Patterns and sequences
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Transcript of Patterns and sequences
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Patterns and SequencesA Prelude to Sequences and Series
Math 2B Lecture 4th Quarter SY 2010-2011
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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.
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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.
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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.
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Visual Patterns can be observed according to changes in the following:
•Direction•Perspective•Order•Size•Quantity
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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.
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Visual Pattern Tests•Identify the characteristic manifested in
each pattern and name the next figure.
Are you ready?
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What is the next figure?
•The next figure is .
•The core is .•There is repetition in the pattern.
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What is the next figure?
•The next figure is .
•There is a change in quantity.
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•The next figure is .
•The change in the pattern is rotation.
What is the next figure?
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?A
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?C
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?C
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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.
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•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.
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•4, 7, 10, 13, 16 is a/an sequence.
• -5, -4, -3, -2, -1, … is a/an sequence.
finite
infinite
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Identify the next term in each sequence.•4, 5, 6, 7, 8, ___•9, 16, 23, 30, ___
937
These are called Increasing Sequences.
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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.
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Identify the next term in each sequence.•0, 1 , 0, 1, 0, ___1
This is called an Alternating Sequence.
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Identify the next term in each sequence.•3, 6, 9, 12, 15, ___•9, 18, 27, 36, ___
1845
These are called Multiples Sequences.
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Identify the next term in each sequence.•1, 4, 9, 16, 25, ___36
This is called a Perfect Square Sequence.
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Identify the next term in each sequence.•1, 8, 27, 64, 125, ___216
This is called a Perfect Cube Sequence.
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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
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Identify the next term in each sequence.•1, 4 , 9, 16, ___25
These numbers are called Square numbers.
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Identify the next term in each sequence.•1, 3, 6, 10, ___15
These numbers are called Triangular numbers.
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Identify the next term in each sequence.•2, 6, 12, 20, ___3
0These numbers are called Rectangular numbers.
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Identify the next term in each sequence.•1, 1, 2, 3, 5, ___8
This sequence is called a Fibonacci sequence.
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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.
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Read the following statement.
The quick
brown foxjumps over the
the lazy dog twice.
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Name the color. Do not read the word.
RedBlueYellowGreenVioletOrange
WhiteBlackBrown
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The End