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Algebra  (...)
Lesson plan to help students understand independent and dependent variables through a fire probability simulation.

Related Topics: algebra, dependent, independent, input, output, probability, variable

Students discover algorithms as they sort shapes into Venn diagrams. Then students compare the efficiency of their algorithms using box plots.

Related Topics: algorithm, box and whisker, box plot, geometry, pattern, polygon, sets, venn diagram

Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.

Related Topics: addition, arithmetic, arithmetic sequences, geometric sequences, graph, iteration, linear functions, multiplication, multiplier, negative number, pattern, positive number, pre-calculus, recursion, recursive functions, sequences

Introduces students to plotting points on the Cartesian coordinate system -- an alternative to "Graphing and the Coordinate Plane."

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, functions, graph, linear equations, linear functions, negative number, planes, slope

Introduces students to modular (clock) arithmetic and how modular arithmetic can be used to encode messages using simple shift, multiple and affine ciphers.

Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, factors, inverse, modular, multiples, multiplication, remainders, shift cipher, subtraction, time

Introduces students to a geometric derivation of the conic sections.

Related Topics: circles, conic section, ellipse, hyperbola, parabola, pre-calculus

Explores derivatives and the idea of infinity using a geometric interpretation of slope.

Related Topics: calculus, derivative, differentiate, function properties, graph, linear equations, linear functions, slides, slope, tangent

Students will graph input/output pairs from a simple linear function in order to gain an understanding of basic linear functions.

Related Topics: cartesian coordinate, coordinate, coordinate plane, functions, graph, linear functions, lines

Introduces students to the vertical line test for graphs of functions.

Related Topics: algebra, cartesian coordinate, constant, continuous distribution, coordinate, coordinate plane, discontinuous, function properties, functions, graph, input, linear equations, linear functions, lines, output, piecewise, vertical line test

Students learn basic ideas about graphing points on the coordinate plane.

Related Topics: algebra, axis, cartesian coordinate, coordinate, coordinate plane, coordinate system, graph, linear functions, lines, negative number, number line, pattern, planes, positive number, quadrant, slope

Demonstrates the connections between formulas and graphs.

Related Topics: algebra, cartesian coordinate, constant, coordinate, coordinate plane, coordinate system, functions, graph, input, intercept, linear equations, linear functions, lines, negative number, output, parabola, slope

Teaches distinguishing between possible and impossible graphs of functions as well as causes of graphical impossibility.

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, distance, function properties, functions, graph, intervals, linear equations, linear functions, lines, pattern, time, vertical line test

Students learn about definite integrals through limits and Riemann sums

Related Topics: area, calculus, estimation, function properties, functions, graph, infinity, integral, integrate, intervals

Introduces the basic ideas needed for understanding functions.

Related Topics: addition, algebra, arithmetic, dependent, functions, independent, input, integers, linear functions, multiplication, output, pattern, subtraction, variable

Students are introduced to correlation between two variables and the line of best fit.

Related Topics: best-fit line, bivariate, cartesian coordinate, coordinate plane, correlation, curve fitting, data, deviations, linear equations, linear functions, regression, residual, scatter plot, slope, statistics, variable

Introduces the basic ideas needed for understanding linear functions.

Related Topics: addition, algebra, arithmetic, associative, commutative, dependent, distributive, division, equivalent, function properties, functions, independent, input, integers, intercept, linear equations, linear functions, multiplication, order of operations, output, pattern, slope, subtraction, table, variable

Demonstrates the connections between formulas, graphs and words.

Related Topics: acceleration, algebra, cartesian coordinate, concave, constant, coordinate, coordinate plane, coordinate system, distance, functions, graph, intervals, linear equations, linear functions, lines, parabola, slope, time, velocity

Introduction to various algorithms for solving single-variable, linear equations.

Related Topics: addition, algorithm, coefficient, fractions, inverse, multiplication, variable

Students will learn about modular arithmetic in order to decipher encrypted messages.

Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, modular, multiples, multiplication, pattern, remainders, shift cipher, subtraction, time

Introduces students to concepts of transformations.

Related Topics: angles, cartesian coordinate, coordinate plane, coordinate system, dimension, distance, flips, geometry, glides, graph, hexagon, image, parallelogram, pattern, planes, polygon, pre-image, reflections, rotation, squares, symmetry, tessellations, transformation, translation, transpose, triangles

Calculus  (...)
Explores derivatives and the idea of infinity using a geometric interpretation of slope.

Related Topics: calculus, derivative, differentiate, function properties, graph, linear equations, linear functions, slides, slope, tangent

Students learn about definite integrals through limits and Riemann sums

Related Topics: area, calculus, estimation, function properties, functions, graph, infinity, integral, integrate, intervals

Introduces students to graphing in the Polar coordinate plane

Related Topics: calculus, coordinate plane, coordinate system, cosine, data plot, graph, polar coordinates, pre-calculus, sine, tangent, trigonometry

Discrete  (...)
Students discover algorithms as they sort shapes into Venn diagrams. Then students compare the efficiency of their algorithms using box plots.

Related Topics: algorithm, box and whisker, box plot, geometry, pattern, polygon, sets, venn diagram

Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.

Related Topics: addition, arithmetic, arithmetic sequences, geometric sequences, graph, iteration, linear functions, multiplication, multiplier, negative number, pattern, positive number, pre-calculus, recursion, recursive functions, sequences

Introduces students to modular (clock) arithmetic and how modular arithmetic can be used to encode messages using simple shift, multiple and affine ciphers.

Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, factors, inverse, modular, multiples, multiplication, remainders, shift cipher, subtraction, time

Introduces conditional probability and the probability of simultaneous events.

Related Topics: comparing, conditional probability, events, experimental probability, fair, fractions, independent, multiplication, percents, probability, probability simulation, probability without replacement, random number, theoretical probability

Students consider the patterns that emerge from agent models and geometric fractals.

Related Topics: agent modeling, fractals, pattern, recursion, self-similarity

Students learn about factoring by using manipulatives and computer applets.

Related Topics: area, division, divisors, factors, multiples, multiplication, rectangles, whole numbers

Finding the factors of whole numbers.

Related Topics: area, division, divisors, factors, multiples, multiplication, rectangles, whole numbers

Uses modular (clock) arithmetic to find patterns in Pascal's Triangle.

Related Topics: addition, arithmetic, division, divisors, integers, modular, pascal's triangle, pascals triangle, pattern, remainders, sum, triangle, whole numbers

Utilizes and reinforces concepts of probability, mean, line plots, experimental data, and chaos in analyzing a forest fire simulation.

Related Topics: agent modeling, chaos, data, decimals, events, experimental probability, fractions, graph, mean, outcomes, percents, probability, probability simulation, simulation, theoretical probability, variance

Introduces students to probability simulation, allowing them to explore computer modeling while learning about probability.

Related Topics: agent modeling, chaos, data, decimals, events, experimental probability, fractions, mean, outcomes, percents, probability, probability simulation, simulation, theoretical probability, variance

Outlines the approach to playing the chaos game and how it relates to geometric fractals.

Related Topics: chaos, experimental probability, fractals, fractions, geometric probability, infinity, iteration, outcomes, pattern, percents, probability, probability simulation, random number, recursion, self-similarity, theoretical probability, triangle

Looks at data structures and their applications to probability theory.

Related Topics: combinatorics, counting, division, divisors, experimental probability, exponents, factors, fair, logarithm, multiplication, outcomes, probability, probability simulation, table, theoretical probability, tree diagram, trials

Introduces students to the vertical line test for graphs of functions.

Related Topics: algebra, cartesian coordinate, constant, continuous distribution, coordinate, coordinate plane, discontinuous, function properties, functions, graph, input, linear equations, linear functions, lines, output, piecewise, vertical line test

Introduces students to concepts that lead to probability.

Related Topics: circle graph, counting, events, experimental probability, fair, geometric probability, outcomes, pie chart, probability, probability simulation, random number, spinner, theoretical probability

Teaches distinguishing between possible and impossible graphs of functions as well as causes of graphical impossibility.

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, distance, function properties, functions, graph, intervals, linear equations, linear functions, lines, pattern, time, vertical line test

Outlines the approach to building fractals by cutting out portions of plane figures.

Related Topics: area, distance, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, multiplication, pattern, percents, perimeter, recursion, scale, segment, self-similarity, sequences, sets

Introduces students to the ideas involved in understanding fractals.

Related Topics: area, distance, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, multiplication, pattern, percents, perimeter, recursion, scale, segment, self-similarity, sequences, sets

Introduces the basic ideas needed for understanding functions.

Related Topics: addition, algebra, arithmetic, dependent, functions, independent, input, integers, linear functions, multiplication, output, pattern, subtraction, variable

Introduces students to simple probability concepts.

Related Topics: combinatorics, comparing, counting, events, experimental probability, fractions, geometric probability, intersection, outcomes, percents, probability, probability simulation, random number, sets, statistics, theoretical probability, trials, union, venn diagram

Looks at how irregular fractals can be generated and how they fit into computer graphics.

Related Topics: chaos, dimension, fractals, geometric sequences, geometry, iteration, logarithm, pattern, planes, polygon, recursion, scale, self-similarity, symmetry

Introduces students to modular (clock) arithmetic and its uses in real world problem-solving.

Related Topics: addition, arithmetic, division, elapsed time, modular, multiplication, remainders, time

Introduces the basic ideas needed for understanding linear functions.

Related Topics: addition, algebra, arithmetic, associative, commutative, dependent, distributive, division, equivalent, function properties, functions, independent, input, integers, intercept, linear equations, linear functions, multiplication, order of operations, output, pattern, slope, subtraction, table, variable

Introduces students to the concept of base ten and how to use other base number systems.

Related Topics: addition, algorithm, arithmetic, base, converting, counting, exponents, modular, multiplication, place value, subtraction

Looks at how Pascal's Triangle can be used to generate Sierpinski triangle-like results.

Related Topics: area, arithmetic, combinatorics, distance, division, factors, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, integers, iteration, length, limit, lines, multiples, multiplication, pascals triangle, pattern, percents, perimeter, quotient, recursion, remainders, scale, segment, self-similarity, sequences, sets, whole numbers

Introduces students to the idea of finding number patterns in the generation of several different types of fractals.

Related Topics: area, arithmetic, chaos, decimals, dimension, fractals, fractions, geometric sequences, geometry, graph, iteration, length, lines, pattern, pythagorean theorem, rectangles, recursion, segment, self-similarity, sequences, surface area, symmetry, triangle

Shows students that number patterns exist in the Pascal's Triangle, and reinforces student's ability to identify patterns.

