Discussions
Algebra • Calculus • Discrete • Geometry • Modeling • Number and Operations • Probability • Statistics • Trigonometry • Other • Show All
Algebra (...)
Aids in the understanding of the geometric and algebraic derivations of conic sections.
Grade Level: Grades 9-12
Related Topics: circles, conic section, ellipse, hyperbola, parabola, pre-calculus
Discusses the correlation coefficient, r, through scatter plots.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: correlation, data, regression, scatter plot
Introduces the notion of using modular arithmetic to encode messages.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, factors, inverse, modular, multiples, multiplication, shift cipher, subtraction
Introduces the concept of the distributive property.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, distributive, integers, multiplication, solving equations, subtraction, variable
Gives an introduction to the concept of a logarithms and shows how logs can be used to calculate fractal dimension.
Grade Level: Grades 9-12, Undergraduate
Related Topics: dimension, estimation, exponents, fractals, logarithm, multiplication
Demonstrates the initial connections between functions and their graphs.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: algebra, cartesian coordinate, coordinate, coordinate plane, coordinate system, function machine, functions, graph, input, lines, output
Shows students why a function must pass the vertical line test to be a function.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: function properties, functions, graph, piecewise, vertical line test
Discusses the notion of functions as a "number machine" with input and output.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: addition, function machine, functions, input, multiplication, output
Introduces students to reading and interpreting graphs.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: concave, constant, distance, functions, graph, slope, velocity
Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: acceleration, constant, distance, graph, intervals, time, velocity
Introduces the concepts of the additive identity and multiplicative identity and how they are used when solving equations.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, division, identity, inverse, multiplication, solving equations, subtraction
Shows what makes a graph represent impossible situations and how to avoid these problems.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: graph, intervals
Introduces and explains the concept of independent and dependent variables and their applications in real-world problems.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: algebra, dependent, function properties, independent, input, linear equations, linear functions, output, solving equations, variable
Introduces students to linear inequalities.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: cartesian coordinate, coordinate, coordinate plane, function properties, graph, inequality, intercept, linear functions, lines, slope
Introduces coordinates through the idea of number lines.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: axis, cartesian coordinate, coordinate, coordinate plane, coordinate system, number line, quadrant
Introduces the concepts of the additive inverse and multiplicative inverse and how they are used when solving equations.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, division, identity, inverse, multiplication, subtraction
Introduces the line of best fit through the use of scatter plots with outliers.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: best-fit line, correlation, linear functions, regression, scatter plot, statistics
Discusses functions of the form y = ___*x + ___.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: functions, intercept, linear equations, linear functions, slope
Discusses the notion of composite functions as several "number machines" with the output of one machine becoming the input of another.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, commutative, distributive, division, equivalent, exponents, functions, input, multiplication, order of operations, output, subtraction
Discusses processes for solving one step algebra problems.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, algebra, coefficient, division, multiplication, solving equations, subtraction
A discussion about graphing functions in the polar coordinate system.
Grade Level: Grades 9-12, Undergraduate
Related Topics: angles, calculus, circles, coordinate, coordinate plane, coordinate system, dependent, independent, limacon, polar coordinates, pre-calculus, radian, sine, trigonometry
A discussion about what the polar coordinate system is and how to graph a point in this system.
Grade Level: Grades 9-12, Undergraduate
Related Topics: angles, calculus, coordinate, coordinate plane, coordinate system, polar coordinates, pre-calculus, quadrant, radian, trigonometry
Discusses the idea of recursion as it pertains to fractals and sequences.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: fractals, generator, initiator, iteration, recursion, recursive functions, sequences
Discusses slope and y-intercept and how they affect a graph.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, functions, intercept, linear equations, linear functions, multiplication, slope, solving equations, translation
Introduces 2 variable functions as ordered pairs and how to operate perform operations on ordered pairs.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: addition, complex number, coordinate, distributive, division, fractals, function machine, functions, imaginary, multiplication, subtraction, variable
Explains how residuals can determine whether a line is a good fit or a bad fit for a set of bivariate data.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: best-fit line, pattern, regression, residual
Calculus (...)
