Discussions

How scales help to represent or mis-represent data in histograms.

Introduces students to the basics of reducing fractions and learning to compare fractions.

Introduces the notion of using modular arithmetic to encode messages.

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

Introduces the concept of the distributive property.

Introduces the concept of elapsed time and teaches students how to calculate elapsed time.

Demonstrates how fractions are added and subtracted.

Explains multiplication and division of fractions.

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

Introduces the concept of an integer.

Introduces the Division of Integers.

Introduction of elementary set operations through internet searching.

Introduces students to estimation.

This discussion shows students how to multiply with fractions and mixed numbers.

Introduces the idea of patterns in numbers and discusses sequences.

Discusses what individual digits represent in multi-digit integers.

Introduces elementary students to sets and elements using shapes.

Reviews long division of integers and modular arithmetic.

Students will learn about classifying angles as acute, right, or obtuse.

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

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

Introduces the concept of elapsed time and teaches students how to calculate elapsed time.

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 students to finding areas and perimeters of irregular shapes on a grid.

Introduces students to the Pythagorean theorem with explanations on what it means and how to use it.

Defines symmetry and demonstrates different types of plane symmetry.

Shows how the set of all Julia Sets are used to create the classic Mandelbrot fractal.

Introduces students to trapezoids and isosceles trapezoids and defines the characteristics necessary to determine each shape.

Examines the mathematical properties of tessellations.

How scales help to represent or mis-represent data in histograms.

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

Shows students why a function must pass the vertical line test to be a function.

Interpreting graphs and their how curved lines represent velocity on a graph of distance vs. time.

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

Introduces students to linear inequalities.

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

Defining and discussing the concepts of central measures of tendency.

Discusses processes for solving one step algebra problems.

A discussion about what the polar coordinate system is and how to graph a point in this system.

Introduces students to the Pythagorean theorem with explanations on what it means and how to use it.

Introduces 2 variable functions as ordered pairs and how to operate perform operations on ordered pairs.

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

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

Introduction of elementary set operations and their connections with probability.

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

Questions about dice lead to a discussion of polyhedra and geometric probability.

Introduction and initial discussion of the concept of probability.

Defining, comparing and contrasting probability with statistics.

Different methods for random fair choice between several numbers.

Discussion of tables as a convenient way to store and count outcomes.

Some problems are tricky; probability theory provides unique ways to check solutions.

How to build box plots, including the two different ways to determine interquartile range.

Discusses the correlation coefficient, r, through scatter plots.

Introduces graphing independent and dependent variables.

Introduces the line of best fit through the use of scatter plots with outliers.

Students learn about the difference between numerical data and categorical data.

Discusses the benefits of using a pie chart.

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

Introduces Stem-and-Leaf Plots to students.

Explains the differences between univariate data and bivariate data.

How class interval size influences the look and interpretation of histograms.

Introduces the notion of chaos as the breakdown in predictability.

Interpreting graphs and their how curved lines represent velocity on a graph of distance vs. time.

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

Reviews Mandelbrot's defining characteristics for fractal objects.

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

The proper meaning of the term fair.

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

Shows students why a function must pass the vertical line test to be a function.

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

Introduces the concept of an integer.

Introduces the Division of Integers.

Introduction of elementary set operations through internet searching.

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

Discusses what individual digits represent in multi-digit integers.

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.

Introduction and initial discussion of the concept of probability.

Defining, comparing and contrasting probability with statistics.

Discusses the idea of recursion as it pertains to fractals and sequences.

Discusses how fractals are self-similar objects.

Introduces elementary students to sets and elements using shapes.

Shows how the set of all Julia Sets are used to create the classic Mandelbrot fractal.

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

Introduces concepts needed to create Venn diagrams.

Discusses integer multiples as repeated addition.

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

A discussion about graphing functions in the polar coordinate system.