Aligned Resources

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

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry

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

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

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Geometry, Number and Operations, Probability

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

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

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Geometry, Number and Operations

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

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

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

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

Introduces students to the ideas involved in understanding fractals.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Geometry, Number and Operations

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

Students learn about definite integrals through limits and Riemann sums

Audiences: Grades 9-12, Undergraduate

Primary Subjects: Algebra, Calculus

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

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

Audiences: Grades 9-12, Undergraduate

Primary Subjects: Discrete, Geometry, Number and Operations

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

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

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Geometry, Number and Operations

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

Students learn about how probability can be represented using geometry.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Geometry, Probability

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

Examines plane symmetry.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

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.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Geometry, Number and Operations

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 students to concepts of transformations.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Geometry

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

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

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry

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

Practice your knowledge of acute, obtuse, and alternate angles. Also, practice relationships between angles - vertical, adjacent, alternate, same-side, and corresponding. Angles is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: acute, angles, assessment, geometry, lines, obtuse, parallel

Explore cross sections of different geometric solids: cone, double cone, cylinder, pyramid, and prism. Manipulate the cross section with slider bars, and see how the graphical representation changes.

Audiences: Grades 9-12, Undergraduate

Primary Subjects: Algebra, Calculus, Geometry, Graphs

Related Topics: algebra, calculus, cartesian coordinate, circles, conic section, coordinate system, ellipse, flyer, graph, hyperbola, parabola, polygon, polyhedra, pre-calculus, prisms, pyramid, radius, rotation, transformation

Create your own fractals by drawing a "line deformation rule" and stepping through the generation of a geometric fractal. Parameters: Grid type, number of bending points on the line.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Geometry, Number and Operations

Related Topics: chaos, fractals, geometric sequences, iteration, pattern, pre-calculus, recursion, scale, self-similarity, sequences, symmetry, transformation

Build a "floor tile" by dragging the corners of a quadrilateral. Learn about tessellation of quadrilateral figures when the shape you built is tiled over an area.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: angles, area, coordinate plane, coordinate system, length, pattern, planes, quadrilaterals, rectangles, reflections, rhombus, rotation, slides, symmetry, tessellations, transformation, translation

Generate complicated geometric fractals by specifying starting polygon and scale factor.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Geometry

Related Topics: fractals, geometry, logarithm, polygon, recursion, scale, self-similarity

InteGreat! allows the user to visually explore the idea of integration through approximating the integral value with partitions. The user controls the number of partitions, the upper and lower limits, and the method used to estimate the integral.

Audiences: Grades 9-12, Undergraduate

Primary Subjects: Algebra, Calculus, Graphs

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

Enter a complex value for "c" in the form of an ordered pair of real numbers. The applet draws the fractal Julia set for that seed value.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: complex number, coordinate plane, coordinate system, fractals, iteration, julia set, mandelbrot set, recursion, recursive functions, sets

Step through the generation of the Koch Snowflake -- a fractal made from deforming the sides of a triangle, and explore number patterns in sequences and geometric properties of fractals.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: decimals, fractals, geometric sequences, infinity, iteration, lines, pre-calculus, recursion, self-similarity, sequences

Plot ordered pairs on the graph, and they will be connected in the order that they are input. This enables you to decide how the pairs should be connected, rather than having the computer connect them from left to right.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Geometry, Graphs, Statistics

Related Topics: cartesian coordinate, coordinate, coordinate plane, coordinate system, data plot, graph, lines, vertical line test

Step through the generation of Sierpinski's Carpet -- a fractal made from subdividing a square into nine smaller squares and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: algebra, area, fractals, fractions, geometric sequences, iteration, pattern, pre-calculus, recursion, recursive functions, self-similarity, sequences

Step through the generation of Sierpinski's Triangle -- a fractal made from subdividing a triangle into four smaller triangles and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: dimension, fractals, fractions, geometric sequences, geometry, iteration, length, pattern, pre-calculus, recursion, recursive functions, self-similarity, sequences, symmetry, triangle

Manipulate dimensions of polyhedra, and watch how the surface area and volume change. Parameters: Type of polyhedron, length, width and height. Surface Area and Volume one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

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

Create a tessellation by deforming a triangle, rectangle or hexagon to form a polygon that tiles the plane. Corners of the polygons may be dragged, and corresponding edges of the polygons may be dragged. Parameters: Colors, starting polygon.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

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

Explore fractals by investigating the relationships between the Mandelbrot set and Julia sets.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: chaos, complex number, coordinate, coordinate plane, exponents, fractals, functions, geometric sequences, geometry, iteration, julia set, mandelbrot set, pattern, recursion, recursive functions, self-similarity, sets