Related Topics: arithmetic, binomial, chaos, coefficient, combinatorics, decimals, dimension, division, divisors, factors, fractals, fractions, geometric sequences, geometry, infinity, integers, iteration, length, lines, multiples, multiplication, pascal's triangle, pattern, probability, rectangles, recursion, remainders, segment, self-similarity, sequences, surface area, symmetry, triangle, whole numbers

This lesson teaches students about theoretical and experimental probability through a series of work stations.

Related Topics: bar graph, conditional probability, events, experimental probability, fair, fractions, geometric probability, monty hall, outcomes, percents, probability, probability simulation, probability with replacement, random number, spinner, theoretical probability, trials

Students learn about probability by predicting the outcome of planned experiments and playing racing games.

Related Topics: data, events, experimental probability, fair, fractions, outcomes, percents, probability, probability simulation, theoretical probability, trials

Students learn about how probability can be represented using geometry.

Related Topics: angles, area, circle graph, circles, counting, decimals, degrees, estimation, events, experimental probability, fair, geometric probability, geometry, length, outcomes, percents, polygon, polyhedra, probability, probability simulation, random number, right angle, spinner, statistics, theoretical probability, volume

Students learn about how probability can be represented using geometry.

Related Topics: angles, circle graph, circles, counting, decimals, estimation, events, experimental probability, fair, fractions, geometric probability, geometry, outcomes, percents, probability, probability simulation, random number, spinner, statistics, theoretical probability

Considers probability concepts on the basis of statistics in professional sports.

Related Topics: experimental probability, probability, statistics, theoretical probability

Students use probability to determine how likely it is for each tree in a small simulated forest to catch on fire.

Related Topics: agent modeling, chaos, decimals, estimation, events, experimental probability, outcomes, percents, probability, probability simulation, simulation, statistics, theoretical probability, variable

A capstone lesson to allow students to build a working definition of fractal.

Related Topics: area, chaos, dimension, distance, experimental probability, exponents, fractals, fractions, generator, geometric probability, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, logarithm, multiplication, outcomes, pattern, percents, perimeter, probability, random number, recursion, scale, segment, self-similarity, sequences, sets, theoretical probability, triangle

Students learn to identify a variety of patterns using sequences and tessellations.

Related Topics: addition, arithmetic, arithmetic sequences, geometric sequences, hexagon, iteration, multiplication, pattern, planes, polygon, recursion, recursive functions, sequences, squares, symmetry, tessellations, triangle

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

Related Topics: algebra, arithmetic, conditional probability, divisors, events, experimental probability, fair, fractions, independent, multiplication, outcomes, percentages, percents, probability, probability simulation, probability with replacement, probability without replacement, random number, sampling, solving equations, theoretical probability, trials

In this lesson, students explore sets, elements, and Venn diagrams.

Related Topics: counting, element, integers, intersection, pattern, sets, union, venn diagram, whole numbers

This lesson is designed to introduce students to the idea of a set and what it means to be a part of a set. Students will experiment with sets in conjunction with the Venn Diagram.

Related Topics: counting, element, pattern, sets, venn diagram

Students will learn about modular arithmetic in order to decipher encrypted messages.

Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, modular, multiples, multiplication, pattern, remainders, shift cipher, subtraction, time

Introduces all of the 2 variable function and prisoner/escapee notions necessary to understand the Mandelbrot set.

Related Topics: chaos, complex number, coordinate, coordinate plane, coordinate system, division, escape, exponents, fractals, functions, geometric sequences, geometry, infinity, iteration, julia set, mandelbrot set, multiplication, pattern, planes, prisoner, radius, recursion, recursive functions, self-similarity, sets, symmetry

Introduces the concept of tree diagrams as a way to compute probability of a multi-step event.

Related Topics: addition, combinatorics, conditional probability, events, experimental probability, exponents, fair, fractions, logarithm, multiples, multiplication, outcomes, percents, probability, probability simulation, random number, theoretical probability, tree diagram, trials

Considers probability problems with unexpected and surprising answers.

Related Topics: combinatorics, conditional probability, events, experimental probability, fair, fractions, monty hall, outcomes, percents, probability, probability simulation, probability with replacement, probability without replacement, proportion, random number, spinner, statistics, strategy, theoretical probability, trials

Related Topics: element, pattern, sets, venn diagram

Geometry  (...)
Students discover algorithms as they sort shapes into Venn diagrams. Then students compare the efficiency of their algorithms using box plots.

Related Topics: algorithm, box and whisker, box plot, geometry, pattern, polygon, sets, venn diagram

Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.

Related Topics: addition, arithmetic, arithmetic sequences, geometric sequences, graph, iteration, linear functions, multiplication, multiplier, negative number, pattern, positive number, pre-calculus, recursion, recursive functions, sequences

Introduces students to quadrilaterals with an emphasis on defining characteristics of parallelograms, rectangles, and trapezoids.

Related Topics: angles, geometry, parallel, parallelogram, polygon, quadrilaterals, rectangles, rhombus, squares, supplemental, tessellations

Introduces students to acute, obtuse, and right angles as well as relationships between angles formed by parallel lines crossed by a transversal.

Related Topics: acute, adjacent, alternate exterior, alternate interior, angles, corresponding, geometry, intersection, lines, obtuse, rays, right angle, transversal, vertical

Students learn about classifying angles by their measure and in relation to angles formed by two lines crossed by a transversal.

Related Topics: acute, angles, degrees, intersection, obtuse, rays, right angle

Comparing shapes with the same areas but different perimeters.

