Math 149S. Capstone Mathematics for Teachers. Spring 2022.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Feb 2 | Last day to ADD classes without permission | ||
| Feb 15 | Last day to DROP classes without a serious and compelling reason and without a grade of W (withdrawal) listed on university transcript | ||
| Apr 20 | Last day to DROP classes for a serious and compelling reason | ||
| See registration calendar for other important dates | |||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 20 | - | - | Introduction. Syllabus and Schedule. Overview of service learning. Math Circle, AMC, Math Kangaroo, Math Field Day, practice sessions. Sign-up sheet. |
| Jan 25 | Service Learning and Students
What is Service Learning? A Student's Guide to Successful Service Learning |
- | More on service learning.
Technology. LaTeX: On-line collaborative LaTeX compilator (Overleaf), On-line LaTeX manual, Sample slides. TikZ package: Sample file, Manual. |
| Jan 26 | 5:30PM-7:30PM, via Zoom. Math Circle, grades 9-12 - participants welcome. | ||
| Jan 27 | - | - | TikZ package continued |
| Jan 29 | 9:50-11:30 AM, via Zoom. Math Circle, grades 4-9 - observers welcome, grades 8-9 - helper needed. | ||
| Feb 1 | - | - | 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-7:00PM, via Zoom. AMC 8 solutions, mostly grades 6-8, observers welcome. | |||
| Feb 3 | Bases other than 10 | Homework 1 | Homework 1 discussion. Bases other than 10, definition, examples, applications, problems. Math club problems, Solutions. |
| Feb 5 | 10:00 AM-12:00 PM grades 5-6 and 9-10, 1:30-3:15 PM grades 3-4, 1:30-3:30 PM grades 7-8. Via Zoom.
Math Kangaroo Prep Grades 5-6 and 7-8 leaders needed; grades 9-10 participants welcome. |
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| Feb 8 | - | Other bases cont. Fractions in other bases. Place value problems. |
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| Feb 9 | 5:30PM-7:30PM, via Zoom. Math Circle, grades 9-12 - participants welcome. | ||
| Feb 10 | - | Homework 2 | Homework 2 discussion. Counting (combinatorics). MFD Prep problems, Solutions, Math club problems, Solutions. |
| Feb 12 | 9:50-11:30 AM. Math Circle, grades 4-9 - observers welcome, grades 8-9 - helper needed. | ||
| Feb 15 | - | - | Combinatorics cont. Binomial coefficients (n choose k). Binomial Theorem. Fresno Math Circle 7-8 problems, Fresno Math Circle 11-12 problems. |
| Feb 17 | - | Homework 3 | Homework 3 discussion.
Review: Study Guide and Sample Problems |
| Feb 19 | 10:00-11:30 AM grades 1-2, 10:00 AM-12:00 PM grades 5-6 and 9-10, 1:30-3:15 PM grades 3-4, 1:30-3:30 PM grades 7-8 and 11-12. Via Zoom.
Math Kangaroo Prep Grades 1-2, 3-4, 5-6, and 7-8 leaders needed; grades 9-10 and 11-12 participants welcome. |
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| Feb 22 | - | - | Test 1 (on topics from Divisibility to Binomial Theorem). |
| Feb 23 | 5:30PM-7:30PM, via Zoom. Math Circle, grades 9-12 - participants welcome. | ||
| Feb 24 | Homework 4: Service Learning Plan, First Draft | Probability.
Fresno Math Circle 11-12 problems: discrete probability, continuous probability. |
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| Feb 26 | 9:50-11:30 AM, via Zoom. Math Circle, grades 4-9 - observers welcome, grades 8-9 - helper needed. | ||
| Feb 28 | 5:30-7:30PM, via Zoom. Math Field Day practice, grades 9-12 - leaders needed. | ||
| Mar 1 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | 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. |
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| Mar 3 | - | 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. Real numbers. Construction of real numbers as equivalence classes of Cauchy sequences of rational numbers. |
| Mar 5 | 10:00 AM-12:00 PM grades 1-2, 5-6, and 9-10, 1:30-3:30 PM grades 3-4, 7-8, and 11-12. Via Zoom.
