Huntsville City Schools - Instructional Guide 2015 - 2016 Course Discrete Math Grade 11 – 12 Math Practices Online Resources The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy). Dan Meyer’s Ted Talk about teaching math: https://youtu.be/qocAoN4jNwc 1. 2. 3. 4. 5. 6. 7. 8. Links to his 3-act activities, sorted by standard: https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYd EhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0 Granite City Math Vocabulary: http://www.graniteschools.org/mathvocabulary/ Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning . For more: 1st Nine Other online resources Weeks 1 Elaboration on each practice from the Common Core website: www.corestandards.org/Math/Practice/ www.opencurriculum.org is a website that curates activities from all over the web, sorted by standard. Kid-friendly language: www.buncombe.k12.nc.us/Page/37507 http://map.mathshell.org/lessons.php has great formative assessments and group activities, searchable by standard. Online tools www.desmos.com is a free online calculator. Excellent for working with linear equations, scatterplots, and best-fit lines. https://teacher.desmos.com/ has some great activities for introducing and working with functions. www.geogebra.org is a free online geometry tool. It is great for working with transformations. “I Can” Statements Resources Standard N/A N/A A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 1) 11. Solve applicationbased logic problems using Venn diagrams, truth tables and matrices 1. I can solve application-based logic problems using Venn diagrams. 2. I can solve application-based logic problems using truth tables. 3. I can solve application-based logic problems using matrices A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 2 and 3) Pacing Recommendation / Date(s) Taught 5 Days (Optional) 22 Days Quality Core Unit 3 Algebra II B-5 to D-6 2 1. Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine properties of integers. 2. Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers. 3. Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. 1. I can use the recursive process and difference equations to create fractals. 2. I can use the recursive process and difference equations to create population grown models. 3. I can use the recursive process and difference equations to create sequences. 4. I can use the recursive process and difference equations to create series. 5. I can use the recursive process and difference equations to create compound interest models. A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 5 with emphasis on Sections 5.1, 5.2, 5.7 and 5.8) Days Website: For Prime numbers www.mathsisfun.com/numbers/primenumbers-advanced.html NMSI Lesson: Exponential Growth and Decay TOTAL DAYS: 39 DAYS 3 2nd Nine Weeks Standard 4. Convert between base ten and other bases. 3. Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. “I Can” Statements Resources 1. I can convert between base ten and other bases. A Survey of Mathematics, Angel, Abbott, Runde (Chapter 4) 1. I can use the recursive process and difference equations to create population growth models. A Survey of Mathematics, Angel, Abbott, Runde (Chapter 6 with emphasis on 6.10) Pacing Recommendation / Date(s) Taught 11 Days 14 Days 4 5. Determine results of operations upon 3 × 3 and larger matrices, including matrix addition and multiplication of a matrix by a matrix, vector, or scalar. 6. Analyze determinants and inverses of 2 × 2, 3 × 3, and larger matrices to determine the nature of the solution set of the corresponding system of equations, including solving systems of equations in three variables by echelon row reduction and matrix inverse. 1. I can determine results of addition upon 3x3 and larger matrices 2. I can determine results of multiplication of a matrix by a matrix, vector, or scalar. 3. I can analyze determinants of of matrices to determine the nature of the solution set of systems of equations. 4. I can use inverses to find the solution set of systems of equations. 5. I can use echelon row reduction to solve for the solution set of systems of equations. A Survey of Mathematics, Angel, Abbott, Runde (Chapter 7) 12 Days TOTAL DAYS: 37 DAYS 3rd Nine Weeks Standard 7. Solve problems through investigation and application of existence and nonexistence of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. 8. Apply algorithms, including Kruskal’s and Prim’s, relating to minimum weight spanning trees, networks, flows, and Steiner trees. “I Can” Statements 1. I can solve problems through investigation and application of existence and nonexistence of Euler paths. 2. I can solve problems through investigation and application of existence and nonexistence of Euler Circuits. 3. I can solve problems through investigation and application of Resources A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 14) Pacing Recommendation / Date(s) Taught 18 days Website: Mathmaniacs.org/lessons/12euler/index.html 5 9. Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the list-processing algorithm, and student-created algorithms. 10. Use vertex-coloring techniques and matching techniques to solve application-based problems. 12. Use combinatorial reasoning and counting techniques to solve application-based problems. existence and nonexistence of Hamilton paths 4. I can solve problems through investigation and application of existence and nonexistence of Hamilton Circuits 5. I can apply algorithms, including Kruskal’s and Prim’s. 6. I can relate minimum weight spanning trees. 7. I can relate networks, flows, and Steiner trees. 8. I can determine a minimum project time using algorithms to schedule tasks in order. 9. I can include critical path analysis. 10. I can do the list-processing algorithm. 11. I can do a student-created algorithms 12. I can use vertex-coloring techniques to solve application-based problems. 13. I can use matching techniques to solve application-based problems. Additional topics include: bridges, connected and disconnected graphs, Nearest Neighbor algorithm, minimumcost spanning tree, interpret probable life expectancy 1. I can use combinatorial reasoning to solve application-based problems. 2. I can use counting techniques to solve application-based problems. Additional topics include: odds, expected value, tree diagram, P(A and B), P (A or B), empirical probability A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 12) 13 days NMSI Lessons: Calculating Tree Diagrams Probability Rules 6 A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 13) 6 days TOTAL DAYS: 37 DAYS 4th Nine Weeks “I Can” Statements Standard Resources Pacing Recommendation / Date(s) Taught 7 N/A N/A 13. Analyze election data to compare election methods and voting apportionment, including determining strength within specific groups. 3. Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 13) A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 15) 10 Days 10 Days Use the lesson: Will the Best Candidate Win? From the websiteIlluminations.nctm.org 1. I can use the recursive process and difference equations to create fractals. 2. I can use the recursive process and difference equations to create population grown models. 3. I can use the recursive process and difference equations to create sequences. 4. I can use the recursive process and difference equations to create series. 5. I can use the recursive process and difference equations to create compound interest models. A Survey of Mathematics – Angel, Abbott, and Runde (Chapter 11 with emphasis on Section 11.3) 12 Days TOTAL DAYS: 32 DAYS 8