Patterns and SequencesA Prelude to Sequences and Series

Math 2B Lecture 4th Quarter SY 2010-2011

Source: http://www.icoachmath.com/SiteMap/Pattern.html

•Patterns – are sets of objects in which all the members are related with each other by a specific rule.

•Visual Patterns – are patterns that consist of elements that can be perceived through the sense of sight.

Source: http://ellie-earlychildhoodmathematics.blogspot.com/2010/10/algebra.html

•Patterns can be shapes, designs or groups of numbers that repeat. Patterns can be seen when investigating items that are around them in their everyday environment.

• The core of a pattern is the shortest string of elements that repeats. Patterns can also be extended.

Patterns possess the following characteristics:

•Change – a change that is observable and predictable, gradual or uniform.

•Elements – patterns can have elements such as colors, shapes, numbers, images, and even words.

•Repetition – a pattern has repetition if its core is repeated over and over.

•Succession - a pattern has succession if the elements form a predictable increase or decrease.

Visual Patterns can be observed according to changes in the following:

•Direction•Perspective•Order•Size•Quantity

Source: http://www.learner.org/teacherslab/math/patterns/logic.html

To produce and extend patterns, we need to:•sort and classify objects by different

properties;•order objects by size or other numerical

property (seriation);•Identify and recognize the core of the

pattern•describe the change that generates the

pattern.

Visual Pattern Tests•Identify the characteristic manifested in

each pattern and name the next figure.

Are you ready?

What is the next figure?

•The next figure is .

•The core is .•There is repetition in the pattern.

What is the next figure?

•The next figure is .

•There is a change in quantity.

•The next figure is .

•The change in the pattern is rotation.

What is the next figure?

?A

?C

?C

Sequences•Sequences are patterns whose elements

are numbers. The elements in a sequence are called terms.

•Each sequence follows a certain rule. Observing the rule is important to predict and identify the next term.

•Sequences can be finite or infinite. A finite sequence contains a countable number of terms, while an infinite sequence is usually represented by a sequence whose end has three dots (…) or an ellipsis.

•4, 7, 10, 13, 16 is a/an sequence.

• -5, -4, -3, -2, -1, … is a/an sequence.

finite

infinite

Identify the next term in each sequence.•4, 5, 6, 7, 8, ___•9, 16, 23, 30, ___

937

These are called Increasing Sequences.

Identify the next term in each sequence.•12, 10, 8, 6, 4, ___•4.5, 2, -0.5, -3, ___

2-5.5

These are called Decreasing Sequences.

Identify the next term in each sequence.•0, 1 , 0, 1, 0, ___1

This is called an Alternating Sequence.

Identify the next term in each sequence.•3, 6, 9, 12, 15, ___•9, 18, 27, 36, ___

1845

These are called Multiples Sequences.

Identify the next term in each sequence.•1, 4, 9, 16, 25, ___36

This is called a Perfect Square Sequence.

Identify the next term in each sequence.•1, 8, 27, 64, 125, ___216

This is called a Perfect Cube Sequence.

Identify the next term in each sequence.•10, 2, 8, 6, 6, 10, ___

•10, 8, 6 • 2, 6, 10

form a sequence.

form a sequence.

4

Identify the next term in each sequence.•1, 4 , 9, 16, ___25

These numbers are called Square numbers.

Identify the next term in each sequence.•1, 3, 6, 10, ___15

These numbers are called Triangular numbers.

Identify the next term in each sequence.•2, 6, 12, 20, ___3

0These numbers are called Rectangular numbers.

Identify the next term in each sequence.•1, 1, 2, 3, 5, ___8

This sequence is called a Fibonacci sequence.

Improving Pattern Skills•Visual discrimination is an important

factor for success in predicting patterns. Here are some figures that will help you train your eye to look at a given figure.

Read the following statement.

The quick

brown foxjumps over the

the lazy dog twice.

Name the color. Do not read the word.

RedBlueYellowGreenVioletOrange

WhiteBlackBrown

The End