5GL.html, @http://math.com/school/subject1/lessons/S1U4L8GL.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 **

** Resources ** ** Professional Texts **

** Literary Texts **

** Informational Texts ** ** Art, Music, and Media **
 * @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.

** 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 ** ** SMART Board Lessons, Promethean Lessons **
 * @http://www.khanacademy.org/math
 * @http://www.tli.net/ TLI Quiz Builder
 * @http://webmath.com//.//
 * 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 ||
 * = English
 * = Math ||= [[image:commoncorepcssd6/Actions-insert-table-icon.png link="@http://inst.pcssd.org/math/CCSS/6/Math6TeachingMatrix.xls"]]
 * = [[image:commoncorepcssd6/PCSSDlogo.JPG link="commoncorepcssd/PCSSD"]]