A discussion about graphing functions in the polar coordinate system.
Grade Level: Grades 9-12, Undergraduate
Related Topics: angles, calculus, circles, coordinate, coordinate plane, coordinate system, dependent, independent, limacon, polar coordinates, pre-calculus, radian, sine, trigonometry
A discussion about what the polar coordinate system is and how to graph a point in this system.
Grade Level: Grades 9-12, Undergraduate
Related Topics: angles, calculus, coordinate, coordinate plane, coordinate system, polar coordinates, pre-calculus, quadrant, radian, trigonometry
Discrete (...)
Shows how modular arithmetic can be thought of as clock arithmetic.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: arithmetic, division, integers, modular, pattern, remainders, time, whole numbers
Introduction of the concept of conditional probability and discussion of its application for problem solving.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: conditional probability, division, events, independent, outcomes, probability, probability simulation
Introduces the notion of using modular arithmetic to encode messages.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, factors, inverse, modular, multiples, multiplication, shift cipher, subtraction
Introduces the proper meaning of the term fair.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: fair, outcomes, probability
Introduction of elementary set operations and their connections with probability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: combinatorics, events, intersection, outcomes, probability, sets, theoretical probability, union, venn diagram
Leads the idea of probability from counting chances to measuring proportions of areas.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: angles, area, circles, counting, degrees, estimation, events, expected value, experimental probability, fair, geometric probability, geometry, probability, right angle, spinner, theoretical probability, theoretical value, volume
Demonstrates the initial connections between functions and their graphs.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: algebra, cartesian coordinate, coordinate, coordinate plane, coordinate system, function machine, functions, graph, input, lines, output
Shows students why a function must pass the vertical line test to be a function.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: function properties, functions, graph, piecewise, vertical line test
Discusses the notion of functions as a "number machine" with input and output.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: addition, function machine, functions, input, multiplication, output
Shows what makes a graph represent impossible situations and how to avoid these problems.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: graph, intervals
Discusses infinity, iterations and limits by referencing fractals and sequences.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: infinity, iteration, limit
Introduces the concept of an integer.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: comparing, counting, integers, negative number, positive number, whole numbers
Introduces the addition and subtraction of integers.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, arithmetic, associative, commutative, counting, grouping, identity, integers, subtraction, whole numbers
Introduces the division of integers.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: arithmetic, division, divisors, integers, remainders, whole numbers
Introduces the multiplication of integers.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, arithmetic, associative, commutative, grouping, integers, inverse, multiplication, negative number, whole numbers
Introduction of elementary set operations through internet searching.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: counting, graph theory, intersection, outcomes, sets, union, venn diagram
Discusses functions of the form y = ___*x + ___.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: functions, intercept, linear equations, linear functions, slope
Discusses the notion of composite functions as several "number machines" with the output of one machine becoming the input of another.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, commutative, distributive, division, equivalent, exponents, functions, input, multiplication, order of operations, output, subtraction
Introduces Pascal's Triangle in terms of probability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: algebra, binomial, coefficient, combinatorics, fractals, infinity, integers, multiplication, pascal's triangle, pascals triangle, permutation, probability, whole numbers
Discusses what individual digits represent in multi-digit integers.
Grade Level: Grades 3-5
Related Topics: base, counting, place value
Compares fractals with one and two dimensional generators.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: chaos, comparing, fractals, generator, infinity, initiator, iteration, pattern, planes, recursion, scale, self-similarity
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.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: chaos, complex number, escape, fractals, geometry, infinity, iteration, julia set, mandelbrot set, pattern, planes, prisoner, radius, recursion, sets
Discusses the relationship between geometry and probability.
