Freaky Fractals

A fractal is an amazing geometric pattern which, when viewed closely, shows itself to be constructed of ever-smaller parts similar to the original. Fractal patterns are everywhere: trees, shells, leaves, ferns, flowers, vegetables, rivers, coastlines, mountains, geologic faults, planetary orbits, circulatory systems, music, clouds, weather, and even lightning bolts!

Grades covered: through 12

Curriculum Topics: Fractals, Patterns, Exponents, Exponential Growth, Decalcomania

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Standards

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

Common Standards Click to View

4.OA.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “”Add 3″” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.||Common Core Mathematics||Grade 4||Operations And Algebraic Thinking||Generate And Analyze Patterns|||5.OA.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “”Add 3″” and the starting number 0, and given the rule “”Add 6″” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.||Common Core Mathematics||Grade 5||Operations And Algebraic Thinking||Analyze Patterns And Relationships

California Standards (Click to View)

1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 23 x 3).||CA Mathematics||Grade 5||01. Number Sense||1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers.|||2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-numbers powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.||CA Mathematics||Grade 7||02. Algebra and Functions||2.0 Students interpret and evaluate expressions involving integer powers and simple roots.|||02.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.||CA Mathematics||Grade 8 – 12||01. Algebra I|||4.0 Students are familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families.||CA Mathematics||Grade 8 – 12||04. Probability and Statistics

Categories include:

Visual and Performing Arts
Grades K-2
Grades 3-5
Grades 6-8
Art
Math

Tags: Geometry, Arts & Crafts, Patterns

Subjects covered: ["Art","Math"]

Freaky Fractals

Standards

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