Related Topics: area, comparing, geometry, integers, length, perimeter, polygon, rectangles, right angle, squares, width

This lesson has students explore areas of rectangular and irregular shapes on a grid to help them understand the concept of area and the units in which area is measured.

Related Topics: area, geometry, length, perimeter, rectangles, right angle, squares, width

Helps students understand there are a variety of ways to solve problems. This lesson also gives students practice in using various methods to find the areas of irregular shapes.

Related Topics: area, geometry, length, rectangles, right angle, squares, width

Introduces students to plotting points on the Cartesian coordinate system -- an alternative to "Graphing and the Coordinate Plane."

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, functions, graph, linear equations, linear functions, negative number, planes, slope

Students learn about the concepts and applications of chaos.

Related Topics: agent modeling, chaos, conditional probability, experimental probability, iteration, outcomes, percents, probability, probability simulation, theoretical probability

Introduces students to a geometric derivation of the conic sections.

Related Topics: circles, conic section, ellipse, hyperbola, parabola, pre-calculus

This lesson utilizes the concepts of cross-sections of three-dimensional figures to demonstrate the derivation of two-dimensional shapes.

Related Topics: conic section, geometry, hyperbola, parabola, polygon, pre-calculus, pyramid

Introduces students to elapsed time and how to calculate it.

Related Topics: addition, counting, elapsed time, modular, subtraction, time

Students practice finding the ending time given the starting time and an elapsed time.

Related Topics: addition, arithmetic, counting, elapsed time, modular, subtraction, time

Students consider the patterns that emerge from agent models and geometric fractals.

Related Topics: agent modeling, fractals, pattern, recursion, self-similarity

Uses modular (clock) arithmetic to find patterns in Pascal's Triangle.

Related Topics: addition, arithmetic, division, divisors, integers, modular, pascal's triangle, pascals triangle, pattern, remainders, sum, triangle, whole numbers

Outlines the approach to playing the chaos game and how it relates to geometric fractals.

Related Topics: chaos, experimental probability, fractals, fractions, geometric probability, infinity, iteration, outcomes, pattern, percents, probability, probability simulation, random number, recursion, self-similarity, theoretical probability, triangle

Explores lines, planes, angles, and polygons in tessellations.

Related Topics: angles, area, flips, geometry, glides, hexagon, length, lines, pattern, perimeter, planes, polygon, rectangles, reflections, regular, rotation, slides, squares, symmetry, tessellations, triangle

Students learn basic ideas about graphing points on the coordinate plane.

Related Topics: algebra, axis, cartesian coordinate, coordinate, coordinate plane, coordinate system, graph, linear functions, lines, negative number, number line, pattern, planes, positive number, quadrant, slope

Outlines the approach to building fractals by cutting out portions of plane figures.

Related Topics: area, distance, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, multiplication, pattern, percents, perimeter, recursion, scale, segment, self-similarity, sequences, sets

Introduces students to the ideas involved in understanding fractals.

Related Topics: area, distance, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, multiplication, pattern, percents, perimeter, recursion, scale, segment, self-similarity, sequences, sets

Looks at how irregular fractals can be generated and how they fit into computer graphics.

Related Topics: chaos, dimension, fractals, geometric sequences, geometry, iteration, logarithm, pattern, planes, polygon, recursion, scale, self-similarity, symmetry

Introduces students to length, perimeter and area.

Related Topics: acute, addition, area, arithmetic, cartesian coordinate, coordinate plane, dimension, distance, geometry, length, multiplication, obtuse, perimeter, planes, polygon, pythagorean theorem, rectangles, subtraction, triangle, width

Introduces students to lines, rays, line segments, and planes.

Related Topics: algebra, axis, coordinate plane, coordinate system, functions, geometry, graph, infinity, lines, number line, planes, rays, segment

Looks at how Pascal's Triangle can be used to generate Sierpinski triangle-like results.

Related Topics: area, arithmetic, combinatorics, distance, division, factors, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, integers, iteration, length, limit, lines, multiples, multiplication, pascals triangle, pattern, percents, perimeter, quotient, recursion, remainders, scale, segment, self-similarity, sequences, sets, whole numbers

Introduces students to the idea of finding number patterns in the generation of several different types of fractals.

Related Topics: area, arithmetic, chaos, decimals, dimension, fractals, fractions, geometric sequences, geometry, graph, iteration, length, lines, pattern, pythagorean theorem, rectangles, recursion, segment, self-similarity, sequences, surface area, symmetry, triangle

Shows students that number patterns exist in the Pascal's Triangle, and reinforces student's ability to identify patterns.

Related Topics: arithmetic, binomial, chaos, coefficient, combinatorics, decimals, dimension, division, divisors, factors, fractals, fractions, geometric sequences, geometry, infinity, integers, iteration, length, lines, multiples, multiplication, pascal's triangle, pattern, probability, rectangles, recursion, remainders, segment, self-similarity, sequences, surface area, symmetry, triangle, whole numbers

Introduces students to the concept of perimeter.

Related Topics: addition, algorithm, arithmetic, geometry, length, perimeter, planes, polygon, rectangles, squares, width

Students learn about perimeter and the units used to measure perimeter using a variety of materials including their hands, feet, rulers, and computer applets.

Related Topics: arithmetic, geometry, length, perimeter, polygon, rectangles, right angle, scale, squares

Students learn about how probability can be represented using geometry.