Grade Level: Grades 3-5
Related Topics: angles, decimals, experimental probability, fractions, outcomes, percents, probability, random number, spinner, theoretical probability
Introduction and initial discussion of the concept of probability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: decimals, experimental probability, fractions, geometric probability, outcomes, percentages, percents, probability, random number, theoretical probability
Computing exact probabilities for the Racing Game leads to the formula for the probability of simultaneous events.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: divisors, events, experimental probability, fractions, independent, multiplication, outcomes, percentages, probability, theoretical probability
Defining, comparing and contrasting probability with statistics.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: comparing, experimental probability, outcomes, probability, statistics, theoretical probability
Reviews Mandelbrot's defining characteristics for fractal objects.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: fractals, generator, infinity, initiator, iteration, length, perimeter, recursion, scale, self-similarity
Discusses the idea of recursion as it pertains to fractals and sequences.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: fractals, generator, initiator, iteration, recursion, recursive functions, sequences
Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: conditional probability, fractions, outcomes, probability with replacement, probability without replacement, sampling, theoretical probability
Discusses how fractals are self-similar objects.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: fractals, iteration, recursion, scale, self-similarity
Gives an introduction to sets and elements.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: counting, element, sets
Introduces elementary students to sets and elements using shapes.
Grade Level: Grades 3-5
Related Topics: element, sets, venn diagram
Discussion of tables as a convenient way to store and count outcomes.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: arithmetic, combinatorics, events, fair, multiplication, outcomes, table
Shows how the set of all Julia Sets are used to create the classic Mandelbrot fractal.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: circles, complex number, dimension, fractals, geometry, iteration, julia set, mandelbrot set, pattern, self-similarity, sets, symmetry
This lesson teaches students about the differences between theoretical and experimental probabilities.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: experimental probability, probability, theoretical probability
Questions about games with more than two dice lead to discussion of trees as another kind of data structure.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: combinatorics, dimension, events, exponents, fair, logarithm, multiples, outcomes, probability, probability tree, tree diagram
Introduces 2 variable functions as ordered pairs and how to operate perform operations on ordered pairs.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: addition, complex number, coordinate, distributive, division, fractals, function machine, functions, imaginary, multiplication, subtraction, variable
Introduces concepts needed to create Venn diagrams.
Grade Level: Grades 3-5
Related Topics: circles, element, sets, venn diagram
Introduces concepts needed to create Venn diagrams.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: circles, element, sets, venn diagram
Discusses integer multiples as repeated addition.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: arithmetic, counting, division, factors, integers, multiples, multiplication, remainders, whole numbers
Reviews long division of integers and modular arithmetic.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: arithmetic, decimals, division, divisors, fractions, mixed numbers, modular, multiples, quotient, remainders, whole numbers
Geometry (...)
Reviews vocabulary and concepts related to the geometry of angles.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: acute, adjacent, alternate exterior, alternate interior, angles, degrees, geometry, intersection, obtuse, parallel, rays, right angle, transversal, vertical
Students will learn about classifying angles as acute, right, or obtuse.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: acute, angles, degrees, intersection, obtuse, rays, right angle
Looks at finding areas of irregular shapes on a grid.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, area, geometry, length, multiplication, polygon, rectangles, subtraction, width
Shows how modular arithmetic can be thought of as clock arithmetic.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: arithmetic, division, integers, modular, pattern, remainders, time, whole numbers
Explains the effect that color has on the patterns we see in tessellations.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: contrast, geometry, graph, hue, illusion, pattern, tessellations, value
Aids in the understanding of the geometric and algebraic derivations of conic sections.
Grade Level: Grades 9-12
Related Topics: circles, conic section, ellipse, hyperbola, parabola, pre-calculus
Aids in the understanding of the relationships among the various conic sections.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: circle graph, conic section, ellipse, hyperbola, parabola, pre-calculus
Aids in the understanding of cross sections of three-dimensional objects.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: circles, conic section, ellipse, geometry, polygon, polyhedra, pre-calculus
Discusses fractal dimension, how that dimension relates to scale, and the formula needed to calculate the fractal dimension of an object.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: dimension, exponents, fractals, length, lines, pattern, scale, self-similarity, squares
Discusses the problem of determining the fractal dimension of irregular fractals and how the scale is indeterminite in these fractals.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: dimension, fractals, scale
Introduces the concept of elapsed time and teaches students how to calculate elapsed time.
