Math 149S. Capstone Mathematics for Teachers. Spring 2019.
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 16 | Last day to withdraw from a course with a serious and compelling reason | ||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 17 | - | - | 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. |
| 5:30PM-7:30PM. Math Circle, grades 9-12 - AMC 10/12 prep. | |||
| Jan 22 | Students and Service Learning
What is Service Learning? A Student's Guide to Successful Service Learning |
Technology. LaTeX: On-line collaborative LaTeX compilator (Overleaf),
On-line LaTeX manual,
Sample LaTeX file, required image file Install LaTeX: MiKTeX (PC), TeXShop (Mac) TikZ package: Sample file, Manual |
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| Jan 24 | - | 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. | |
| 5:30PM-7:30PM. AMC 10/12 prep, mostly grades 8-12. | |||
| Jan 26 | 9:45-11:30 AM. Math Circle, grades 3-8. | ||
| Jan 29 | Bases other than 10 | Homework 1 | Homework 1 discussion. Bases other than 10, definition, examples, applications, problems. Math club problems, Solutions |
| Jan 31 | - | Other bases cont. Fractions in other bases. Place value problems. |
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| 5:30PM-7:30PM. Math Circle, grades 9-12 - AMC 10/12 prep. | |||
| Feb 2 | 9:30-11:45 AM, 1:15-3:30 PM. Math Kangaroo Prep (grades 1-2, 5-6, 9-10 in the morning, grades 3-4 and 7-8 in the afternoon). | ||
| Feb 5 | - | Homework 2 | Homework 2 discussion. Counting (combinatorics). MFD Prep problems, Solutions, Math club problems, Solutions |
| Feb 7 | - | - | Combinatorics cont. Fresno Math Circle 11-12 problems. Binomial coefficients (n choose k) |
| Feb 9 | 9:45-11:30 AM. Math Circle, grades 3-8. | ||
| 2:00-4:30PM. Math Field Prep, grades 6-8 - leaders found. | |||
| Feb 12 | - | Homework 3 | Homework 3 discussion.
Binomial Theorem. Probability. |
| Feb 14 | - | - | 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 19 | Homework 4 | Homework 4 discussion. | |
| Feb 21 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | 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. |
| 5:30PM-8:00PM. Math Field Day Prep, grades 9-10 and 11-12 - leaders found, observers welcome. | |||
| Feb 23 | 9:45-11:30 AM. Math Circle, grades 3-8 - helpers found. | ||
| Feb 26 | Homework 5 | Homework 5 discussion. 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. Review: Study Guide and Sample Problems |
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| Feb 28 | - | - | Review, questions and answers, more problems. Service Learning Plan. |
| 5:30PM-7:30PM. Math Circle, grades 9-12 - observers welcome. | |||
| Mar 2 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep (grades 1-2, 5-6, 9-10 in the morning, grades 3-4 and 7-8 in the afternoon) - leaders found. | ||
| Mar 5 | - | - | Test 1.
Test discussion. |
| Mar 7 | - | - | Real numbers. Construction of real numbers as equivalence classes of Cauchy sequences of rational numbers. Complex numbers. Definition and representation in R2 using rectangular and polar coordinates. Geometric interpretation of complex numbers multiplication. |
| 5:30PM-8:00PM. Math Field Day Prep, grades 6-8, 9-10, and 11-12 - leaders found, observers welcome. | |||
| Mar 9 | 9:45-11:30 AM. Math Circle, grades 3-8 - helpers found. | ||
| Mar 12 | - | Homework 6 | Homework 6 discussion. Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields. |
| Mar 14 | - | - | More examples of groups and fields, e.g. braid group. The picture hanging on two nails problem. |
| 5:30PM-7:30PM. Math Circle, grades 9-12 - observers welcome. | |||
| Mar 16 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep (grades 1-2, 5-6, 9-10 in the morning, grades 3-4 and 7-8 in the afternoon) - leaders found. | ||
| Mar 19 | - | Homework 7 | Homework 7 discussion. Functions. Definitions of important terms (function, domain, codomain, range, graph, intercept, root). |
| Mar 21 | - | - | Functions continued. Equations. The concept of equation. Questions. |
| 5:00-7:30 PM, ED 140. Math Kangaroo competition, grades 1-12 - helpers found. | |||
| Mar 23 | 9:45-11:30 AM. Math Circle, grades 3-8 - helpers found. | ||
| Mar 26 | - | Homework 8 | Homework 8 discussion. Polynomials. Polynomial equations. Roots and graphs of polynomials. Solving polynomial equations and inequalities. Review: Study Guide and Sample Problems |
| Mar 28 | - | - | Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities. Quadratic formula. Factoring quadratic polynomials. |
| 5:30PM-7:30PM. Math Circle, Integration Bee prep - participants welcome. | |||
| Mar 30 | 9:45-11:45 AM. Math Kangaroo solutions, grades 1-10 (followed by the awards ceremony), leaders found. | ||
| 2:00-4:30PM. Math Field Prep, grades 6-8 - leaders found. | |||
| Apr 2 | - | - | Test 2. Test discussion. |
| Apr 4 | - | Polynomials continued. Vieta's formulas. Problems. | |
| 5:30PM-8:00PM. Math Field Day Prep, grades 9-10, and 11-12 - leaders found. | |||
| Apr 6 | 9:45-11:30 AM. Math Circle, grades 3-8 - helpers found. | ||
| Apr 9 | - | Homework 9 | Homework 9 discussion. Geometry. Proofs of the Pythagorean theorem. Coordinate Geometry. Distance formula |
| Apr 11 | - | - | Coordinate Geometry (cont.) Equations of circle and ellipse. Coordinate geometry problems Math Field Day games. Final Project |
| 5:30PM-7:30PM. Math Circle, grades 9-12 - observers welcome. | |||
| Apr 16 | Spring recess | ||
| Apr 18 | Spring recess | ||
| Apr 20 | 9:45-11:30 AM. Math Circle, grades 3-8 - helpers found. | ||
| Apr 23 | - | Homework 10 | Homework 10 discussion. Proportional reasoning in geometry (similarity). Areas and volumes of similar figures/solids. Problems on similarity |
| Apr 25 | - | Homework 11 | Homework 11 discussion.
Ratios, rates, proportional reasoning. Math club problems Study Guide and Sample Problems |
| 5:30PM-7:30PM. Math Circle, grades 9-12 - observers welcome. | |||
| Apr 27 | 8AM-4PM, on campus. Math Field Day competition for grades 6-12. As many helpers as possible are needed! Please sign up in advance. |
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| Apr 30 | - | - | Test 3. Test discussion. |
| May 2 | - | Homework 12 | Homework 12 discussion. Presentations: Field Experience |
| May 4 | 9:45 AM -2:45 PM. Math Circle and grading contest - helpers found. | ||
| May 7 | - | - | Presentations: Field Experience (cont.) |
| May 9 | Faculty consultation day. Consultation hours: 11 AM - 1 PM | ||
| May 10 | Faculty consultation day. Consultation hours: 9 AM - 12 PM | ||
| May 16 | - | - | Final Project due: submit via email (typed in LaTeX) by 11:59 PM. |