Related Topics: angles, area, circle graph, circles, counting, decimals, degrees, estimation, events, experimental probability, fair, geometric probability, geometry, length, outcomes, percents, polygon, polyhedra, probability, probability simulation, random number, right angle, spinner, statistics, theoretical probability, volume

Students learn about how probability can be represented using geometry.

Related Topics: angles, circle graph, circles, counting, decimals, estimation, events, experimental probability, fair, fractions, geometric probability, geometry, outcomes, percents, probability, probability simulation, random number, spinner, statistics, theoretical probability

A capstone lesson to allow students to build a working definition of fractal.

Related Topics: area, chaos, dimension, distance, experimental probability, exponents, fractals, fractions, generator, geometric probability, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, logarithm, multiplication, outcomes, pattern, percents, perimeter, probability, random number, recursion, scale, segment, self-similarity, sequences, sets, theoretical probability, triangle

Students learn how the Pythagorean Theorem works and how to apply it.

Related Topics: algebra, angles, area, arithmetic, cartesian coordinate, coordinate plane, distance, exponents, geometry, hypotenuse, length, perimeter, pythagorean theorem, right angle, slides, solving equations, squares, triangles, trigonometry

Students learn to identify a variety of patterns using sequences and tessellations.

Related Topics: addition, arithmetic, arithmetic sequences, geometric sequences, hexagon, iteration, multiplication, pattern, planes, polygon, recursion, recursive functions, sequences, squares, symmetry, tessellations, triangle

In this lesson, students explore sets, elements, and Venn diagrams.

Related Topics: counting, element, integers, intersection, pattern, sets, union, venn diagram, whole numbers

This lesson is designed to introduce students to the idea of a set and what it means to be a part of a set. Students will experiment with sets in conjunction with the Venn Diagram.

Related Topics: counting, element, pattern, sets, venn diagram

Introduces students to the concepts of surface area and volume.

Related Topics: area, arithmetic, dimension, geometry, integers, length, polyhedra, prisms, surface area, volume

This lesson teaches students how to find the surface area of non-rectangular prisms.

Related Topics: area, dimension, geometry, length, polyhedra, prisms, rectangles, slant height, surface area, triangle, volume

This lesson teaches students how to find the surface area of rectangular prisms.

Related Topics: area, dimension, geometry, length, polyhedra, prisms, rectangles, surface area

Examines plane symmetry.

Related Topics: angles, area, geometry, glides, hexagon, illusion, length, pattern, planes, polygon, rectangles, reflections, regular, rotation, segment, squares, symmetry, tessellations, transformation, translation, triangle

Introduces all of the 2 variable function and prisoner/escapee notions necessary to understand the Mandelbrot set.

Related Topics: chaos, complex number, coordinate, coordinate plane, coordinate system, division, escape, exponents, fractals, functions, geometric sequences, geometry, infinity, iteration, julia set, mandelbrot set, multiplication, pattern, planes, prisoner, radius, recursion, recursive functions, self-similarity, sets, symmetry

This lesson shows elementary students how they can know, for certain, that rigid motions like reflections, rotations, and translations create a shape congruent to the original.

Related Topics: congruent, reflections, rotation, transformation, translation

Introduces students to concepts of transformations.

Related Topics: angles, cartesian coordinate, coordinate plane, coordinate system, dimension, distance, flips, geometry, glides, graph, hexagon, image, parallelogram, pattern, planes, polygon, pre-image, reflections, rotation, squares, symmetry, tessellations, transformation, translation, transpose, triangles

Students learn about finding the area of a triangle.

Related Topics: area, cartesian coordinate, coordinate plane, distance, geometry, length, right angle, squares, triangle, triangles, width

Explore the mathematical nature of art and tilings and looks at the role of math in nature and our culture.

Related Topics: angles, area, contrast, geometry, glides, graph, hexagon, hue, illusion, length, lines, pattern, planes, polygon, rectangles, reflections, regular, rotation, segment, squares, symmetry, tessellations, transformation, translation, triangle, value

This lesson teaches students how to find the volume of non-rectangular prisms.

Related Topics: area, depth, dimension, geometry, height, length, multiplication, polyhedra, prisms, rectangles, slant height, squares, surface area, triangle, volume, width

This lesson teaches students how to find the volume of rectangular prisms.

Related Topics: area, depth, dimension, geometry, height, length, multiplication, polyhedra, prisms, rectangles, squares, triangle, volume, width

Modeling  (...)
Lesson plan to help students understand independent and dependent variables through a fire probability simulation.

Related Topics: algebra, dependent, independent, input, output, probability, variable

Students consider the patterns that emerge from agent models and geometric fractals.

Related Topics: agent modeling, fractals, pattern, recursion, self-similarity

Introduction to various estimation methods through the simulation of a forest fire.

Related Topics: estimation, probability, probability simulation

Utilizes and reinforces concepts of probability, mean, line plots, experimental data, and chaos in analyzing a forest fire simulation.

Related Topics: agent modeling, chaos, data, decimals, events, experimental probability, fractions, graph, mean, outcomes, percents, probability, probability simulation, simulation, theoretical probability, variance

Introduces students to probability simulation, allowing them to explore computer modeling while learning about probability.

Related Topics: agent modeling, chaos, data, decimals, events, experimental probability, fractions, mean, outcomes, percents, probability, probability simulation, simulation, theoretical probability, variance

Teaches distinguishing between possible and impossible graphs of functions as well as causes of graphical impossibility.