Grade Level: Grades 3-5
Related Topics: counting, elapsed time, modular, time
Teaches students how to calculate ending time given the starting time and elapsed time.
Grade Level: Grades 3-5
Related Topics: elapsed time, modular, time
Gives an introduction to the concept of a logarithms and shows how logs can be used to calculate fractal dimension.
Grade Level: Grades 9-12, Undergraduate
Related Topics: dimension, estimation, exponents, fractals, logarithm, multiplication
Discusses the process of finding the surface area of a rectangular prism.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: addition, area, length, polyhedra, prisms, rectangles, surface area, width
Introduces the concept of surface area in relation to a triangular prism
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: addition, area, polyhedra, prisms, slant height, surface area, triangle
Introduces the concept of volume of a rectangular prism.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: depth, length, multiplication, prisms, rectangles, volume, width
Introduces the concept of finding volume of a triangular prism
Grade Level: Grades 6-8, Grades 9-12
Related Topics: depth, height, length, multiplication, prisms, triangle, triangles, volume
Leads the idea of probability from counting chances to measuring proportions of areas.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: angles, area, circles, counting, degrees, estimation, events, expected value, experimental probability, fair, geometric probability, geometry, probability, right angle, spinner, theoretical probability, theoretical value, volume
Discusses infinity, iterations and limits by referencing fractals and sequences.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: infinity, iteration, limit
Introduces coordinates through the idea of number lines.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: axis, cartesian coordinate, coordinate, coordinate plane, coordinate system, number line, quadrant
Introduces students to lines, rays, line segments, and planes.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: axis, coordinate plane, coordinate system, infinity, lines, planes, rays, segment
Looks at several optical illusions.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: geometry, illusion, pattern, segment, tessellations
Introduces students to parallelograms and rhombbi and defines the characteristics necessary to determine each shape.
Grade Level: Grades 3-5
Related Topics: geometry, length, parallel, parallelogram, polygon, quadrilaterals, rhombus
Introduces a method for finding perimeters of irregular shapes on a grid.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, algorithm, arithmetic, geometry, length, multiplication, perimeter, rectangles, width
Introduces a method for finding perimeters of rectangular shapes on a grid.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, arithmetic, geometry, length, multiplication, perimeter, rectangles, width
Compares fractals with one and two dimensional generators.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: chaos, comparing, fractals, generator, infinity, initiator, iteration, pattern, planes, recursion, scale, self-similarity
Questions about dice lead to a discussion of polyhedra and geometric probability.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: angles, geometry, length, polygon, polyhedra
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.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: chaos, complex number, escape, fractals, geometry, infinity, iteration, julia set, mandelbrot set, pattern, planes, prisoner, radius, recursion, sets
Discusses the relationship between geometry and probability.
Grade Level: Grades 3-5
Related Topics: angles, decimals, experimental probability, fractions, outcomes, percents, probability, random number, spinner, theoretical probability
Reviews Mandelbrot's defining characteristics for fractal objects.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: fractals, generator, infinity, initiator, iteration, length, perimeter, recursion, scale, self-similarity
Introduces students to quadrilaterals and defines the characteristics of the polygon.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: geometry, parallelogram, polygon, quadrilaterals, rectangles, rhombus, squares
Introduces students to rectangles and squares and defines the characteristics necessary to
determine each shape.
Grade Level: Grades 3-5
Related Topics: angles, comparing, geometry, length, parallel, parallelogram, polygon, rectangles, right angle, squares
Discusses the idea of recursion as it pertains to fractals and sequences.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: fractals, generator, initiator, iteration, recursion, recursive functions, sequences
Discusses how fractals are self-similar objects.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: fractals, iteration, recursion, scale, self-similarity
Introduces elementary students to sets and elements using shapes.
