Chapter 97th Grade Math

Patterns and Graphs 1/5

Horizontal and vertical scalesDo not have to use the same

interval or measurement

5040302010

15 30 45 60 75 90 105

SECONDS

Feet

Scale and

Intervals

Should be chosen based on the given information

Scale and Intervals

Bacteria Growth

Time Number of Bacteria

0 5

20 10

40 15

60 20

80 60

Begin drawing a graph by choosing the scale and interval

Remember, data pairs form points on the graph

Graphing

Bacteria Growth

Time Number of Bacteria

0 5

20 10

40 15

60 20

80 60

Use your prepared graph to plot the data points

Use your graph to find other information

Estimating

How many bacteria would be present after 10 seconds? 30 seconds?

About how long would it take to grow 16 bacteria?

Bacteria growth is effected by the environment, does the graph show a time interval when the environment might have changed?

If the growth rate had remained consistent, how many bacteria would be present after 80 seconds? 160 seconds?

WorkbookPage 149 – 150# all

You Try

Numbers and Sequences 1/11A set of numbers that follow a pattern

Four rules

Arithmetic

Geometric

Both

Neither

Sequences

Sequence changes by adding a fixed number

Arithmetic Sequence

Called a common difference

The common difference can be positive or negative.

2, 5, 8, 11, . . .

7, 7, 7, 7, 7, . . .

63, 54. 45. 36, . . .

Find the common difference, rule, and next 5 terms

http://www.rmeducation.com/files/image/sequences.jpg

Sequence changes by multiplying a fixed number

Geometric Sequence

Called a common ratio

Remember that ratios can be whole numbers or fractions

3, 3, 3, 3, . . . 3, -6, 12, -24, . . . 100, 50, 25, 12.5, . . .

Find the common ratio, rule, and next 5 terms

1/10, 1/30, 1/90, 1/270, . . .

Sequence changes by multiplying a fixed number or adding a common difference

Both

Uncommon

0, 0, 0, 0, . . . .

-3, -3, -3, -3, . . .

5, 5, 5, 5, . . .

Find the rule and next 5 terms

1/2, 1/2, 1/2, 1/2, . . .

Sequence does not have a common difference or ratio

Neither

Have to be creative to find a pattern

1, 1, 2, 3, 5, 8, 13, 21, . . .

5, 6, 8, 11, 15, . . .

3, 6, 18, 62, . . .

Find the rule and next 5 terms

10, 100, 10000, 100000000, . . .

You Try WorkbookPage 151-152

Patterns and Tables 1/12A representation of a number pattern

The pattern can be used to make or complete a table

Tables

Number of puppies

1 3 5 9

Number of paws

4 12 20 36

Rules can be written out with words or expressed as a variable expression

Writing rules

Number of puppies times 4 paws

4p

Find how many paws 12 puppies have

100 puppies

A million puppies

Write the rule as a variable expression

Find s and t

Find the 100th term

N 2 s 6 12

P 14 35 42 t

You Try WorkbookPage 153-154