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, distance, function properties, functions, graph, intervals, linear equations, linear functions, lines, pattern, time, vertical line test

Demonstrates the connections between formulas, graphs and words.

Related Topics: acceleration, algebra, cartesian coordinate, concave, constant, coordinate, coordinate plane, coordinate system, distance, functions, graph, intervals, linear equations, linear functions, lines, parabola, slope, time, velocity

Number and Operations  (...)
Students discover algorithms as they sort shapes into Venn diagrams. Then students compare the efficiency of their algorithms using box plots.

Related Topics: algorithm, box and whisker, box plot, geometry, pattern, polygon, sets, venn diagram

Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.

Related Topics: addition, arithmetic, arithmetic sequences, geometric sequences, graph, iteration, linear functions, multiplication, multiplier, negative number, pattern, positive number, pre-calculus, recursion, recursive functions, sequences

Introduces students to modular (clock) arithmetic and how modular arithmetic can be used to encode messages using simple shift, multiple and affine ciphers.

Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, factors, inverse, modular, multiples, multiplication, remainders, shift cipher, subtraction, time

Introduces students to fractions and explores basic mathematical operations with fractions, comparing fractions, and converting fractions into decimals or percents.

Related Topics: comparing, converting, decimals, denominator, division, divisors, factors, fractions, number line, numerator, ordering, proportion, rational numbers, reducing fraction, subtraction

Introduction to various estimation methods through the simulation of a forest fire.

Related Topics: estimation, probability, probability simulation

Students practice and improve upon their estimation skills.

Related Topics: area, comparing, counting, estimation, length, scale

Introduces students to making estimations.

Related Topics: addition, area, arithmetic, comparing, counting, division, estimation, length, multiplication, percentages, percents, scale, subtraction

Students learn about factoring by using manipulatives and computer applets.

Related Topics: area, division, divisors, factors, multiples, multiplication, rectangles, whole numbers

Finding the factors of whole numbers.

Related Topics: area, division, divisors, factors, multiples, multiplication, rectangles, whole numbers

Uses modular (clock) arithmetic to find patterns in Pascal's Triangle.

Related Topics: addition, arithmetic, division, divisors, integers, modular, pascal's triangle, pascals triangle, pattern, remainders, sum, triangle, whole numbers

Outlines the approach to playing the chaos game and how it relates to geometric fractals.

Related Topics: chaos, experimental probability, fractals, fractions, geometric probability, infinity, iteration, outcomes, pattern, percents, probability, probability simulation, random number, recursion, self-similarity, theoretical probability, triangle

Students learn how to convert from fractions to decimals.

Related Topics: addition, converting, decimals, denominator, division, fractions, numerator, rational numbers, reducing fraction, subtraction

Students learn how to convert from fractions to percentages.

Related Topics: converting, decimals, denominator, division, fractions, multiplication, numerator, percentages, percents, rational numbers, reducing fraction

Introduces students to fractions and explores basic mathematical operations with fractions, comparing fractions, and converting fractions into decimals or percents.

Related Topics: addition, arithmetic, decimals, denominator, division, fractions, inverse, lowest common denominator, multiplication, numerator, percents, rational numbers, subtraction

Students and teacher play a game called "Fraction King" to understand the idea of taking fractional parts of whole numbers then use manipulatives and several computer applets to cement the idea.

Related Topics: arithmetic, comparing, denominator, fractions, multiplication, number line, numerator, ordering, rational numbers, subtraction

Students get practice working with conversion of fractions, decimals, percents through using several of the Interactivate activities.

Related Topics: area, circle graph, circles, converting, decimals, division, fractions, percents, pie chart, proportion, rational numbers

Outlines the approach to building fractals by cutting out portions of plane figures.

Related Topics: area, distance, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, multiplication, pattern, percents, perimeter, recursion, scale, segment, self-similarity, sequences, sets

Introduces students to the ideas involved in understanding fractals.

Related Topics: area, distance, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, multiplication, pattern, percents, perimeter, recursion, scale, segment, self-similarity, sequences, sets

Looks at how irregular fractals can be generated and how they fit into computer graphics.

Related Topics: chaos, dimension, fractals, geometric sequences, geometry, iteration, logarithm, pattern, planes, polygon, recursion, scale, self-similarity, symmetry

Introduces students to modular (clock) arithmetic and its uses in real world problem-solving.

Related Topics: addition, arithmetic, division, elapsed time, modular, multiplication, remainders, time

Reinforces skills associated with multiplying fractions and mixed numbers.

Related Topics: arithmetic, denominator, division, fractions, geometric sequences, graph, improper, iteration, mixed numbers, multiplication, numerator, recursion, sequences, whole numbers

Introduces students to the concept of base ten and how to use other base number systems.

Related Topics: addition, algorithm, arithmetic, base, converting, counting, exponents, modular, multiplication, place value, subtraction

Looks at how Pascal's Triangle can be used to generate Sierpinski triangle-like results.

Related Topics: area, arithmetic, combinatorics, distance, division, factors, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, integers, iteration, length, limit, lines, multiples, multiplication, pascals triangle, pattern, percents, perimeter, quotient, recursion, remainders, scale, segment, self-similarity, sequences, sets, whole numbers

Introduces students to the idea of finding number patterns in the generation of several different types of fractals.

