Algebra (26)
Aids in the understanding of the geometric and algebraic derivations of conic sections.
Discusses the correlation coefficient, r, through scatter plots.
Introduces the notion of using modular arithmetic to encode messages.
Introduces the concept of the distributive property.
Gives an introduction to the concept of a logarithms and shows how logs can be used to calculate fractal dimension.
Demonstrates the initial connections between functions and their graphs.
Shows students why a function must pass the vertical line test to be a function.
Discusses the notion of functions as a "number machine" with input and output.
Introduces students to reading and interpreting graphs.
Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.
Introduces the concepts of the additive identity and multiplicative identity and how they are used when solving equations.
Shows what makes a graph represent impossible situations and how to avoid these problems.
Introduces and explains the concept of independent and dependent variables and their applications in real-world problems.
Introduces students to linear inequalities.
Introduces coordinates through the idea of number lines.
Introduces the concepts of the additive inverse and multiplicative inverse and how they are used when solving equations.
Introduces the line of best fit through the use of scatter plots with outliers.
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 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.
A discussion about graphing functions in the polar coordinate system.
Discusses the idea of recursion as it pertains to fractals and sequences.
Discusses slope and y-intercept and how they affect a graph.
Introduces 2 variable functions as ordered pairs and how to operate perform operations on ordered pairs.
Explains how residuals can determine whether a line is a good fit or a bad fit for a set of bivariate data.
Calculus (2)
A discussion about what the polar coordinate system is and how to graph a point in this system.
A discussion about graphing functions in the polar coordinate system.
Discrete (41)
Shows how modular arithmetic can be thought of as clock arithmetic.
Introduction of the concept of conditional probability and discussion of its application for problem solving.
Introduces the notion of using modular arithmetic to encode messages.
Introduces the proper meaning of the term fair.
Introduction of elementary set operations and their connections with probability.
Leads the idea of probability from counting chances to measuring proportions of areas.
Demonstrates the initial connections between functions and their graphs.
Shows students why a function must pass the vertical line test to be a function.
Discusses the notion of functions as a "number machine" with input and output.
Shows what makes a graph represent impossible situations and how to avoid these problems.
Discusses infinity, iterations and limits by referencing fractals and sequences.
Introduces the concept of an integer.
Introduces the addition and subtraction of integers.
Introduces the division of integers.
Introduces the multiplication of integers.
Introduction of elementary set operations through internet searching.
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.
Introduces Pascal's Triangle in terms of probability.
Discusses what individual digits represent in multi-digit integers.
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.
Introduction and initial discussion of the concept of probability.
Computing exact probabilities for the Racing Game leads to the formula for the probability of simultaneous events.
Defining, comparing and contrasting probability with statistics.
Discusses the relationship between geometry and probability.
Reviews Mandelbrot's defining characteristics for fractal objects.
Discusses the idea of recursion as it pertains to fractals and sequences.
Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.
Discusses how fractals are self-similar objects.
Gives an introduction to sets and elements.
Introduces elementary students to sets and elements using shapes.
Discussion of tables as a convenient way to store and count outcomes.
Shows how the set of all Julia Sets are used to create the classic Mandelbrot fractal.
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 2 variable functions as ordered pairs and how to operate perform operations on ordered pairs.
Introduces concepts needed to create Venn diagrams.
Introduces concepts needed to create Venn diagrams.
Discusses integer multiples as repeated addition.
Reviews long division of integers and modular arithmetic.
Geometry (45)
Reviews vocabulary and concepts related to the geometry of angles.
Students will learn about classifying angles as acute, right, or obtuse.
Looks at finding areas of irregular shapes on a grid.
Shows how modular arithmetic can be thought of as clock arithmetic.
Explains the effect that color has on the patterns we see in tessellations.
Aids in the understanding of the geometric and algebraic derivations of conic sections.
Aids in the understanding of the relationships among the various conic sections.