Grade Level: Grades 3-5
Related Topics: element, sets, venn diagram
Introduces students to finding areas and perimeters of irregular shapes on a grid.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, area, dimension, geometry, length, multiplication, perimeter, rectangles, subtraction, width
Introduces the concept of the slant height of a triangle and how to find its measure using the Pythagorean theorem.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: depth, length, prisms, pythagorean theorem, right angle, slant height, triangle, triangles, width
Introduces students to the Pythagorean theorem with explanations on what it means and how to use it.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: angles, area, exponents, hypotenuse, length, pythagorean theorem, right angle, solving equations, squares, triangle, triangles, trigonometry
Defines symmetry and demonstrates different types of plane symmetry.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: geometry, glides, pattern, planes, polygon, reflections, rotation, symmetry, tessellations, transformation, translation
Looks at the history of tessellations, why they are important and examines some patterns in nature and art.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: angles, geometry, lines, pattern, polygon, symmetry, tessellations
Shows how the set of all Julia Sets are used to create the classic Mandelbrot fractal.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: circles, complex number, dimension, fractals, geometry, iteration, julia set, mandelbrot set, pattern, self-similarity, sets, symmetry
Introduces students to the concepts of transformations.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: angles, distance, geometry, reflections, rotation, symmetry, transformation, translation, triangle
Introduces students to trapezoids and isosceles trapezoids and defines the characteristics necessary to determine each shape.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: geometry, isosceles, lines, parallel, parallelogram, quadrilaterals, trapezoid
Introduces students to the concepts of surface area and volume.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: area, dimension, surface area, volume
Examines the mathematical properties of tessellations.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: angles, geometry, hexagon, pattern, planes, polygon, regular, squares, tessellations, triangle
Modeling (...)
Helps students to understand the differences and similarities between Agent Modeling and Systems Modeling.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: agent modeling, systems modeling
Introduces the concept of algorithms and how algorithms affect mathematics.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, algorithm, arithmetic, decimals, estimation, fractions, multiplication, pattern
Introduces the notion of chaos as the breakdown in predictability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: chaos, fractals, function properties, graph theory, outcomes, pattern, probability simulation
Shows the wide spread use of fractals and chaos in science and nature.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: chaos, fractals, predator-prey, probability simulation
Introduces students to reading and interpreting graphs.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: concave, constant, distance, functions, graph, slope, velocity
Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: acceleration, constant, distance, graph, intervals, time, velocity
Shows what makes a graph represent impossible situations and how to avoid these problems.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: graph, intervals
Introduces and explains the concept of independent and dependent variables and their applications in real-world problems.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: algebra, dependent, function properties, independent, input, linear equations, linear functions, output, solving equations, variable
Number and Operations (...)
Introduces the concept of algorithms and how algorithms affect mathematics.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, algorithm, arithmetic, decimals, estimation, fractions, multiplication, pattern
Discusses the base ten system and how it differs from other base number systems.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: base, counting, exponents
Shows how modular arithmetic can be thought of as clock arithmetic.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: arithmetic, division, integers, modular, pattern, remainders, time, whole numbers
Introduces students to the basics of reducing fractions and learning to compare fractions.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, comparing, denominator, division, fractions, multiplication, numerator, subtraction, whole numbers
Discusses methods of converting from the base ten system to another base number system.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: base, converting, counting
Introduces the notion of using modular arithmetic to encode messages.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, factors, inverse, modular, multiples, multiplication, shift cipher, subtraction
Deals with converting fractions into decimals.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: converting, decimals, denominator, division, fractions, numerator
Discusses fractal dimension, how that dimension relates to scale, and the formula needed to calculate the fractal dimension of an object.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: dimension, exponents, fractals, length, lines, pattern, scale, self-similarity, squares
Discusses the problem of determining the fractal dimension of irregular fractals and how the scale is indeterminite in these fractals.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: dimension, fractals, scale
Introduces the concept of the distributive property.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, distributive, integers, multiplication, solving equations, subtraction, variable
The question of fairness in a game of two dice leads to the concept of divisibility.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: division, divisors, events, factors, fair, outcomes, theoretical probability
Gives an introduction to the concept of a logarithms and shows how logs can be used to calculate fractal dimension.
