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

Audiences: Grades 6-8, Grades 9-12

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

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 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

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

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

Primary Subjects: Discrete, Geometry, Number and Operations

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

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

Step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence of an infinite sequence of numbers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Number and Operations

Related Topics: decimals, distance, fractals, geometric sequences, infinity, iteration, length, logarithm, multiplication, pattern, percentages, percents, proportion, rational numbers, recursion, recursive functions, self-similarity, sequences