|
| Algorithm Discussion |
Introduces the concept of algorithms and how algorithms affect mathematics.
Grades 6-8, Grades 9-12
| | Class Interval Discussion: Scale and Impression |
How scales help to represent or mis-represent data in histograms.
Grades 6-8, Grades 9-12
| | Clocks and Modular Arithmetic Discussion |
Shows how modular arithmetic can be thought of as clock arithmetic.
Grades 6-8, Grades 9-12
| | Comparing Fractions Discussion |
Introduces students to the basics of reducing fractions and learning to compare fractions.
Grades 6-8
| | Cryptography and Ciphers Discussion |
Introduces the notion of using modular arithmetic to encode messages.
Grades 6-8
| | Decimals Discussion |
Deals with converting fractions into decimals.
Grades 6-8
| | Dimension and Scale Discussion |
Discusses fractal dimension, how that dimension relates to scale, and the formula needed to calculate the fractal dimension of an object.
Grades 6-8, Grades 9-12
| | Dimension for Irregular Fractals Discussion |
Discusses the problem of determining the fractal dimension of irregular fractals and how the scale is indeterminite in these fractals.
Grades 6-8, Grades 9-12
| | Divisibility Discussion |
The question of fairness in a game of two dice leads to the concept of divisibility.
Grades 6-8, Grades 9-12
| | Exponents and Logarithms Discussion |
Gives an introduction to the concept of a logarithms and shows how logs can be used to calculate fractal dimension.
Grades 6-8, Grades 9-12
| | Fraction Adding and Subtracting |
Demonstrates how fractions are added and subtracted.
Grades 6-8
| | Fraction Multiplying and Dividing |
Explains multiplication and division of fractions.
Grades 6-8
| | Fractions Discussion |
Discusses the introductory concept of a fraction.
Grades 6-8
| | Infinity and Iteration Discussion |
Discusses infinity, iterations and limits by referencing fractals and sequences.
Grades 6-8, Grades 9-12
| | Integer Addition and Subtraction Discussion |
Introduces the addition and subtraction of integers.
Grades 3-5, Grades 6-8
| | Integer Discussion |
Introduces the concept of an integer.
Grades 3-5, Grades 6-8
| | Integer Division Discussion |
Introduces the Division of Integers.
Grades 3-5, Grades 6-8
| | Integer Multiplication Discussion |
Introduces the multiplication of integers.
Grades 3-5, Grades 6-8
| | Internet Search and Set Operations Discussion |
Introduction of elementary set operations through internet searching.
Grades 6-8, Grades 9-12
| | Making Estimates Discussion |
Introduces students to estimation.
Grades 3-5, Grades 6-8
| | Multiplying Decimals and Mixed Numbers Discussion |
A review of the definition of decimals and mixed numbers as well as a description of multiplying decimal numbers.
Grades 6-8
| | Percents Discussion |
Covers the basics of converting fractions into percents.
Grades 6-8
| | Probability of Simultaneous Events Discussion |
Computing exact probabilities for the Racing Game leads to the formula for the probability of simultaneous events.
Grades 6-8, Grades 9-12
| | What are Multiples Discussion |
Discusses integer multiples as repeated addition.
Grades 3-5, Grades 6-8
| | What are Remainders Discussion |
Reviews long division of integers and modular arithmetic.
Grades 3-5, Grades 6-8
|
| Angles Discussion |
Reviews vocabulary and concepts related to the geometry of angles.
Grades 6-8, Grades 9-12
| | Area Discussion |
Looks at finding areas of irregular shapes on a grid.
Grades 3-5, Grades 6-8
| | Clocks and Modular Arithmetic Discussion |
Shows how modular arithmetic can be thought of as clock arithmetic.
Grades 6-8, Grades 9-12
| | Color in Tessellations Discussion |
Explains the effect that color has on the patterns we see in tessellations.
Grades 6-8, Grades 9-12
| | Dimension and Scale Discussion |
Discusses fractal dimension, how that dimension relates to scale, and the formula needed to calculate the fractal dimension of an object.
