Discussion List
Numberand`Operations • Geometry • Algebra • Probability • Statis
tics • Modeling • Discrete • Other
Number and Operations (36)
Algorithm
Introduces the concept of algorithms and how algorithms affect
mathematics.
(Grades 3-5, Grades 6-8)
Base Ten
Discusses the base ten system and how it differs from other base number
systems.
(Grades 3-5, Grades 6-8)
Class Intervals: Scale and Impression
How scales help to represent or mis-represent data in histograms.
(Grades 6-8, Grades 9-12)
Clocks and Modular Arithmetic
Shows how modular arithmetic can be thought of as clock arithmetic.
(Grades 3-5, Grades 6-8, Grades 9-12)
Comparing Fractions
Introduces students to the basics of reducing fractions and learning to
compare fractions.
(Grades 3-5, Grades 6-8)
1
Converting From Base Ten
Discusses methods of converting from the base ten system to another
base number system.
(Grades 3-5, Grades 6-8, Grades 9-12)
Cryptography and Ciphers
Introduces the notion of using modular arithmetic to encode messages.
(Grades 6-8, Grades 9-12)
Decimals
Deals with converting fractions into decimals.
(Grades 6-8)
Dimension and Scale
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
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)
Distributive Property
Introduces the concept of the distributive property.
(Grades 6-8, Grades 9-12)
Divisibility
The question of fairness in a game of two dice leads to the concept of
divisibility.
(Grades 6-8, Grades 9-12)
2
Elapsed Time
Introduces the concept of elapsed time and teaches students how to
calculate elapsed time.
(Grades 3-5)
Exponents and Logarithms
Gives an introduction to the concept of a logarithms and shows how logs
can be used to calculate fractal dimension.
(Grades 9-12, Undergraduate)
Fraction Adding and Subtracting
Demonstrates how fractions are added and subtracted.
(Grades 3-5, Grades 6-8)
Fraction Conversion
Discusses how to convert from fractions to decimals.
(Grades 3-5, Grades 6-8)
Fraction Multiplying and Dividing
Explains multiplication and division of fractions.
(Grades 6-8)
Fractions
Discusses the introductory concept of a fraction.
(Grades 3-5, Grades 6-8)
Identity Properties
Introduces the concepts of the additive identity and multiplicative identity
and how they are used when solving equations.
(Grades 6-8, Grades 9-12)
3
Infinity and Iteration
Discusses infinity, iterations and limits by referencing fractals and
sequences.
(Grades 6-8, Grades 9-12)
Integer
Introduces the concept of an integer.
(Grades 3-5, Grades 6-8)
Integer Addition and Subtraction
Introduces the addition and subtraction of integers.
(Grades 3-5, Grades 6-8)
Integer Division
Introduces the Division of Integers.
(Grades 6-8)
Integer Multiplication
Introduces the multiplication of integers.
(Grades 6-8)
Internet Search and Set Operations
Introduction of elementary set operations through internet searching.
(Grades 3-5, Grades 6-8, Grades 9-12)
Inverse Properties
Introduces the concepts of the additive inverse and multiplicative inverse
and how they are used when solving equations.
(Grades 6-8, Grades 9-12)
4
Making Estimates
Introduces students to estimation.
(Grades 3-5, Grades 6-8)
Multiplying Decimal Numbers
A review of the definition of decimals and mixed numbers as well as a
description of multiplying decimal numbers.
(Grades 6-8)
Multiplying Fractions and Mixed Numbers
This discussion shows students how to multiply with fractions and mixed
numbers.
(Grades 3-5, Grades 6-8)
Order of Operations
Introduces the convention of order of operations.
(Grades 3-5, Grades 6-8)
Pattern
Introduces the idea of patterns in numbers and discusses sequences.
(Grades 3-5, Grades 6-8)
Percents
Covers the basics of converting fractions into percents.
(Grades 3-5, Grades 6-8)
Place Value
Discusses what individual digits represent in multi-digit integers.
(Grades 3-5)
5
Probability of Simultaneous Events
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
Discusses integer multiples as repeated addition.
(Grades 3-5, Grades 6-8)
What are Remainders
Reviews long division of integers and modular arithmetic.
(Grades 3-5, Grades 6-8)
Geometry (39)
Angles
Reviews vocabulary and concepts related to the geometry of angles.
(Grades 6-8, Grades 9-12)
Angles (Elementary)
Students will learn about classifying angles as acute, right, or obtuse.
