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Foundations of Mathematics 120

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Foundations of Mathematics 120 Foundations of Mathematics 120 Curriculum Implemented September 2013 New Brunswick Department of Education and Early Childhood Development 2015 Acknowledgements The New Brunswick Department of Education and Early Childhood Development gratefully acknowledges the contributions of the following groups and individuals toward the development of the New Brunswick Foundations of Mathematics 120 Curriculum Guide: The Western and Northern Canadian Protocol (WNCP) for Collaboration in Education: The Common Curriculum Framework for Grade 10-12 Mathematics, January 2008. New Brunswick Foundations of Mathematics 120 curriculum is based on the Outcomes and Achievement Indicators of WNCP Foundations of Mathematics Grade 12. Reproduced (and/or adapted) by permission. All rights reserved. Newfoundland and Labrador Department of Education, Prince Edward Island Department of Education and Early Childhood Development. The NB High School Mathematics Curriculum Development Advisory Committee of Bev Amos, Roddie Duguay, Suzanne Gaskin, Nicole Giberson, Karen Glynn, Beverlee Gonzales, Ron Manuel, Stacey Leger, Jane Pearson, Elaine Sherrard, Alyssa Sankey (UNB), Mahin Salmani (UNB), Maureen Tingley (UNB), Guohua Yan (UNB). The NB Grade 12 Curriculum Development Writing Team of Carolyn Campbell, Mary Clarke, Gail Coates, Megan Crosby, Richard Cuming, Geordie Doak, Nancy Everett, Ryan Hachey, Nancy Hodnett, Wendy Hudon, Wendy Johnson, Julie Jones, Andrea Linton, Brad Lynch, Erin MacDougall, Sheridan Mawhinney, Chris McLaughlin, Nick Munn, Yvan Pelletier, Parise Plourde, Tony Smith, Anne Spinney, Glen Spurrell. Martha McClure, Learning Specialist, 9-12 Mathematics and Science, NB Department of Education The Mathematics Learning Specialists, Numeracy Leads, and Mathematics teachers of New Brunswick who provided invaluable input and feedback throughout the development and implementation of this document. Table of Contents Curriculum Overview for Grades 10-12 Mathematics .................................................................... 1 BACKGROUND AND RATIONALE ....................................................................................... 1 BELIEFS ABOUT STUDENTS AND MATHEMATICS LEARNING ........................................ 2 Goals for Mathematically Literate Students ......................................................................... 2 Opportunities for Success ................................................................................................... 3 Diverse Cultural Perspectives ............................................................................................. 3 Adapting to the Needs of All Learners ................................................................................. 4 Universal Design for Learning ............................................................................................. 4 Connections across the Curriculum ..................................................................................... 4 NATURE OF MATHEMATICS ................................................................................................ 5 Change ............................................................................................................................... 5 Constancy ........................................................................................................................... 5 Patterns .............................................................................................................................. 6 Relationships ...................................................................................................................... 6 Spatial Sense ...................................................................................................................... 6 Uncertainty .......................................................................................................................... 7 ASSESSMENT ....................................................................................................................... 8 CONCEPTUAL FRAMEWORK FOR 10-12 MATHEMATICS ................................................. 9 Communication [C]............................................................................................................ 10 Problem Solving [PS] ........................................................................................................ 10 Connections [CN] .............................................................................................................. 11 Mental Mathematics and Estimation [ME] ......................................................................... 11 Technology [T] .................................................................................................................. 12 Visualization [V] ................................................................................................................ 12 Reasoning [R] ................................................................................................................... 13 ESSENTIAL GRADUATION LEARNINGS ........................................................................... 14 PATHWAYS AND TOPICS................................................................................................... 15 Goals of Pathways ............................................................................................................ 15 Design of Pathways .......................................................................................................... 15 Outcomes and Achievement Indicators ............................................................................. 16 Instructional Focus ............................................................................................................ 16 SUMMARY ........................................................................................................................... 17 CURRICULUM DOCUMENT FORMAT ................................................................................ 18 Specific Curriculum Outcomes .......................................................................................................... 19 Statistics .............................................................................................................................. 20 S1: Demonstrate an understanding of normal distribution, including standard deviation and 풛- scores. .............................................................................................................................. 20 S2: Interpret statistical data, using confidence intervals, confidence levels, margin of error.25 Logical Reasoning .............................................................................................................. 29 LR1: Analyze puzzles and games that involve numerical and logical reasoning, using problem- solving strategies. ............................................................................................................. 29 LR2: Solve problems that involve the application of set theory. ......................................... 33 LR3: Solve problems that involve conditional statements. ................................................. 36 Probability ........................................................................................................................... 39 P1: Interpret and assess the validity of odds and probability statements. .......................... 39 P2: Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events. .............................................................................................................................. 41 P3: Solve problems that involve the probability of two events. .......................................... 43 P4: Solve problems that involve the fundamental counting principle. ................................ 45 P5: Solve problems that involve permutations ................................................................... 48 P6: Solve problems that involve combinations. ................................................................. 52 P7: Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers). ........................................................... 55 Relations and Functions .................................................................................................... 58 RF1: Represent data using polynomial functions (of degree ≤ 3), to solve problems. ........ 58 RF2: Represent data using exponential and logarithmic functions, to solve problems. ...... 64 RF3: Represent data, using sinusoidal functions, to solve problems. ................................ 69 SUMMARY OF CURRICULUM OUTCOMES .................................................................................... 74 z-score Chart ............................................................................................................................................ 75 REFERENCES ......................................................................................................................................... 77 Curriculum Overview for Grades 10-12 Mathematics Curriculum Overview for Grades 10-12 Mathematics BACKGROUND AND RATIONALE Mathematics curriculum is shaped by a vision which fosters the development of mathematically literate students who can extend and apply their learning and who are effective participants in society. It is essential the mathematics curriculum reflects current
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