Related Topics: area, arithmetic, chaos, decimals, dimension, fractals, fractions, geometric sequences, geometry, graph, iteration, length, lines, pattern, pythagorean theorem, rectangles, recursion, segment, self-similarity, sequences, surface area, symmetry, triangle

Shows students that number patterns exist in the Pascal's Triangle, and reinforces student's ability to identify patterns.

Related Topics: arithmetic, binomial, chaos, coefficient, combinatorics, decimals, dimension, division, divisors, factors, fractals, fractions, geometric sequences, geometry, infinity, integers, iteration, length, lines, multiples, multiplication, pascal's triangle, pattern, probability, rectangles, recursion, remainders, segment, self-similarity, sequences, surface area, symmetry, triangle, whole numbers

Students practice arithmetic skills. Can be tailored for practice of all types of single operation arithmetic ranging from simple addition to operations with integers and decimals.

Related Topics: addition, algorithm, arithmetic, coordinate, data, decimals, division, fractions, graph, integers, linear equations, linear functions, multiplication, subtraction

A capstone lesson to allow students to build a working definition of fractal.

Related Topics: area, chaos, dimension, distance, experimental probability, exponents, fractals, fractions, generator, geometric probability, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, logarithm, multiplication, outcomes, pattern, percents, perimeter, probability, random number, recursion, scale, segment, self-similarity, sequences, sets, theoretical probability, triangle

Students learn to identify a variety of patterns using sequences and tessellations.

Related Topics: addition, arithmetic, arithmetic sequences, geometric sequences, hexagon, iteration, multiplication, pattern, planes, polygon, recursion, recursive functions, sequences, squares, symmetry, tessellations, triangle

In this lesson, students explore sets, elements, and Venn diagrams.

Related Topics: counting, element, integers, intersection, pattern, sets, union, venn diagram, whole numbers

This lesson is designed to introduce students to the idea of a set and what it means to be a part of a set. Students will experiment with sets in conjunction with the Venn Diagram.

Related Topics: counting, element, pattern, sets, venn diagram

Students will learn about modular arithmetic in order to decipher encrypted messages.

Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, modular, multiples, multiplication, pattern, remainders, shift cipher, subtraction, time

Introduces all of the 2 variable function and prisoner/escapee notions necessary to understand the Mandelbrot set.

Related Topics: chaos, complex number, coordinate, coordinate plane, coordinate system, division, escape, exponents, fractals, functions, geometric sequences, geometry, infinity, iteration, julia set, mandelbrot set, multiplication, pattern, planes, prisoner, radius, recursion, recursive functions, self-similarity, sets, symmetry

Related Topics: element, pattern, sets, venn diagram

Probability  (...)
Students learn about the concepts and applications of chaos.

Related Topics: agent modeling, chaos, conditional probability, experimental probability, iteration, outcomes, percents, probability, probability simulation, theoretical probability

Introduces conditional probability and the probability of simultaneous events.

Related Topics: comparing, conditional probability, events, experimental probability, fair, fractions, independent, multiplication, percents, probability, probability simulation, probability without replacement, random number, theoretical probability

Utilizes and reinforces concepts of probability, mean, line plots, experimental data, and chaos in analyzing a forest fire simulation.

Related Topics: agent modeling, chaos, data, decimals, events, experimental probability, fractions, graph, mean, outcomes, percents, probability, probability simulation, simulation, theoretical probability, variance

Introduces students to probability simulation, allowing them to explore computer modeling while learning about probability.

Related Topics: agent modeling, chaos, data, decimals, events, experimental probability, fractions, mean, outcomes, percents, probability, probability simulation, simulation, theoretical probability, variance

Outlines the approach to playing the chaos game and how it relates to geometric fractals.

Related Topics: chaos, experimental probability, fractals, fractions, geometric probability, infinity, iteration, outcomes, pattern, percents, probability, probability simulation, random number, recursion, self-similarity, theoretical probability, triangle

Looks at data structures and their applications to probability theory.

Related Topics: combinatorics, counting, division, divisors, experimental probability, exponents, factors, fair, logarithm, multiplication, outcomes, probability, probability simulation, table, theoretical probability, tree diagram, trials

Introduces students to concepts that lead to probability.

Related Topics: circle graph, counting, events, experimental probability, fair, geometric probability, outcomes, pie chart, probability, probability simulation, random number, spinner, theoretical probability

Introduces students to simple probability concepts.

Related Topics: combinatorics, comparing, counting, events, experimental probability, fractions, geometric probability, intersection, outcomes, percents, probability, probability simulation, random number, sets, statistics, theoretical probability, trials, union, venn diagram

This lesson teaches students about theoretical and experimental probability through a series of work stations.

Related Topics: bar graph, conditional probability, events, experimental probability, fair, fractions, geometric probability, monty hall, outcomes, percents, probability, probability simulation, probability with replacement, random number, spinner, theoretical probability, trials

Students learn about probability by predicting the outcome of planned experiments and playing racing games.

Related Topics: data, events, experimental probability, fair, fractions, outcomes, percents, probability, probability simulation, theoretical probability, trials

Students learn about how probability can be represented using geometry.

Related Topics: angles, area, circle graph, circles, counting, decimals, degrees, estimation, events, experimental probability, fair, geometric probability, geometry, length, outcomes, percents, polygon, polyhedra, probability, probability simulation, random number, right angle, spinner, statistics, theoretical probability, volume

Students learn about how probability can be represented using geometry.