Math Kangaroo Prep Grades 1-2, 3-4, 5-6, and 7-8 leaders needed; grades 9-10 and 11-12 participants welcome. |
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| Mar 8 | - | - | Complex numbers. Definition and representation in R2 using rectangular and polar coordinates. Geometric interpretation of complex numbers multiplication. |
| Mar 9 | 5:30PM-7:30PM, via Zoom. Math Circle, grades 9-12 - participants welcome. | ||
| Mar 10 | - | Homework 6 | Homework 6 discussion. Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields. |
| 5:00-7:00PM, via Zoom. Math Field Day practice, grades 6-8 - leaders needed. | |||
| Mar 12 | 9:50-11:30 AM, via Zoom. Math Circle, grades 4-9 - observers welcome, grades 8-9 - helper needed. | ||
| Mar 15 | - | - | Functions. Definitions of important terms (function, domain, codomain, range, graph, intercept, root). |
| Mar 17 | - | Homework 7 | Review: Study Guide and Sample Problems |
| 4:30-7:30PM, IT 294. Math Kangaroo Competition, grades 1-12 - helpers needed. | |||
| Mar 22 | - | - | Test 2 (on topics from Probability to Algebraic Structures). |
| Mar 23 | 5:30PM-7:30PM, via Zoom. Math Circle, dedicated to MFD practice, grades 9-12 - participants welcome. | ||
| Mar 24 | - | Homework 8: Service Learning Plan, Final Version | Equations. The concept of equation. Questions. |
| Mar 26 | 9:50-11:30 AM, via Zoom. Math Circle, grades 4-9 - observers welcome, grades 8-9 - helper needed. | ||
| 1:00PM-3:00PM, PB 011. Math Field Day Practice, grades 6-8 - leaders needed. | |||
| Mar 29 | - | - | Polynomials. Polynomial equations. Roots and graphs of polynomials. Solving polynomial equations and inequalities.
Overleaf file with this discussion. |
| Mar 31 | Cesar Chavez Day - no classes | ||
| Apr 2 | 10:00 AM-12:00 PM, via Zoom. Math Kangaroo Solutions and Awards, grades 1-12 - leaders needed. | ||
| 2:00PM-approx.4:30PM, S2 109. Central Valley Integration Bee,
High School/College/Fresno State - participants, observers welcome.
To participate, register by Thursday, March 31 at the above link. |
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| Apr 5 | - | - | Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities.
Overleaf file with this discussion. Quadratic formula. Factoring quadratic polynomials. Vieta's formulas. Math Circle materials. |
| Apr 6 | 5:30PM-7:30PM, via Zoom. Math Circle, grades 9-12 - participants welcome. | ||
| Apr 7 | - | Homework 9 | Homework 9 questions/answers. Geometry. Proofs of the Pythagorean theorem. Coordinate Geometry. Distance formula. Equations of circle and ellipse. Coordinate geometry problems. |
| 5:30-7:30PM, PB 136. Math Field Day practice session, grades 9-12 - leaders needed. | |||
| Apr 9 | 9:50-11:30 AM. Math Circle, grades 4-9 - observers welcome, grades 8-9 - helper needed. | ||
| Apr 12 | Spring break | ||
| Apr 14 | Spring break | ||
| Apr 19 | - | - | Similarity. Areas and volumes of similar figures/solids.
Math club problems. More problems on similarity. |
| Apr 20 | 5:30PM-7:30PM, via Zoom. Math Circle, grades 9-12 - participants welcome. | ||
| Apr 21 | - | Homework 10 | Homework 10 discussion. Proportional reasoning |
| Apr 23 | 9:50-11:30 AM, via Zoom. Math Circle, grades 4-9 - observers welcome, grades 8-9 - helper needed. | ||
| Apr 26 | - | - | Math Field Day games. Final Project |
| Apr 28 | - | Homework 11 | Review: Study Guide and Sample Problems |
| Apr 30 | Math Field Day, grades 6-12 - helpers needed. On campus. | ||
| May 3 | - | - | Test 3 (on topics from Functions to Similarity). |
| May 4 | 5:30PM-7:30PM, via Zoom. Math Circle, grades 9-12 - participants welcome. | ||
| May 5 | - | - | Presentations: Service Learning |
| May 7 | Time TBD. Via ZoomMath Circle, grades 8-9 - helpers needed. | ||
| May 10 | - | - | Presentations: Service Learning (cont.) |
| May 12 | Faculty consultation day. Consultation hours: 9:30-10:30 in PB 340 (for all classes), 1-2 in S2 321 (for Math 149 only) | ||
| May 13 | Faculty consultation day. Consultation hours: 9-11 in PB 340 (for all classes) | ||
| May 17 | - | - | Final Project due 11:59 PM. |