Aligned Resources

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

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

Build your own polygon and transform it in the Cartesian coordinate system. Experiment with reflections across any line, revolving around any line (which yields a 3-D image), rotations about any point, and translations in any direction.

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

Primary Subjects: Algebra, Calculus, Geometry, Graphs

Related Topics: angles, calculus, coordinate, coordinate plane, coordinate system, flips, geometry, glides, graph, polygon, polyhedra, reflections, rotation, symmetry, transformation, translation, transpose

Students work step-by-step through the generation of a different Hilbert-like Curve (a fractal made from deforming a line by bending it), allowing them to 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: decimals, fractals, fractions, geometric sequences, geometry, iteration, length, pattern, self-similarity, sequences, surface area, symmetry

Step through the generation of a Hilbert Curve -- a fractal made from deforming a line by bending it, and 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: chaos, fractals, geometric sequences, geometry, iteration, length, lines, pattern, recursion, self-similarity, sequences

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

Explore the world of translations, reflections, and rotations in the Cartesian coordinate system by transforming squares, triangles and parallelograms. Parameters: Shape, x or y translation, x or y reflection, angle of rotation.

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

Primary Subjects: Geometry, Graphs

Related Topics: cartesian coordinate, coordinate plane, coordinate system, flips, geometry, glides, graph, hexagon, image, polygon, pre-image, reflections, rotation, symmetry, transformation, translation, transpose, triangle

Build your own polygon and transform it in the Cartesian coordinate system. Experiment with reflections across any line, rotations about any point, and translations in any direction. Parameters: Shape, x or y translation, x or y reflection, angle of rotation

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

Primary Subjects: Geometry, Graphs

Related Topics: angles, cartesian coordinate, coordinate, coordinate plane, coordinate system, flips, geometry, glides, graph, image, linear equations, polygon, pre-image, reflections, rotation, symmetry, transformation, translation, transpose