Math 149. Capstone Mathematics for Teachers. Spring 2018.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Jan 29 | Last day to add a course without a permission number | ||
| Feb 5 | Last day to drop a course online | ||
| Feb 12 | Last day to add a course with a permission number | ||
| Feb 12 | Last day to drop a course without a "W" on your transcript | ||
| Apr 17 | Last day to withdraw from a course with a serious and compelling reason | ||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 16 | - | - | Introduction. Syllabus & Schedule. Field Experience. Single Subject Credential Requirements. An advanced perspective. Overview of the field experience. Math Circle, AMC, Math Kangaroo, Math Field Day, prep sessions. |
| Jan 18 | 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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| 5:30PM-7:30PM. Math Circle - AMC 10/12 prep, grades 9-12. | |||
| Jan 20 | 9:45-11:30 AM. Math Circle, grades 4-10. | ||
| Jan 23 | - | 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. | |
| Jan 25 | Bases other than 10 | Homework 1 | Homework 1 discussion. Bases other than 10, definition, examples, applications, problems. Math club problems, Solutions |
| 5:30PM-7:30PM. Math Circle - AMC 10/12 prep, grades 9-12. | |||
| Jan 27 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep (grades 1-2, 5-6, 9-10 in the morning, and grades 3-4, 7-8, 11-12 in the afternoon). | ||
| Jan 30 | - | Other bases cont. Divisibility tests in other bases. Place value problems. |
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| Feb 1 | - | Homework 2 | Homework 2 discussion. Counting (combinatorics). Fresno Math Circle 11-12 problems. Binomial coefficients (n choose k). |
| 5:30PM-7:30PM. Math Circle - AMC 10/12 prep, grades 9-12. | |||
| Feb 3 | 9:45-11:30 AM. Math Circle, grades 4-10. | ||
| Feb 6 | - | - | Combinatorics cont. MFD Prep problems, Solutions, Math club problems, Solutions |
| Feb 8 | - | Homework 3 | Homework 3 discussion.
Binomial Theorem. Probability. |
| Feb 10 | 9:00AM-12:00PM. Math Field Prep, grades 6-12. | ||
| Feb 13 | - | Field Experience Plan | Probability cont.
Fresno Math Circle 11-12 problems: discrete probability, continuous probability. Discussion of and preparation for field experience. |
| Feb 15 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | Homework 4 | Homework 4 discussion.
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. |
| Feb 17 | 9:45-11:30 AM. Math Circle, grades 4-10. | ||
| Feb 20 | - | Rational numbers. Definition used in high school. Formal construction of rational numbers (as equivalence classes of pairs of integers). | |
| Feb 22 | Homework 5 | Homework 5 discussion. Rational numbers as terminating/repeating decimals. Review: Study Guide and Sample Problems |
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| 5:30PM-7:30PM. AMC 10/12 Solutions, grades 9-12. | |||
| Feb 24 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep (grades 1-2, 5-6, 9-10 in the morning, and grades 3-4, 7-8, 11-12 in the afternoon). | ||
| Feb 27 | - | - | Test 1.
Test discussion. |
| Mar 1 | - | - | 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-7:30PM. Math Circle, grades 11-12. | |||
| Mar 3 | 9:45-11:30 AM. Math Circle, grades 4-10. | ||
| Mar 6 | - | - | Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields. More examples of groups and fields, e.g. braid group. |
| Mar 8 | - | Homework 6 | Homework 6 discussion. More examples of groups and fields continued. Discussion of field experience. |
| 5:30PM-7:30PM. Math Circle - Math Field Day Prep, grades 9-12. | |||
| Mar 10 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep (grades 1-2, 5-6, 9-10 in the morning, and grades 3-4, 7-8, 11-12 in the afternoon). | ||
| Mar 13 | - | - | Functions. Definitions of important terms (function, domain, codomain, range, graph, intercept, root). |
| Mar 15 | - | Homework 7 | Homework 7 discussion. Functions continued. |
| 5:20-7:30 PM, ED 140. Math Kangaroo competition, grades 1-12. | |||
| Mar 17 | 9:45-11:30 AM. Math Circle, grades 4-10. | ||
| Mar 20 | - | - | Functions continued. Equations. The concept of equation. Questions. |
| Mar 22 | - | Homework 8 | Homework 8 discussion. Polynomials. Polynomial equations. Roots and graphs of polynomials. Solving polynomial equations and inequalities. Review: Study Guide and Sample Problems |
| 5:30PM-7:30PM. Math Circle - Integration Bee Prep, grades 11-12. | |||
| Mar 24 | 9:45-11:45 AM. Math Kangaroo solutions, grades 1-12 (followed by the awards ceremony) | ||
| Mar 27 | Spring recess | ||
| Mar 29 | Spring recess | ||
| Mar 31 | 9:45-11:30 AM. Math Circle, grades 4-10. | ||
| Apr 3 | - | - | Test 2. |
| Apr 5 | - | - | Discussion of field experience. Mathematica software. Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities. Quadratic formula. Factoring quadratic polynomials. |
| Apr 7 | 9:00AM-12:00PM. Math Field Prep, grades 6-12. | ||
| Apr 10 | - | Polynomials continued. Vieta's formulas. Problems. | |
| Apr 12 | - | Homework 9 | Homework 9 discussion. Geometry. Proofs of the Pythagorean theorem. Coordinate Geometry. Distance formula |
| 6:45PM until winners have been determined (until 8:30-10PM in the past). High School Integration Bee. S2 109. | |||
| Apr 14 | 9:45-11:30 AM. Math Circle, grades 4-10. | ||
| Apr 17 | - | - | Coordinate Geometry (cont.) Equations of circle and ellipse. Coordinate geometry problems |
| Apr 19 | - | Homework 10 | Homework 10 discussion. |
| Apr 21 | 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 24 | - | - | Sharing Math Field Day experiences. Final Project |
| Apr 26 | - | Homework 11 | Homework 11 discussion. Proportional reasoning in geometry (similarity). Areas and volumes of similar figures/solids. Problems on similarity Ratios, rates, proportional reasoning. Math club problems Study Guide and Sample Problems |
| College Integration Bee. Flyer | |||
| Apr 28 | 9:45-11:30 AM. Math Circle, grades 4-10. | ||
| May 1 | - | - | Test 3. |
| May 3 | - | Homework 12 | Homework 12 discussion. Presentations: Field Experience |
| May 8 | - | - | Presentations: Field Experience (cont.) |
| May 10 | Faculty consultation day. Consultation hours: 9-12 and 1-3 | ||
| May 12 | 9:45-11:30 AM and approx. 12:30-2:30. Math Circle and grading contest, grades 8-10. | ||
| May 17 | - | - | Final Project due: submit via email (typed in LaTeX) by 11:59 PM. |