Aids in the understanding of cross sections of three-dimensional objects.
Discusses fractal dimension, how that dimension relates to scale, and the formula needed to calculate the fractal dimension of an object.
Discusses the problem of determining the fractal dimension of irregular fractals and how the scale is indeterminite in these fractals.
Introduces the concept of elapsed time and teaches students how to calculate elapsed time.
Teaches students how to calculate ending time given the starting time and elapsed time.
Gives an introduction to the concept of a logarithms and shows how logs can be used to calculate fractal dimension.
Introduces the concept of volume of a rectangular prism.
Introduces the concept of finding volume of a triangular prism
Leads the idea of probability from counting chances to measuring proportions of areas.
Discusses infinity, iterations and limits by referencing fractals and sequences.
Introduces coordinates through the idea of number lines.
Introduces students to lines, rays, line segments, and planes.
Looks at several optical illusions.
Introduces students to parallelograms and rhombbi and defines the characteristics necessary to determine each shape.
Introduces a method for finding perimeters of irregular shapes on a grid.
Introduces a method for finding perimeters of rectangular shapes on a grid.
Compares fractals with one and two dimensional generators.
Questions about dice lead to a discussion of polyhedra and geometric probability.
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.
Discusses the relationship between geometry and probability.
Reviews Mandelbrot's defining characteristics for fractal objects.
Introduces students to quadrilaterals and defines the characteristics of the polygon.
Introduces students to rectangles and squares and defines the characteristics necessary to determine each shape.
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.
Introduces students to finding areas and perimeters of irregular shapes on a grid.
Introduces the concept of the slant height of a triangle and how to find its measure using the Pythagorean theorem.
Introduces students to the Pythagorean theorem with explanations on what it means and how to use it.
Introduces students to the concepts of surface area and volume.
Discusses the process of finding the surface area of a rectangular prism.
Introduces the concept of surface area in relation to a triangular prism
Defines symmetry and demonstrates different types of plane symmetry.
Looks at the history of tessellations, why they are important and examines some patterns in nature and art.
Shows how the set of all Julia Sets are used to create the classic Mandelbrot fractal.
Introduces students to the concepts of transformations.
Introduces students to trapezoids and isosceles trapezoids and defines the characteristics necessary to determine each shape.
Examines the mathematical properties of tessellations.
Modeling (8)
Helps students to understand the differences and similarities between Agent Modeling and Systems Modeling.
Introduces the concept of algorithms and how algorithms affect mathematics.
Introduces the notion of chaos as the breakdown in predictability.
Shows the wide spread use of fractals and chaos in science and nature.
Introduces students to reading and interpreting graphs.
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 and explains the concept of independent and dependent variables and their applications in real-world problems.
Number and Operations (39)
Introduces the concept of algorithms and how algorithms affect mathematics.
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.
Introduces students to the basics of reducing fractions and learning to compare fractions.
Discusses methods of converting from the base ten system to another base number system.
Introduces the notion of using modular arithmetic to encode messages.
Deals with converting fractions into decimals.
Discusses fractal dimension, how that dimension relates to scale, and the formula needed to calculate the fractal dimension of an object.
Discusses the problem of determining the fractal dimension of irregular fractals and how the scale is indeterminite in these fractals.
Introduces the concept of the distributive property.
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.
Demonstrates how fractions are added and subtracted.
Discusses how to convert from fractions to decimals.
Explains multiplication and division of fractions.
Discusses the introductory concept of a fraction.
Introduces the concepts of the additive identity and multiplicative identity and how they are used when solving equations.
Discusses infinity, iterations and limits by referencing fractals and sequences.
Introduces the concept of an integer.
Introduces the addition and subtraction of integers.
Introduces the division of integers.
Introduces the multiplication of integers.
Introduction of elementary set operations through internet searching.
Introduces the concepts of the additive inverse and multiplicative inverse and how they are used when solving equations.