Grades 6-8, Grades 9-12
| | Dimension for Irregular Fractals Discussion |
Discusses the problem of determining the fractal dimension of irregular fractals and how the scale is indeterminite in these fractals.
Grades 6-8, Grades 9-12
| | From Geometry to Probability Discussion |
Leads the idea of probability from counting chances to measuring proportions of areas.
Grades 6-8, Grades 9-12
| | Lines, Rays, Line Segments, and Planes |
Introduces students to lines, rays, line segments, and planes.
Grades 3-5, Grades 6-8
| | Optical Illusions Discussion |
Looks at several optical illusions.
Grades 6-8, Grades 9-12
| | Parallelograms |
Introduces students to parallelograms and rhombbi and defines the characteristics necessary to determine each shape.
Grades 6-8, Grades 9-12
| | Perimeter Explorer Discussion |
Introduces a method for finding perimeters of irregular shapes on a grid.
Grades 3-5, Grades 6-8
| | Plane Figure Fractals Discussion |
Compares fractals with one and two dimensional generators.
Grades 6-8, Grades 9-12
| | Polyhedra Discussion |
Questions about dice lead to a discussion of polyhedra and geometric probability.
Grades 6-8
| | Prisoners and Escapees--Julia Sets Discussion |
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.
Grades 6-8, Grades 9-12
| | Properties of Fractals Discussion |
Reviews Mandelbrot's defining characteristics for fractal objects.
Grades 6-8, Grades 9-12
| | Quadrilaterals |
Introduces students to quadrilaterals and defines the characteristics of the polygon.
Grades 3-5, Grades 6-8
| | Rectangles |
Introduces students to rectangles and squares and defines the characteristics necessary to determine each shape.
Grades 3-5, Grades 6-8
| | Recursion Discussion |
Discusses the idea of recursion as it pertains to fractals and sequences.
Grades 6-8, Grades 9-12
| | Self-Similarity Discussion |
Discusses how fractals are self-similar objects.
Grades 6-8, Grades 9-12
| | Shape Explorer Discussion |
Introduces students to finding areas and perimeters of irregular shapes on a grid.
Grades 3-5, Grades 6-8
| | Squaring the Triangle |
Introduces students to the Pythagorean theorem with explanations on what it means and how to use it.
Grades 6-8, Grades 9-12
| | Standard Deviation Discussion |
Introduces standard deviaton and describes how to compute it.
Grades 9-12
| | Symmetry in Tessellations Discussion |
Defines symmetry and demonstrates different types of plane symmetry.
Grades 6-8, Grades 9-12
| | Tessellations in the World Discussion |
Looks at the history of tessellations, why they are important and examines some patterns in nature and art.
Grades 6-8, Grades 9-12
| | The Mandelbrot Set Discussion |
Shows how the set of all Julia Sets are used to create the classic Mandelbrot fractal.
Grades 6-8, Grades 9-12
| | Translations, Reflections, and Rotations Discussion |
Introduces students to the concepts of transformations.
Grades 6-8, Grades 9-12
| | Trapezoids |
Introduces students to trapezoids and isosceles trapezoids and defines the characteristics necessary to determine each shape.
Grades 3-5, Grades 6-8
| | Understanding Surface Area and Volume Discussion |
Introduces students to the concepts of surface area and volume.
Grades 6-8
| | What are Tessellations Discussion |
Examines the mathematical properties of tessellations.
Grades 6-8, Grades 9-12
|
| "The Bell Curve" Revisited |
Finishes up the discussion of the book as well as exploring individual differences versus group expected values.
Grades 6-8, Grades 9-12
| | Class Interval Discussion: Scale and Impression |
How scales help to represent or mis-represent data in histograms.
Grades 6-8, Grades 9-12
| | Dimension and Scale Discussion |
Discusses fractal dimension, how that dimension relates to scale, and the formula needed to calculate the fractal dimension of an object.
Grades 6-8, Grades 9-12
| | Exponents and Logarithms Discussion |
Gives an introduction to the concept of a logarithms and shows how logs can be used to calculate fractal dimension.
