Math 149S. Capstone Mathematics for Teachers. Spring 2020.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Jan 31 | Last day to add a course without a permission number | ||
| Feb 7 | Last day to drop a course online | ||
| Feb 13 | Last day to drop a course without a "W" on your transcript | ||
| Feb 14 | Last day to add a course with a permission number | ||
| Apr 15 | Last day to withdraw from a course with a serious and compelling reason | ||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 21 | - | - | Introduction. Syllabus & Schedule. Service Learning. Single Subject Credential Requirements. An advanced perspective. Overview of service learning. Math Circle, AMC, Math Kangaroo, Math Field Day, prep sessions. |
| Jan 23 | Service Learning and Students
What is Service Learning? A Student's Guide to Successful Service Learning |
- | More on service learning. Time line, expectations, and other details.
Technology. LaTeX: On-line collaborative LaTeX compilator (Overleaf), On-line LaTeX manual, Sample LaTeX file, required image file TikZ package: Sample file, Manual |
| 5:30PM-7:30PM. Math Circle - AMC 10/12 prep, mostly grades 8-12 - observers/participants welcome. | |||
| Jan 28 | - | TikZ package continued | |
| Jan 30 | - | Natural numbers, Integers.
Divisibility. Divisibility tests for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 25, 100. Decimal (base 10) representation. | |
| 5:00PM-7:30PM. AMC 10/12 competition, mostly grades 8-12 - helpers found. | |||
| Feb 1 | 9:45-11:30 AM. Math Circle, grades 4-9 - helpers found. | ||
| Feb 4 | Bases other than 10 | Homework 1 | Homework 1 discussion. Bases other than 10, definition, examples, applications, problems. Math club problems, Solutions |
| Feb 6 | - | Other bases cont. Fractions in other bases. Place value problems. |
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| 5:30PM-7:30PM. Math Circle, grades 9-12 - MFD prep - observers/participants welcome. | |||
| Feb 8 | 9:30-11:45 AM, 1:15-3:30 PM. Math Kangaroo Prep Grades 1-2, 5-6, in the morning, grades 3-4 and 7-8 in the afternoon - leaders found. Grades 9-10 in the morning, 11-12 in the afternoon - observers welcome. |
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| Feb 11 | - | Homework 2 | Homework 2 discussion. Counting (combinatorics). MFD Prep problems, Solutions, Math club problems, Solutions |
| Feb 13 | - | - | Combinatorics cont. Binomial coefficients (n choose k). Fresno Math Circle 7-8 problems, Fresno Math Circle 11-12 problems. |
| Feb 15 | 9:45-11:30 AM. Math Circle, grades 4-9, helpers found. | ||
| Feb 18 | - | Homework 3 | Homework 3 discussion.
Binomial Theorem. Probability. |
| Feb 20 | - | - | Probability cont.
Fresno Math Circle 11-12 problems: discrete probability, continuous probability. Discussion of and preparation for field experience. |
| 5:30PM-7:30PM. Math Circle, grades 9-12 - AMC 10/12 solutions and awards - observers welcome. | |||
| Feb 22 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep Grades 1-2, 5-6, in the morning, grades 3-4 and 7-8 in the afternoon - leaders found. Grades 9-10 in the morning, 11-12 in the afternoon - observers welcome. |
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| Feb 25 | Homework 4 | Homework 4 discussion. Review: Study Guide and Sample Problems |
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| Feb 27 | Test 1.
Test discussion. |
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| 5:30PM-7:30PM. Math Field Day Prep, grades 6-8 - leaders found. | |||
| Feb 29 | 9:45-11:30 AM. Math Circle, grades 4-9 - leaders found. | ||
| Mar 3 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | Homework 5: Service Learning Plan | Natural numbers revisited. Axiomatic construction of natural numbers (Peano postulates for N)
Integers revisited. Construction: integers as equivalence classes of pairs (differences) of natural numbers. |
| Deadline to submit an abstract for Spring Western AMS Meeting, Fresno, CA, May 2-3, 2020
Special Session on Math Circle Games and Puzzles that Teach Deep Mathematics flyer Conference website |
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| Mar 5 | - | - | Rational numbers.
Definition used in high school. Formal construction of rational numbers (as equivalence classes of pairs of integers).
Rational numbers as terminating/repeating decimals. Real numbers. Construction of real numbers as equivalence classes of Cauchy sequences of rational numbers. |
| 5:15PM-7:30PM. Math Circle - Math Field Day prep, grades 9-12, leaders found. | |||
| Mar 7 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep Grades 1-2, 5-6, in the morning, grades 3-4 and 7-8 in the afternoon - leaders found. Grades 9-10 in the morning, 11-12 in the afternoon - mock test - participants/observers very welcome. |
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| Mar 10 | - | Homework 6 | Homework 6 discussion.
