District Curriculum Overview

 

Subject:   Mathematics                                      Course:  338 Quantitative Reasoning                                      Grade Level: 9 – 12

 

Concepts

Topics/Units

Content/Skills

Essential Activities/Agreements

Developing some tools in the realm of number theory

Number Theory

·         Unique Sums

·         Modular Arithmetic

·         Infinite Series

·         Alternatives to Base 10 (both whole numbers and fractions)

·         Quick Basic programming

·         Portfolio

·         Homework assignments

·         Class participation

Observing and analyzing behavior of dynamical systems.

Solving for equilibrium.

Distinguishing between converging systems, periodic systems, and chaotic systems.

Dynamical Systems

 

·         Linear Recursion

·         Parameters versus variables

·         Logistic Model

·         Convergence & Periodicity

·         Web diagrams (graphical iteration)

·         Bifurcation diagram

·         Portfolio

·         Homework assignments

·         Class participation

·         Midyear exam

Understanding chaos and following recursive rules to create fractals.

Distinguish between topological dimension and self-similarity dimension.

Chaos/Fractals

·         Sensitivity versus stability

·         Arithmetic in the complex plane

·         Julia Sets and Mandelbrot Set

·         Self-similarity

·         Fractional Dimension

·         Portfolio

·         Homework assignments

·         Class participation

Understanding randomness and

importance of sample size.

Using counting methods, including multiplication principle, factorial, trees, and “choose” to determine probabilities

Chance

·         Randomness

·         Polling simulations

·         Combinatorics

·         Margin of error/confidence levels

 

·         Portfolio

·         Homework assignments

·         Class participation

·         Final exam

Using estimation techniques for Fermi problems.

Using one-to-one correspondence in transfinite arithmetic.

Establishing countability of the rational numbers, and uncountability of the continuum

Cardinality

·         Very large numbers

·         Countable infinity

·         Uncountable infinity

·         Cantor set

·         Transfinite arithmetic

·         Continuum hypothesis

·         Portfolio

·         Homework assignments

·         Class participation