Grade Level: Grades 9-12, Undergraduate
Related Topics: dimension, estimation, exponents, fractals, logarithm, multiplication
Demonstrates how fractions are added and subtracted.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, denominator, division, fractions, lowest common denominator, multiplication, numerator, subtraction
Discusses how to convert from fractions to decimals.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: converting, decimals, fractions
Explains multiplication and division of fractions.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: arithmetic, denominator, division, fractions, inverse, multiplication, numerator
Discusses the introductory concept of a fraction.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: denominator, division, divisors, factors, fractions, integers, numerator, reducing fraction, whole numbers
Introduces the concepts of the additive identity and multiplicative identity and how they are used when solving equations.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, division, identity, inverse, multiplication, solving equations, subtraction
Discusses infinity, iterations and limits by referencing fractals and sequences.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: infinity, iteration, limit
Introduces the concept of an integer.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: comparing, counting, integers, negative number, positive number, whole numbers
Introduces the addition and subtraction of integers.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, arithmetic, associative, commutative, counting, grouping, identity, integers, subtraction, whole numbers
Introduces the division of integers.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: arithmetic, division, divisors, integers, remainders, whole numbers
Introduces the multiplication of integers.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, arithmetic, associative, commutative, grouping, integers, inverse, multiplication, negative number, whole numbers
Introduction of elementary set operations through internet searching.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: counting, graph theory, intersection, outcomes, sets, union, venn diagram
Introduces the concepts of the additive inverse and multiplicative inverse and how they are used when solving equations.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: addition, division, identity, inverse, multiplication, subtraction
Introduces students to estimation.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: comparing, estimation
A review of the definition of decimals as well as a description of multiplying decimal numbers.
Grade Level: Grades 6-8
Related Topics: decimals, fractions, integers, multiplication
This discussion shows students how to multiply with fractions and mixed numbers.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: denominator, fractions, improper, mixed numbers, multiplication, numerator, whole numbers
Introduces the convention of order of operations.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, division, exponents, grouping, multiplication, order of operations, parentheses, subtraction
Introduces the idea of patterns in numbers and discusses sequences.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: arithmetic sequences, pattern, sequences
Covers the basics of converting fractions into percents.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: denominator, division, fractions, multiplication, numerator, percents, reducing fraction
Discusses what individual digits represent in multi-digit integers.
Grade Level: Grades 3-5
Related Topics: base, counting, place value
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.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: chaos, complex number, escape, fractals, geometry, infinity, iteration, julia set, mandelbrot set, pattern, planes, prisoner, radius, recursion, sets
Discusses the idea of recursion as it pertains to fractals and sequences.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: fractals, generator, initiator, iteration, recursion, recursive functions, sequences
Discusses how fractals are self-similar objects.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: fractals, iteration, recursion, scale, self-similarity
Gives an introduction to sets and elements.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: counting, element, sets
Introduces elementary students to sets and elements using shapes.
Grade Level: Grades 3-5
Related Topics: element, sets, venn diagram
Shows how the set of all Julia Sets are used to create the classic Mandelbrot fractal.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: circles, complex number, dimension, fractals, geometry, iteration, julia set, mandelbrot set, pattern, self-similarity, sets, symmetry
Discusses integer multiples as repeated addition.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: arithmetic, counting, division, factors, integers, multiples, multiplication, remainders, whole numbers
Reviews long division of integers and modular arithmetic.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: arithmetic, decimals, division, divisors, fractions, mixed numbers, modular, multiples, quotient, remainders, whole numbers
Probability (...)
