Patterns

9/1 and 9/6

What is a pattern?• A set of shapes or numbers that are repeated in a

predictable way

• Understanding patterns is a basic skill for further mathematics and will help us to go on to functions and graphing equations

• You will be able to see and understand the way things work together, we organize our world, and organize our daily lives

Finding Patterns

• PART 1: Is It a Pattern?

• PART 2: Identifying the Core of a Pattern

• PART 3: Extending the Pattern

Is it a pattern?

Patterns in Art

Leonardo Da Vinci

•Used patterns in his artwork•The Da Vinci Challenge

– Flower of Life• Objective is to score the most

points by creating patterns• You can block your opponents

from making patterns• When no more patterns are

possible, the game is over

Patterns in Music

• Choral and Instrumental–Patterns in composing music–Chorus, bridge, verse–Notes, chords

Patterns are also in Codes

Braille is also a Pattern

Braille is one of the most important codes in the world - it is used by blind people to read and write.

It is easy: there are six dot positions, and the dots are raised up (so you can feel them) in special patterns.

Each pattern of dots is a "character" (a letter or number, etc)

Identifying the Core

•The core of a pattern is the shortest string of elements that repeat

•Worksheet: For each pattern, describe the core of the pattern and extend it one more term

Numeric Patterns

• Find the change between each term

–Adding, Subtracting, Multiplying, Dividing–Examples:

• 1, 3, 5, 7…• .1, .2, .3, .4…• 8, 6, 4, 2…

• Picture patterns you can see what changes or moves

Sequence Tables

Use tables to organize data…

-Term number is the number in the sequence-Sequence number is the actual pattern

Term # 0 1 2 3 4 5

Sequence # 1 2 3 4 5 …

Linear Review

• Linear sequences add the same number to each next term and graph in a straight line

• Non-Linear sequences add different number patterns (like odd numbers) and graph with a bend or a peak

Patterns Review

•Numbers or shapes that repeat in a predictable way

•The core is the shortest string of elements before it repeats

•Picture Patterns

•Numeric Patterns

Pascal’s Triangle

•Complete the pattern by filling in the missing numbers

•Answer the questions and color in the patterns

Pascal’s Triangle

The pattern in Pascal's triangle is created by adding the two

numbers above to get the number below.

Some Common Patterns in Pascal’s Triangle

The Sierpinksi Triangle

Other views of The Sierpinksi Triangle

Pascal’s Triangle can also lead us to the Fibonacci

Sequence!

Fibonacci

The Fibonacci NumbersThe original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances.

Fibonacci Numbers in Rectangles and Ancient

Architecture

Fibonacci Numbers in Shell Spirals

Fibonacci Numbers in Flowers and Plants