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CMS Curriculum Guides 2011-2012 6th Grade Math Honors Unit Title: Prime Time Suggested Time: Unit does not begin until day 8. Unit will take approximately 14 days. Enduring understanding (Big Idea): 1. Determining the factors of whole numbers. 2. Finding greatest common factors and generating multiples. 3. Determining prime factorization. 4. Classifying numbers as prime or composite. (FOUND IN TEACHER’S EDITION ON MATHEMATICAL HIGHLIGHTS PAGE) Essential Questions: Will breaking a number into factors help me solve the problem? What relationships will doing that help me see? What do the factors and multiples of the numbers tell me about the situation? How can I find the factors of the numbers? How can I find the multiples? What common factors and common multiples do the numbers have? (FOUND IN TEACHER’S EDITION ON MATHEMATICAL HIGHLIGHTS PAGE) Unit Plans (FOUND IN TEACHER’S EDITION ON PLANNING FOR THE UNIT PAGE) Prior to Investigation 1: 1. Formative testing will be within the first 10 days of school. 2. Review the order of operations. 3. Teach students the expectations on answering CMP2 questions. Investigation 1 Factors and Multiples Problem 1.1- pages 6-9 ACE #1-7, 28-31, 39 Problem 1.2- pages 9-11 ACE #8-16, 32-34, 40-44 Problem 1.3- pages 11-13 ACE #17-27, 35-38, 45-49 Common Core Standards Alignment/Mathematical Practices Connection to 2003 Standards 6.EE.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms described verbally 1.05 Develop fluency in the use of factors, multiples, exponential notation, and prime factorization. Mathematical Practices: 3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically. Investigation 2 Whole Number Patterns and Relationships Problem 2.1- pages 22-24 ACE #1-9, 22-24; 31-33 Problem 2.2- pages 24-26 ACE #10-16, 25, 34-35 Problem 2.3- pages 26- 29 ACE #17-21, 26-30, 36-41 Math Reflections 7. Look for and make use of structure. 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 CMS Curriculum Guides 2011-2012 6th Grade Math Honors two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2. Mathematical Practices: 1. Make sense of problems and persevere in solving them. 4. Model with Mathematics. 5. Use appropriate tools strategically. Investigation 3 Common Multiples and Common Factors Problem 3.1- pages 37-38 ACE #1-8, 31, 32 Problem 3.2- pages 39-40 ACE #9-15, 33-35, 37, 38 Problem 3.3- pages 40-41 ACE #16-23, 39-41 Problem 3.4- page 41 ACE #24-30, 36, 42-44 7. Look for and make use of structure. 6.NS.4 (shown above) 6.EE.2.b (shown above) Mathematical Practices: 1.05 Develop fluency in the use of factors, multiples, exponential notation, and prime factorization. 8. Look for and express regularity in repeated reasoning. Investigation 4 Factorizations Problem 4.1- pages 49-50 ACE #1-3, 25, 26, 34 Problem 4.2- pages 50-52 ACE #4-18, 27-30, 35 Problem 4.3- pages 53-55 ACE #19-24, 32-33, 36 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2.b (shown above) Investigation 5 Putting It All Together Problem 5.1- pages 61-64 ACE #1-25 6.EE.2.b (shown above) 1.05 Develop fluency in the use of factors, multiples, exponential notation, and prime factorization. Prior Knowledge: 1. Learning and applying multiplication and division facts; applying the division algorithm (elementary school) 2. Learning and applying multiplication facts; counting by 2’s, 3’s, etc. (elementary school) 3. Learning and applying multiplication and division facts; testing numbers for divisibility (elementary school) 4. Applying multiplication, addition, and division facts; comparing positive whole numbers (elementary school) . (FOUND IN TEACHER’S EDITION ON CONTENT CONNECTIONS TO OTHER UNITS PAGE) CMS Curriculum Guides 2011-2012 6th Grade Math Honors Essential Terms Developed in This Unit (FOUND IN TEACHER’S Useful Terms Referenced in This Unit EDITION ON PLANNING FOR THE UNIT PAGE) *All vocabulary is used when teaching honors. common factor common multiple composite number conjecture dimensions (whole number) divisor even number exponent (whole number) factor factor pair factorization greatest common factor least common multiple odd number prime factorization prime number proper factor square number Venn diagram abundant number adjacent primes deficient number divisible by distinct Fundamental Theorem of Arithmetic intersection near-perfect number perfect number relatively prime twin primes Resources (FOUND IN TEACHER’S EDITION ON PROGRAM RESOURCES EACH BOOK) Lab-Sheet Additional Practice/Skills Worksheets CMP2 Website –online & technology resources Formal Assessment Check-Ups Partner Quiz Unit Test Assessment Options Notebook check Multiple-Choice Question Bank ExamView CD-ROM Parent Guide-Unit Letters PAGE – BASICALLY THE SAME RESOURCES IN CMS Curriculum Guides 2011-2012 6th Grade Math Honors Spanish Assessment Resources PHSchool.com TeacherExpress CD-ROM LessonLab Online Courses Unit Technology Tips