(Grades 3-5)
Area
Looks at finding areas of irregular shapes on a grid.
(Grades 3-5, Grades 6-8)
Clocks and Modular Arithmetic
Shows how modular arithmetic can be thought of as clock arithmetic.
(Grades 3-5, Grades 6-8, Grades 9-12)
6
Color in Tessellations
Explains the effect that color has on the patterns we see in tessellations.
(Grades 3-5, Grades 6-8, Grades 9-12)
Dimension and Scale
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
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)
Elapsed Time
Introduces the concept of elapsed time and teaches students how to
calculate elapsed time.
(Grades 3-5)
Elapsed Time Two
Teaches students how to calculate ending time given the starting time
and elapsed time.
(Grades 3-5)
Finding the Surface Area of a Rectangular Prism
Discusses the process of finding the surface area of a rectangular prism.
(Grades 6-8, Grades 9-12)
Finding the Surface Area of a Triangular Prism
Introduces the concept of surface area in relation to a triangular prism
(Grades 6-8, Grades 9-12)
7
Finding the Volume of a Rectangular Prism
Introduces the concept of volume of a rectangular prism.
(Grades 6-8, Grades 9-12)
Finding the Volume of a Triangular Prism
Introduces the concept of finding volume of a triangular prism
(Grades 6-8, Grades 9-12)
From Geometry to Probability
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, Grades 9-12)
Optical Illusions
Looks at several optical illusions.
(Grades 3-5, Grades 6-8, Grades 9-12)
Parallelograms
Introduces students to parallelograms and rhombbi and defines the
characteristics necessary to determine each shape.
(Grades 3-5)
Perimeter Algorithm
Introduces a method for finding perimeters of irregular shapes on a grid.
(Grades 3-5, Grades 6-8)
8
Perimeter Explorer
Introduces a method for finding perimeters of rectangular shapes on a
grid.
(Grades 3-5, Grades 6-8)
Plane Figure Fractals
Compares fractals with one and two dimensional generators.
(Grades 6-8, Grades 9-12)
Polyhedra
Questions about dice lead to a discussion of polyhedra and geometric
probability.
(Grades 3-5, Grades 6-8)
Prisoners and Escapees--Julia Sets
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)
Probability and Geometry (elementary)
Discusses the relationship between geometry and probability.
(Grades 3-5)
Properties of Fractals
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.
9
(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)
Recursion
Discusses the idea of recursion as it pertains to fractals and sequences.
(Grades 6-8, Grades 9-12)
Self-Similarity
Discusses how fractals are self-similar objects.
(Grades 3-5, Grades 6-8, Grades 9-12)
Shape Explorer
Introduces students to finding areas and perimeters of irregular shapes
on a grid.
(Grades 3-5, Grades 6-8)
Slant Height
Introduces the concept of the slant height of a triangle and how to find its
measure using the Pythagorean theorem.
(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)
Standard Deviation
10
Introduces standard deviaton and describes how to compute it.
(Grades 6-8, Grades 9-12, Undergraduate)
Symmetry in Tessellations
Defines symmetry and demonstrates different types of plane symmetry.
(Grades 3-5, Grades 6-8)
Tessellations in the World
Looks at the history of tessellations, why they are important and
examines some patterns in nature and art.
(Grades 3-5, Grades 6-8, Grades 9-12)
The Mandelbrot Set
Shows how the set of all Julia Sets are used to create the classic
Mandelbrot fractal.
(Grades 6-8, Grades 9-12, Undergraduate)
Translations, Reflections, and Rotations
Introduces students to the concepts of transformations.
(Grades 3-5, 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
Introduces students to the concepts of surface area and volume.
(Grades 3-5, Grades 6-8)
11
What are Tessellations
Examines the mathematical properties of tessellations.
(Grades 3-5, Grades 6-8)
Algebra (24)
"The Bell Curve" Revisited
Finishes up the discussion of the book as well as exploring individual
differences versus group expected values.
(Grades 9-12, Undergraduate)
Class Intervals: Scale and Impression
How scales help to represent or mis-represent data in histograms.
(Grades 6-8, Grades 9-12)
Dimension and Scale
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
Gives an introduction to the concept of a logarithms and shows how logs
can be used to calculate fractal dimension.
(Grades 9-12, Undergraduate)
From Graphs to Function Machines and Back
Demonstrates the initial connections between functions and their graphs.
