Discussions

Discusses the base ten system and how it differs from other base number systems.

Shows how modular arithmetic can be thought of as clock arithmetic.

Discusses methods of converting from the base ten system to another base number system.

Deals with converting fractions into decimals.

Discusses the problem of determining the fractal dimension of irregular fractals and how the scale is indeterminite in these fractals.

The question of fairness in a game of two dice leads to the concept of divisibility.

Gives an introduction to the concept of a logarithms and shows how logs can be used to calculate fractal dimension.

Discusses how to convert from fractions to decimals.

Discusses the introductory concept of a fraction.

Discusses infinity, iterations and limits by referencing fractals and sequences.

Introduces the addition and subtraction of integers.

Introduces the multiplication of integers.

Introduces the concepts of the additive inverse and multiplicative inverse and how they are used when solving equations.

A review of the definition of decimals and mixed numbers as well as a description of multiplying decimal numbers.

Introduces the idea of patterns in numbers and discusses sequences.

Discusses what individual digits represent in multi-digit integers.

Discusses integer multiples as repeated addition.

Looks at finding areas of irregular shapes on a grid.

Explains the effect that color has on the patterns we see in tessellations.

Discusses the problem of determining the fractal dimension of irregular fractals and how the scale is indeterminite in these fractals.

Discusses the process of finding the surface area of a rectangular prism.

Introduces the concept of volume of a rectangular prism.

Leads the idea of probability from counting chances to measuring proportions of areas.

Looks at several optical illusions.

Introduces a method for finding perimeters of irregular shapes on a grid.

Compares fractals with one and two dimensional generators.

Defines the notion of prisoners and escapees as they pertain to iterative functions. A prisoner ultimately changes to a constant while escapees iterate to infinity.

Reviews Mandelbrot's defining characteristics for fractal objects.

Introduces students to rectangles and squares and defines the characteristics necessary to determine each shape.

Discusses how fractals are self-similar objects.

Introduces the concept of the slant height of a triangle and how to find its measure using the Pythagorean theorem.

Introduces standard deviaton and describes how to compute it.

Looks at the history of tessellations, why they are important and examines some patterns in nature and art.

Introduces students to the concepts of transformations.

Introduces students to the concepts of surface area and volume.

Discusses fractal dimension, how that dimension relates to scale, and the formula needed to calculate the fractal dimension of an object.

Demonstrates the initial connections between functions and their graphs.

Discusses the notion of functions as a "number machine" with input and output.

Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.

Shows what makes a graph represent impossible situations and how to avoid these problems.

Introduces coordinates through the idea of number lines.

Discusses functions of the form y = ___*x + ___.

Discusses the notion of composite functions as several "number machines" with the output of one machine becoming the input of another.

Discusses slope and y-intercept and how they affect a graph.

An introduction to the normal distribution and the debate over the 1994 book, "The Bell Curve."

Introduction of the concept of conditional probability and discussion of its application for problem solving.

The proper meaning of the term fair.

Introduction and discussion of the concept of expected value.

Introduces Pascal's Triangle in terms of probability.

Discusses the relationship between geometry and probability.

Computing exact probabilities for the Racing Game leads to the formula for the probability of simultaneous events.

Reviews Mandelbrot's defining characteristics for fractal objects.

Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.

This lesson teaches students about the differences between theoretical and experimental probabilities.

Questions about games with more than two dice lead to discussion of trees as another kind of data structure.

Introduces positive and negative relationships and independent and dependent variables of bivariate data.

Discusses continuous versus discrete distributions.

Introduces how to calculate residuals of bivariate data.

Differences and similarities between the two types of graphs.

Defining and discussing the concepts of central measures of tendency.

Explains how outliers affect data.

Defining, comparing and contrasting probability with statistics.

Introduces standard deviaton and describes how to compute it.

An introduction to the normal distribution and the debate over the 1994 book, "The Bell Curve."

Explains how residuals can determine whether a line is a good fit or a bad fit for a set of bivariate data.

Shows the wide spread use of fractals and chaos in science and nature.

Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.

Discusses infinity, iterations and limits by referencing fractals and sequences.

Gives an introduction to sets and elements.

Shows the wide spread use of fractals and chaos in science and nature.