Grades 6-8, Grades 9-12
| | From Graphs to Function Machines and Back Discussion |
Demonstrates the initial connections between functions and their graphs.
Grades 6-8
| | Functions and the Vertical Line Test |
Shows students why a function must pass the vertical line test to be a function.
Grades 6-8, Grades 9-12
| | Functions as Processes or Rules Discussion: "Function Machines" |
Discusses the notion of functions as a "number machine" with input and output.
Grades 6-8
| | Gathering Information from Graphs Discussion |
Interpreting graphs and their how curved lines represent velocity on a graph of distance vs. time.
Grades 6-8, Grades 9-12
| | Graphing Time, Distance, Velocity and Acceleration |
Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.
Grades 6-8, Grades 9-12
| | Impossible Graphs Discussion |
Shows what makes a graph represent impossible situations and how to avoid these problems.
Grades 6-8
| | Introduction to the Coordinate Plane and Coordinates Discussion |
Introduces coordinates through the idea of number lines.
Grades 6-8
| | Linear Functions |
Discusses functions of the form y = ___*x + ___.
Grades 6-8
| | Mean, Median, and Mode Discussion |
Defining and discussing the concepts of central measures of tendency.
Grades 6-8, Grades 9-12
| | Multi-Step Functions Discussion |
Discusses the notion of composite functions as several "number machines" with the output of one machine becoming the input of another.
Grades 6-8, Grades 9-12
| | Slope and Y-intercept Discussion |
Discusses slope and y-intercept and how they affect a graph.
Grades 6-8, Grades 9-12
| | Squaring the Triangle |
Introduces students to the Pythagorean theorem with explanations on what it means and how to use it.
Grades 6-8, Grades 9-12
| | The Normal Distribution and "The Bell Curve" Discussion |
An introduction to the normal distribution and the debate over the 1994 book, "The Bell Curve."
Grades 6-8, Grades 9-12
| | Two Variable Functions Discussion |
Introduces 2 variable functions as ordered pairs and how to operate perform operations on ordered pairs.
Grades 6-8, Grades 9-12
|
| Chaos Discussion |
Introduces the notion of chaos as the breakdown in predictability.
Grades 6-8, Grades 9-12
| | Chaos is Everywhere Discussion |
Shows the wide spread use of fractals and chaos in science and nature.
Grades 6-8, Grades 9-12
| | Conditional Probability Discussion |
Introduction of the concept of conditional probability and discussion of its application for problem solving.
Grades 6-8, Grades 9-12
| | Divisibility Discussion |
The question of fairness in a game of two dice leads to the concept of divisibility.
Grades 6-8, Grades 9-12
| | Equally Likely (Fair) Choice Discussion |
The proper meaning of the term fair.
Grades 3-5, Grades 6-8
| | Events and Set Operations Discussion |
Introduction of elementary set operations and their connections with probability.
Grades 6-8, Grades 9-12
| | Expected Value Discussion |
Introduction and discussion of the concept of expected value.
Grades 6-8, Grades 9-12
| | From Geometry to Probability Discussion |
Leads the idea of probability from counting chances to measuring proportions of areas.
Grades 6-8, Grades 9-12
| | Pascal |
Introduces Pascal's Triangle in terms of probability.
Grades 6-8, Grades 9-12
| | Polyhedra Discussion |
Questions about dice lead to a discussion of polyhedra and geometric probability.
Grades 6-8
| | Probability and Outcome Discussion |
Introduction and initial discussion of the concept of probability.
Grades 6-8, Grades 9-12
| | Probability of Simultaneous Events Discussion |
Computing exact probabilities for the Racing Game leads to the formula for the probability of simultaneous events.
Grades 6-8, Grades 9-12
| | Probability vs. Statistics Discussion |
Defining, comparing and contrasting probability with statistics.
Grades 6-8, Grades 9-12
| | Properties of Fractals Discussion |
Reviews Mandelbrot's defining characteristics for fractal objects.
Grades 6-8, Grades 9-12
| | Random Number Generators Discussion |
Different methods for random fair choice between several numbers.
Grades 3-5, Grades 6-8
| | Replacement Discussion |
Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.