(Grades 6-8, Grades 9-12)
Functions and the Vertical Line Test
12
Shows students why a function must pass the vertical line test to be a
function.
(Grades 6-8, Grades 9-12, Undergraduate)
Functions as Processes or Rules: "Function Machines"
Discusses the notion of functions as a "number machine" with input and
output.
(Grades 3-5, Grades 6-8, Grades 9-12)
Gathering Information from Graphs
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, Undergraduate)
Identity Properties
Introduces the concepts of the additive identity and multiplicative identity
and how they are used when solving equations.
(Grades 6-8, Grades 9-12)
Impossible Graphs
Shows what makes a graph represent impossible situations and how to
avoid these problems.
(Grades 6-8, Grades 9-12)
Inequalities
Introduces students to linear inequalities.
(Grades 6-8, Grades 9-12)
13
Introduction to the Coordinate Plane and Coordinates
Introduces coordinates through the idea of number lines.
(Grades 3-5, Grades 6-8)
Inverse Properties
Introduces the concepts of the additive inverse and multiplicative inverse
and how they are used when solving equations.
(Grades 6-8, Grades 9-12)
Linear Functions
Discusses functions of the form y = ___*x + ___.
(Grades 6-8, Grades 9-12)
Mean, Median, and Mode
Defining and discussing the concepts of central measures of tendency.
(Grades 6-8, Grades 9-12)
Multi-Step Functions
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)
One Step Algebra
Discusses processes for solving one step algebra problems.
(Grades 6-8, Grades 9-12)
Plotting Functions in the Polar Coordinate System
A discussion about graphing functions in the polar coordinate system.
(Grades 9-12, Undergraduate)
14
Polar Coordinates
A discussion about what the polar coordinate system is and how to graph
a point in this system.
(Grades 9-12, Undergraduate)
Slope and Y-intercept
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"
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
Introduces 2 variable functions as ordered pairs and how to operate
perform operations on ordered pairs.
(Grades 6-8, Grades 9-12, Undergraduate)
Probability (21)
Chaos
Introduces the notion of chaos as the breakdown in predictability.
(Grades 6-8, Grades 9-12)
15
Chaos is Everywhere
Shows the wide spread use of fractals and chaos in science and nature.
(Grades 6-8, Grades 9-12)
Conditional Probability
Introduction of the concept of conditional probability and discussion of its
application for problem solving.
(Grades 6-8, Grades 9-12)
Divisibility
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
The proper meaning of the term fair.
(Grades 3-5, Grades 6-8)
Events and Set Operations
Introduction of elementary set operations and their connections with
probability.
(Grades 6-8, Grades 9-12)
Expected Value
Introduction and discussion of the concept of expected value.
(Grades 6-8, Grades 9-12)
From Geometry to Probability
16
Leads the idea of probability from counting chances to measuring
proportions of areas.
(Grades 6-8, Grades 9-12)
Pascal's Triangle
Introduces Pascal's Triangle in terms of probability.
(Grades 6-8, Grades 9-12)
Polyhedra
Questions about dice lead to a discussion of polyhedra and geometric
probability.
(Grades 3-5, Grades 6-8)
Probability and Geometry (elementary)
Discusses the relationship between geometry and probability.
(Grades 3-5)
Probability and Outcome
Introduction and initial discussion of the concept of probability.
(Grades 6-8, Grades 9-12)
Probability of Simultaneous Events
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
Defining, comparing and contrasting probability with statistics.
(Grades 3-5, Grades 6-8, Grades 9-12)
Properties of Fractals
Reviews Mandelbrot's defining characteristics for fractal objects.
17
(Grades 6-8, Grades 9-12)
Random Number Generators
Different methods for random fair choice between several numbers.
(Grades 3-5, Grades 6-8)
Replacement
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 of tables as a convenient way to store and count outcomes.
(Grades 6-8, Grades 9-12)
Theoretical Versus Experimental Probability
This lesson teaches students about the differences between theoretical
and experimental probabilities.
(Grades 6-8, Grades 9-12)
Think and Check!
Some problems are tricky; probability theory provides unique ways to
check solutions.
(Grades 6-8, Grades 9-12)
Trees as Data Structures
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, Undergraduate)
18
Statistics (21)
Bar Graph
Discusses the benefits of using a bar graph to examine data.