Introduces the notion of chaos as the breakdown in predictability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: chaos, fractals, function properties, graph theory, outcomes, pattern, probability simulation
Shows the wide spread use of fractals and chaos in science and nature.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: chaos, fractals, predator-prey, probability simulation
Introduction of the concept of conditional probability and discussion of its application for problem solving.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: conditional probability, division, events, independent, outcomes, probability, probability simulation
Discusses continuous versus discrete distributions.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: experimental probability, histogram, infinity, normal distribution, outcomes, skewed distribution, statistics, theoretical probability
The question of fairness in a game of two dice leads to the concept of divisibility.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: division, divisors, events, factors, fair, outcomes, theoretical probability
Introduces the proper meaning of the term fair.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: fair, outcomes, probability
Introduction of elementary set operations and their connections with probability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: combinatorics, events, intersection, outcomes, probability, sets, theoretical probability, union, venn diagram
Introduction and discussion of the concept of expected value.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: average, expected value, fair, outcomes, probability
Leads the idea of probability from counting chances to measuring proportions of areas.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: angles, area, circles, counting, degrees, estimation, events, expected value, experimental probability, fair, geometric probability, geometry, probability, right angle, spinner, theoretical probability, theoretical value, volume
Introduces Pascal's Triangle in terms of probability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: algebra, binomial, coefficient, combinatorics, fractals, infinity, integers, multiplication, pascal's triangle, pascals triangle, permutation, probability, whole numbers
Questions about dice lead to a discussion of polyhedra and geometric probability.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: angles, geometry, length, polygon, polyhedra
Discusses the relationship between geometry and probability.
Grade Level: Grades 3-5
Related Topics: angles, decimals, experimental probability, fractions, outcomes, percents, probability, random number, spinner, theoretical probability
Introduction and initial discussion of the concept of probability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: decimals, experimental probability, fractions, geometric probability, outcomes, percentages, percents, probability, random number, theoretical probability
Computing exact probabilities for the Racing Game leads to the formula for the probability of simultaneous events.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: divisors, events, experimental probability, fractions, independent, multiplication, outcomes, percentages, probability, theoretical probability
Defining, comparing and contrasting probability with statistics.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: comparing, experimental probability, outcomes, probability, statistics, theoretical probability
Different methods for random fair choice between several numbers.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: experimental probability, fair, probability simulation, spinner, theoretical probability
Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: conditional probability, fractions, outcomes, probability with replacement, probability without replacement, sampling, theoretical probability
Discussion of tables as a convenient way to store and count outcomes.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: arithmetic, combinatorics, events, fair, multiplication, outcomes, table
This lesson teaches students about the differences between theoretical and experimental probabilities.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: experimental probability, probability, theoretical probability
Some problems are tricky; probability theory provides unique ways to check solutions.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: conditional probability, experimental probability, monty hall, probability simulation
Questions about games with more than two dice lead to discussion of trees as another kind of data structure.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: combinatorics, dimension, events, exponents, fair, logarithm, multiples, outcomes, probability, probability tree, tree diagram
Statistics (...)
Finishes up the discussion of the book as well as exploring individual differences versus group expected values.
Grade Level: Grades 9-12, Undergraduate
Related Topics: bell curve, continuous distribution, deviations, histogram, mean, normal distribution, outcomes, probability, standard deviation
Discusses the benefits of using a bar graph to examine data.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: bar graph, categorical, data, frequency, graph, statistics
Introduces positive and negative relationships and independent and dependent variables of bivariate data.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: correlation, data, dependent, independent, regression, statistics, variable
How to build box plots, including the two different ways to determine interquartile range.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: box plot, interquartile range, maximum, mean, median, minimum, percentages, quartile, range, statistics
Shows how scales help to represent or misrepresent data in histograms.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: bar graph, data, graph, histogram, intervals, scale, statistics
Discusses continuous versus discrete distributions.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: experimental probability, histogram, infinity, normal distribution, outcomes, skewed distribution, statistics, theoretical probability
Discusses the correlation coefficient, r, through scatter plots.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: correlation, data, regression, scatter plot
Introduces how to calculate residuals of bivariate data.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: best-fit line, data, dependent, independent, regression, residual, subtraction
Introduces students to reading and interpreting graphs.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: concave, constant, distance, functions, graph, slope, velocity
Introduces graphing independent and dependent variables.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: correlation, dependent, independent, regression, scatter plot
Analyzing graphs and creating velocity graphs from distance and acceleration from velocity.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: acceleration, constant, distance, graph, intervals, time, velocity
Differences and similarities between the two types of graphs.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: bar graph, comparing, histogram, statistics
Shows what makes a graph represent impossible situations and how to avoid these problems.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: graph, intervals
Introduces the line of best fit through the use of scatter plots with outliers.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: best-fit line, correlation, linear functions, regression, scatter plot, statistics
Defining and discussing the concepts of central measures of tendency.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: histogram, mean, measures of central tendency, median, mode, statistics
Students learn about the difference between numerical data and categorical data.