Grades 6-8, Grades 9-12
| | Tables and Combinatorics Discussion |
Discussion of tables as a convenient way to store and count outcomes.
Grades 6-8, Grades 9-12
| | Think and Check! Discussion |
Some problems are tricky; probability theory provides unique ways to check solutions.
Grades 6-8, Grades 9-12
| | Trees as Data Structures Discussion |
Questions about games with more than two dice lead to discussion of trees as another kind of data structure.
Questions about games with more than two dice lead to discussion of trees as another kind of data structure.
Grades 6-8, Grades 9-12
|
| Bivariate Data Relations |
Introduces positive and negative relationships and independent and dependent variables of bivariate data.
Grades 6-8, Grades 9-12
| | Box Plot Discussion |
How to build box plots, including the two different ways to determine interquartile range.
Grades 6-8, Grades 9-12
| | Continuous Distributions Discussion: Infinite Trials, Infinite Possibilities |
Discusses continuous versus discrete distributions.
Grades 6-8, Grades 9-12
| | Correlation Coefficients |
Discusses the correlation coefficient, r, through scatter plots.
Grades 6-8, Grades 9-12
| | Finding Residuals |
Introduces how to calculate residuals of bivariate data.
Grades 6-8, Grades 9-12
| | Graphing and Interpreting Bivariate Data |
Introduces graphing independent and dependent variables.
Grades 6-8, Grades 9-12
| | Histograms vs. Bar Graphs Discussion |
Differences and similarities between the two types of graphs.
Grades 6-8
| | Line of Best Fit |
Introduces the line of best fit through the use of scatter plots with outliers.
Grades 6-8, Grades 9-12
| | Mean, Median, and Mode Discussion |
Defining and discussing the concepts of central measures of tendency.
Grades 6-8, Grades 9-12
| | Probability vs. Statistics Discussion |
Defining, comparing and contrasting probability with statistics.
Grades 6-8, Grades 9-12
| | Replacement Discussion |
Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.
Grades 6-8, Grades 9-12
| | Standard Deviation Discussion |
Introduces standard deviaton and describes how to compute it.
Grades 9-12
| | Stem-and-Leaf Plots Discussion |
Introduces Stem-and-Leaf Plots to students.
Grades 6-8, Grades 9-12
| | The Normal Distribution and "The Bell Curve" Discussion |
An introduction to the normal distribution and the debate over the 1994 book, "The Bell Curve."
Grades 6-8, Grades 9-12
| | Univariate Data and Bivariate Data |
Explains the differences between univariate data and bivariate data.
Grades 6-8, Grades 9-12
| | Using Residuals to Identify a Line of Good Fit |
Explains how residuals can determine whether a line is a good fit or a bad fit for a set of bivariate data.
Grades 6-8, Grades 9-12
| | Vertical Scale Discussion: Increase or Decrease? |
How class interval size influences the look and interpretation of histograms.
Grades 6-8
|
| Algorithm Discussion |
Introduces the concept of algorithms and how algorithms affect mathematics.
Grades 6-8, Grades 9-12
| | Chaos Discussion |
Introduces the notion of chaos as the breakdown in predictability.
Grades 6-8, Grades 9-12
| | Chaos is Everywhere Discussion |
Shows the wide spread use of fractals and chaos in science and nature.
Grades 6-8, Grades 9-12
| | Gathering Information from Graphs Discussion |
Interpreting graphs and their how curved lines represent velocity on a graph of distance vs. time.
Grades 6-8, Grades 9-12
| | Graphing Time, Distance, Velocity and Acceleration |
Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.
Grades 6-8, Grades 9-12
| | Impossible Graphs Discussion |
Shows what makes a graph represent impossible situations and how to avoid these problems.
Grades 6-8
| | Infinity and Iteration Discussion |
Discusses infinity, iterations and limits by referencing fractals and sequences.
Grades 6-8, Grades 9-12
| | Properties of Fractals Discussion |
Reviews Mandelbrot's defining characteristics for fractal objects.
Grades 6-8, Grades 9-12
|
|
|
|
|