(Grades 3-5, Grades 6-8)
Bivariate Data Relations
Introduces positive and negative relationships and independent and
dependent variables of bivariate data.
(Grades 6-8, Grades 9-12)
Box Plot
How to build box plots, including the two different ways to determine
interquartile range.
(Grades 6-8, Grades 9-12)
Continuous Distributions: 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, Undergraduate)
Finding Residuals
Introduces how to calculate residuals of bivariate data.
(Grades 9-12, Undergraduate)
19
Graphing and Interpreting Bivariate Data
Introduces graphing independent and dependent variables.
(Grades 9-12, Undergraduate)
Histograms vs. Bar Graphs
Differences and similarities between the two types of graphs.
(Grades 3-5, Grades 6-8, Grades 9-12)
Line of Best Fit
Introduces the line of best fit through the use of scatter plots with outliers.
(Grades 6-8, Grades 9-12, Undergraduate)
Mean, Median, and Mode
Defining and discussing the concepts of central measures of tendency.
(Grades 6-8, Grades 9-12)
Numerical and Categorical Data
Students learn about the difference between numerical data and
categorical data.
(Grades 6-8)
Outliers
Explains how outliers affect data.
(Grades 6-8, Grades 9-12, Undergraduate)
Pie Chart
Discusses the benefits of using a pie chart.
(Grades 3-5, Grades 6-8)
Probability vs. Statistics
20
Defining, comparing and contrasting probability with statistics.
(Grades 3-5, Grades 6-8, Grades 9-12)
Replacement
Extends the notion of conditional probability by discussing the effects of
replacement on drawing multiple objects.
(Grades 6-8, Grades 9-12)
Standard Deviation
Introduces standard deviaton and describes how to compute it.
(Grades 6-8, Grades 9-12, Undergraduate)
Stem-and-Leaf Plots
Introduces Stem-and-Leaf Plots to students.
(Grades 3-5, Grades 6-8, Grades 9-12)
The Normal Distribution and "The Bell Curve"
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 9-12, Undergraduate)
21
Vertical Scale: Increase or Decrease?
How class interval size influences the look and interpretation of
histograms.
(Grades 3-5, Grades 6-8, Grades 9-12)
Modeling (8)
Algorithm
Introduces the concept of algorithms and how algorithms affect
mathematics.
(Grades 3-5, Grades 6-8)
Chaos
Introduces the notion of chaos as the breakdown in predictability.
(Grades 6-8, Grades 9-12)
Chaos is Everywhere
Shows the wide spread use of fractals and chaos in science and nature.
(Grades 6-8, Grades 9-12)
Gathering Information from Graphs
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, Undergraduate)
Impossible Graphs
22
Shows what makes a graph represent impossible situations and how to
avoid these problems.
(Grades 6-8, Grades 9-12)
Infinity and Iteration
Discusses infinity, iterations and limits by referencing fractals and
sequences.
(Grades 6-8, Grades 9-12)
Properties of Fractals
Reviews Mandelbrot's defining characteristics for fractal objects.
(Grades 6-8, Grades 9-12)
Discrete (4)
Events and Set Operations
Introduction of elementary set operations and their connections with
probability.
(Grades 6-8, Grades 9-12)
Internet Search and Set Operations
Introduction of elementary set operations through internet searching.
(Grades 3-5, Grades 6-8, Grades 9-12)
Sets
Gives an introduction to sets and elements.
(Grades 3-5, Grades 6-8)
23
Venn Diagrams
Introduces concepts needed to create Venn diagrams.
(Grades 3-5, Grades 6-8, Grades 9-12)
Other (6)
Algorithm
Introduces the concept of algorithms and how algorithms affect
mathematics.
(Grades 3-5, Grades 6-8)
Chaos
Introduces the notion of chaos as the breakdown in predictability.
(Grades 6-8, Grades 9-12)
Chaos is Everywhere
Shows the wide spread use of fractals and chaos in science and nature.
(Grades 6-8, Grades 9-12)
Infinity and Iteration
Discusses infinity, iterations and limits by referencing fractals and
sequences.
(Grades 6-8, Grades 9-12)
Plotting Functions in the Polar Coordinate System
A discussion about graphing functions in the polar coordinate system.
(Grades 9-12, Undergraduate)
Polar Coordinates
24
A discussion about what the polar coordinate system is and how to graph
a point in this system.
(Grades 9-12, Undergraduate)
25