PATTERNS. There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic.

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Presentation transcript:

PATTERNS

There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Lets begin with Linear patterns. They are probably the easiest to recognize because the change is related to slope of a line.

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic EXAMPLE #1 : What pattern is shown in the graph ?

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic EXAMPLE #1 : What pattern is shown in the graph ?

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic EXAMPLE #1 : What pattern is shown in the graph ?

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic EXAMPLE #1 : What pattern is shown in the graph ?

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Geometric patterns can be represented numerically and generalized algebraically.

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Geometric patterns can be represented numerically and generalized algebraically.

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks…

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2)+13 Build #1

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2) rows of 2 plus 1 2(2)+15 Build #1 Build #2

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2) rows of 2 plus 1 2(2) rows of 2 plus 1 3(2)+17 Build #1 Build #2 Build #3

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2) rows of 2 plus 1 2(2) rows of 2 plus 1 3(2)+17 Build #1 Build #2 Build #3 The number changing in each build is the number of rows of two.

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2) rows of 2 plus 1 2(2) rows of 2 plus 1 3(2)+17 Build #1 Build #2 Build #3

PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression 1 st Find the difference for each consecutive term 14 – (-1) = – 14 = – 39 = – 74 = 45

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression Since the differences are NOT CONSTANT, we need to find the difference between the differences we just found…

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ?

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ? The difference is constant, so a linear pattern.

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ? The difference is constant, so a linear pattern. The pattern is decreasing so coefficient will be negative.

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ?

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ?

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ?

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #4 : Write the first five terms of the pattern from the given expression below.

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #4 : Write the first five terms of the pattern from the given expression below. Just start plugging in values for “n” starting with 1…

Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #4 : Write the first five terms of the pattern from the given expression below. Just start plugging in values for “n” starting with 1…

EXAMPLE #5 : What function does the pattern below represent ?

First differences are not constant…

EXAMPLE #5 : What function does the pattern below represent ?