Grade Level: Grades 6-8
Related Topics: categorical, data, numerical, statistics
Explains how outliers affect data.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: best-fit line, mean, outlier, statistics
Discusses the benefits of using a pie chart.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: categorical, circle graph, histogram, pie chart
Defining, comparing and contrasting probability with statistics.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: comparing, experimental probability, outcomes, probability, statistics, theoretical probability
Introduces standard deviaton and describes how to compute it.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: mean, squares, standard deviation, statistics, sum, variance
Introduces Stem-and-Leaf Plots to students.
Grade Level: Grades 3-5, Grades 6-8, Grades 9-12
Related Topics: mean, median, mode, statistics, stem and leaf
An introduction to the normal distribution and the debate over the 1994 book, "The Bell Curve."
Grade Level: Grades 9-12, Undergraduate
Related Topics: bell curve, mean, measures of central tendency, median, mode, normal distribution, probability, standard deviation, statistics
Explains the differences between univariate data and bivariate data.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: bar graph, bivariate, box plot, correlation, data, mean, median, mode, pie chart, quartile, range, regression, scatter plot, table, univariate
Explains how residuals can determine whether a line is a good fit or a bad fit for a set of bivariate data.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: best-fit line, pattern, regression, residual
How class interval size influences the look and interpretation of histograms.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: bar graph, histogram, length, scale, statistics
Trigonometry (...)
A discussion about graphing functions in the polar coordinate system.
Grade Level: Grades 9-12, Undergraduate
Related Topics: angles, calculus, circles, coordinate, coordinate plane, coordinate system, dependent, independent, limacon, polar coordinates, pre-calculus, radian, sine, trigonometry
A discussion about what the polar coordinate system is and how to graph a point in this system.
Grade Level: Grades 9-12, Undergraduate
Related Topics: angles, calculus, coordinate, coordinate plane, coordinate system, polar coordinates, pre-calculus, quadrant, radian, trigonometry
Introduces students to the Pythagorean theorem with explanations on what it means and how to use it.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: angles, area, exponents, hypotenuse, length, pythagorean theorem, right angle, solving equations, squares, triangle, triangles, trigonometry
Other (...)
Introduces the concept of algorithms and how algorithms affect mathematics.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: addition, algorithm, arithmetic, decimals, estimation, fractions, multiplication, pattern
Introduces the notion of chaos as the breakdown in predictability.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: chaos, fractals, function properties, graph theory, outcomes, pattern, probability simulation
Shows the wide spread use of fractals and chaos in science and nature.
Grade Level: Grades 6-8, Grades 9-12
Related Topics: chaos, fractals, predator-prey, probability simulation
Introduces the concept of elapsed time and teaches students how to calculate elapsed time.
Grade Level: Grades 3-5
Related Topics: counting, elapsed time, modular, time
Teaches students how to calculate ending time given the starting time and elapsed time.
Grade Level: Grades 3-5
Related Topics: elapsed time, modular, time
Introduces the concept of energy and the law of conservation of energy.
Grade Level: Grades 9-12
Related Topics:
Discusses infinity, iterations and limits by referencing fractals and sequences.
Grade Level: Grades 6-8, Grades 9-12, Undergraduate
Related Topics: infinity, iteration, limit
Introduces concepts needed to create Venn diagrams.
Grade Level: Grades 3-5
Related Topics: circles, element, sets, venn diagram
Introduces concepts needed to create Venn diagrams.
Grade Level: Grades 3-5, Grades 6-8
Related Topics: circles, element, sets, venn diagram
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