Introduces students to estimation.
A review of the definition of decimals as well as a description of multiplying decimal numbers.
This discussion shows students how to multiply with fractions and mixed numbers.
Introduces the convention of order of operations.
Introduces the idea of patterns in numbers and discusses sequences.
Covers the basics of converting fractions into percents.
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.
Discusses the idea of recursion as it pertains to fractals and sequences.
Discusses how fractals are self-similar objects.
Gives an introduction to sets and elements.
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.
Discusses integer multiples as repeated addition.
Reviews long division of integers and modular arithmetic.
Probability (21)
Introduces the notion of chaos as the breakdown in predictability.
Shows the wide spread use of fractals and chaos in science and nature.
Introduction of the concept of conditional probability and discussion of its application for problem solving.
Discusses continuous versus discrete distributions.
The question of fairness in a game of two dice leads to the concept of divisibility.
Introduces the proper meaning of the term fair.
Introduction of elementary set operations and their connections with probability.
Introduction and discussion of the concept of expected value.
Leads the idea of probability from counting chances to measuring proportions of areas.
Introduces Pascal's Triangle in terms of probability.
Questions about dice lead to a discussion of polyhedra and geometric probability.
Introduction and initial discussion of the concept of probability.
Computing exact probabilities for the Racing Game leads to the formula for the probability of simultaneous events.
Defining, comparing and contrasting probability with statistics.
Discusses the relationship between geometry and probability.
Different methods for random fair choice between several numbers.
Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.
Discussion of tables as a convenient way to store and count outcomes.
This lesson teaches students about the differences between theoretical and experimental probabilities.
Some problems are tricky; probability theory provides unique ways to check solutions.
Questions about games with more than two dice lead to discussion of trees as another kind of data structure.
Science (9)
Introduces the concept of algorithms and how algorithms affect mathematics.
Introduces the notion of chaos as the breakdown in predictability.
Shows the wide spread use of fractals and chaos in science and nature.
Introduces the concept of elapsed time and teaches students how to calculate elapsed time.
Teaches students how to calculate ending time given the starting time and elapsed time.
Introduces the concept of energy and the law of conservation of energy.
Discusses infinity, iterations and limits by referencing fractals and sequences.
Introduces concepts needed to create Venn diagrams.
Introduces concepts needed to create Venn diagrams.
Statistics (25)
Discusses the benefits of using a bar graph to examine data.
Introduces positive and negative relationships and independent and dependent variables of bivariate data.
How to build box plots, including the two different ways to determine interquartile range.
Shows how scales help to represent or misrepresent data in histograms.
Discusses continuous versus discrete distributions.
Discusses the correlation coefficient, r, through scatter plots.
Introduces how to calculate residuals of bivariate data.
Introduces students to reading and interpreting graphs.
Introduces graphing independent and dependent variables.
Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.
Differences and similarities between the two types of graphs.
Shows what makes a graph represent impossible situations and how to avoid these problems.
Introduces the line of best fit through the use of scatter plots with outliers.
Defining and discussing the concepts of central measures of tendency.
Students learn about the difference between numerical data and categorical data.
Explains how outliers affect data.
Discusses the benefits of using a pie chart.
Defining, comparing and contrasting probability with statistics.
Introduces standard deviaton and describes how to compute it.
Introduces Stem-and-Leaf Plots to students.
Finishes up the discussion of the book as well as exploring individual differences versus group expected values.
An introduction to the normal distribution and the debate over the 1994 book, "The Bell Curve."
Explains the differences between univariate data and bivariate data.
Explains how residuals can determine whether a line is a good fit or a bad fit for a set of bivariate data.
How class interval size influences the look and interpretation of histograms.
Trigonometry (3)
A discussion about what the polar coordinate system is and how to graph a point in this system.
A discussion about graphing functions in the polar coordinate system.
Introduces students to the Pythagorean theorem with explanations on what it means and how to use it.