Complex numbers. Definition and representation in R2 using rectangular and polar coordinates. Geometric interpretation of complex numbers multiplication. |
| Mar 12 | - | - | Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields. |
| Mar 14 | 9:45-11:30 AM. Math Circle, grades 4-9 - helpers found. | ||
| Mar 17 | No classes; on-line office hours will be tried via Canvas Chat, Wednesday and Thursday 2-3pm. | ||
| Mar 19 | |||
| Mar 24 | - | Homework 7 | See Module "Functions, polynomials, equations, inequalities" on Canvas. Participate in two Discussions.
Functions. Definitions of important terms (function, domain, codomain, range, graph, intercept, root). Equations. The concept of equation. Questions. Answers have been posted on Canvas. |
| 4-5 PM. Problem Solving Playground via Zoom: https://fresnostate.zoom.us/j/5233106532. Flyer | |||
| Mar 26 | - | - | Polynomials. Polynomial equations. Roots and graphs of polynomials. Solving polynomial equations and inequalities. Read the file "Polynomial equations and inequalities" on Canvas.
Review: Study Guide and Sample Problems. See Discussion and Sample Test (in Quizzes) on Canvas. |
| Mar 28 | Math Circle, grades 4-9 - problems/solutions will be sent out electronically. See Module on SL on Canvas. | ||
| Mar 31 | Cesar Chavez Holiday - no classes | ||
| Apr 2 | - | Homework 8 | Test 2. Will be posted in Quizzes on Canvas, available between 1-4PM, 1 h 15 min time limit.
Test answers will be posted on Canvas. |
| Apr 7 | Spring recess | ||
| Apr 9 | Spring recess | ||
| Apr 11 | Math Circle, grades 4-9 - problems/solutions will be sent out electronically. See Module on SL on Canvas. | ||
| Apr 14 | - | Homework 9 | Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities.
Read the file "Quadratic inequalities" on Canvas.
Quadratic formula. Factoring quadratic polynomials. Vieta's formulas. Problems. See the file "quadratic inequalities math circle" on Canvas, read the text and try problems 1-8. The file contains solutions to all problems. |
| 4-5 PM. Problem Solving Playground via Zoom: https://fresnostate.zoom.us/j/5233106532. | |||
| Apr 16 | - | Geometry. Proofs of the Pythagorean theorem. Coordinate Geometry. Distance formula. Equations of circle and ellipse. Coordinate geometry problems See Module "Geometry" on Canvas. Read the file "Distance formula" and participate in two discussions. |
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| Math Circle, grades 9-12 - problems will be sent out electronically. | |||
| Apr 21 | - | Homework 10 | Ratios, rates, proportional reasoning. Proportional reasoning in geometry (similarity). Areas and volumes of similar figures/solids.
Math club problems. More problems on similarity. See Module "Geometry" on Canvas. Read the file "Similarity and perimeter, area, and volume" and participate in a discussion. |
| 4-5 PM. Problem Solving Playground via Zoom: https://fresnostate.zoom.us/j/5233106532. | |||
| Apr 23 | - | - | Study Guide and Sample Problems Math Field Day games. Final Project See Module "Final project" on Canvas. Zoom meeting during regular class time (questions/answers about the study guide and final project) |
| Apr 25 | Math Circle, grades 4-9 - problems/solutions will be sent out electronically. See Module on SL on Canvas. | ||
| Apr 28 | - | - | Presentations: Service Learning, via Zoom during regular class time |
| 4-5 PM. Problem Solving Playground via Zoom: https://fresnostate.zoom.us/j/5233106532. | |||
| Apr 30 | - | Homework 11 | Presentations: Service Learning (cont.), via Zoom during regular class time
Time permitting: homework 11 discussion. |
| Math Circle, grades 9-12 - problems/solutions will be sent out electronically. | |||
| May 5 | - | - | Test 3. Will be posted in Quizzes on Canvas, available between 1-4 PM, 1 h 15 min time limit.
Test answers will be posted on Canvas. |
| 4-5 PM. Problem Solving Playground via Zoom: https://fresnostate.zoom.us/j/5233106532. | |||
| May 7 | Faculty consultation day. Consultation hours: 11 AM - 12 PM any class, 2-3 PM Math 149 only, via Zoom: https://fresnostate.zoom.us/j/94294017263 | ||
| May 8 | Faculty consultation day. Consultation hours: 11AM - 12 PM and 1-3 PM any class, via Zoom: https://fresnostate.zoom.us/j/94294017263 | ||
| May 9 | Math Circle problem solving contest administered online - helpers needed. | ||
| May 14 | - | - | Final Project due: submit via overleaf by 11:59 PM. |