Related Topics: angles, circle graph, circles, counting, decimals, estimation, events, experimental probability, fair, fractions, geometric probability, geometry, outcomes, percents, probability, probability simulation, random number, spinner, statistics, theoretical probability

Considers probability concepts on the basis of statistics in professional sports.

Related Topics: experimental probability, probability, statistics, theoretical probability

Students use probability to determine how likely it is for each tree in a small simulated forest to catch on fire.

Related Topics: agent modeling, chaos, decimals, estimation, events, experimental probability, outcomes, percents, probability, probability simulation, simulation, statistics, theoretical probability, variable

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

Related Topics: algebra, arithmetic, conditional probability, divisors, events, experimental probability, fair, fractions, independent, multiplication, outcomes, percentages, percents, probability, probability simulation, probability with replacement, probability without replacement, random number, sampling, solving equations, theoretical probability, trials

Introduces the concept of tree diagrams as a way to compute probability of a multi-step event.

Related Topics: addition, combinatorics, conditional probability, events, experimental probability, exponents, fair, fractions, logarithm, multiples, multiplication, outcomes, percents, probability, probability simulation, random number, theoretical probability, tree diagram, trials

Considers probability problems with unexpected and surprising answers.

Related Topics: combinatorics, conditional probability, events, experimental probability, fair, fractions, monty hall, outcomes, percents, probability, probability simulation, probability with replacement, probability without replacement, proportion, random number, spinner, statistics, strategy, theoretical probability, trials

Statistics  (...)
Students learn what bar graphs are used for, how to interpret the data presented, and how to organize their own data using bar graphs.

Related Topics: bar graph, categorical, data, height, scale, statistics

Introduces students to quartiles and box plots.

Related Topics: box and whisker, box plot, data, mean, measures of central tendency, median, mode, quartile, range, statistics

Introduces students to plotting points on the Cartesian coordinate system -- an alternative to "Graphing and the Coordinate Plane."

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, functions, graph, linear equations, linear functions, negative number, planes, slope

Introduction and fine points of using bar graphs and histograms.

Related Topics: bar graph, categorical, comparing, counting, data, graph, histogram, intervals, length, mean, numerical, scale, skewed distribution, standard deviation, statistics

Teaches distinguishing between possible and impossible graphs of functions as well as causes of graphical impossibility.

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, distance, function properties, functions, graph, intervals, linear equations, linear functions, lines, pattern, time, vertical line test

This lesson allows students to learn what bar graphs are used for, how to interpret the data presented, and how to organize their own data using bar graphs.

Related Topics: bar graph, categorical, circles, counting, data, squares, statistics, triangle

Introduces statistical measures of center.

Related Topics: arithmetic, histogram, mean, measures of central tendency, median, mode, range, sets, statistics, sum

Students are introduced to correlation between two variables and the line of best fit.

Related Topics: best-fit line, bivariate, cartesian coordinate, coordinate plane, correlation, curve fitting, data, deviations, linear equations, linear functions, regression, residual, scatter plot, slope, statistics, variable

This lesson will challenge students to think creatively by having them design and build water balloon catchers from random scrap materials, while requiring them to take into consideration a multitude of variables. Students will then construct at least two bar graphs to be used in a commercial advocating the purchase of their group's catcher.

Related Topics: bar graph, counting, data, graph, histogram, intervals, lines, mean, median, mode, pie chart, probability, range, skewed distribution, standard deviation, statistics

Demonstrates the connections between formulas, graphs and words.

Related Topics: acceleration, algebra, cartesian coordinate, concave, constant, coordinate, coordinate plane, coordinate system, distance, functions, graph, intervals, linear equations, linear functions, lines, parabola, slope, time, velocity

Looks at statistics and data analysis concepts from the practical questions that arise in everyday life.

Related Topics: bar graph, fractions, histogram, percentages, percents, statistics

Introduces students to stem-and-leaf plots and calculating the mean, median, and mode from the plots.

Related Topics: arithmetic, data, data plot, graph, histogram, mean, measures of central tendency, median, mode, range, statistics, stem and leaf

Introduces the normal distribution and looks at the bell curve controversy.

Related Topics: area, arithmetic, bell curve, continuous distribution, deviations, experimental probability, exponential, histogram, infinity, mean, measures of central tendency, median, mode, normal distribution, outcomes, percents, probability, range, skewed distribution, squares, standard deviation, statistics, theoretical probability, trials, variance

Students learn about the difference between univariate and bivariate data and understand how to choose the best graph to display the data.

Related Topics: bar graph, bivariate, box and whisker, box plot, cartesian coordinate, categorical, circle graph, circles, coordinate, coordinate plane, correlation, curve fitting, data, data plot, deviations, double bar graph, graph, histogram, intervals, mean, measures of central tendency, median, mode, numerical, outlier, percentages, percents, pie chart, quartile, range, regression, residual, scale, scatter plot, skewed distribution, standard deviation, statistics, stem and leaf, table, univariate

Trigonometry  (...)
Introduces students to graphing in the Polar coordinate plane

Related Topics: calculus, coordinate plane, coordinate system, cosine, data plot, graph, polar coordinates, pre-calculus, sine, tangent, trigonometry

Students learn how the Pythagorean Theorem works and how to apply it.

Related Topics: algebra, angles, area, arithmetic, cartesian coordinate, coordinate plane, distance, exponents, geometry, hypotenuse, length, perimeter, pythagorean theorem, right angle, slides, solving equations, squares, triangles, trigonometry

Other  (...)
Introduces students to elapsed time and how to calculate it.  