**Patterns in Algebra? Algebra in Patterns?**

Patterns are all around us! By observing patterns, we can better understand the world around us, unravel the mysteries of the past, and predict occurrences of the future. Mathematics frequently involves a search for patterns.

Why Study Patterns?

Do Now:

Complete the following patterns.

4, 4, 4, 4, 4, __, __, __, __

0, 2, 4, 6, 8,__, __, __, __

3, 9, 27, 81, __, __, __, __

a, b, c, d, e, __, __, __, __

For example:

1, 1, 2, 3, 5, 8, __, __, __

1, 4, 9, 16, 25, __, __, __

1/2, 3/4, 7/8, 15/16, __, __, __

1, 0.5, 0.25, 0.125, __, __, __

Not all patterns are so obvious...

Other patterns are found in nature

Patterns can be found in art forms

Let's investigate some patterns

that we can model geometrically...

Guess My Rule....Homework Assignment

Pattern Guidelines

You can only use number patterns twice.

You must use at least one graphical pattern and or nature pattern.

To create your pattern you may use numbers, music notation, graphics, letters, words, etc....

Assignment

1. Come up with 5 recurring patterns on your own using any phenomena to model your pattern after.

2. Present your best two patterns to a friend and have them guess your rule and then write a brief description for your rule. Attach their explanation to your patterns to hand in next class.

3. Present both your rule and the pattern explanation attempts for homework check.

What would a pattern look like for this triangle?

Sierpinski’s Triangle

Building Blocks Table

Use the figures to determine how many blocks are required for the foundation of a building based on the number of floors it has.

Make the next building.

Find and use the pattern to predict the number of blocks needed in the foundation for a 30 floor building.

Blocks of Buildings

Now Guess the Pattern...

Toothpick Patterns of Triangles cont…

A bug population has invaded your classroom. One day you notice 16 bug, which increase their population by 50% each week.

Use a table to model the situation as weeks go by without extermination.

Bugs, Bugs, Everywhere!

Fig. 3

Fig. 2

Fig. 1

Use your toothpicks to model the following figures. Then model figure four and five.

1. How many toothpicks does it take to reproduce each figure? 2. How many toothpicks lie on the perimeter of each figure?

Complete the table below and find a rule for finding the number of toothpicks in the perimeter of each figure. Then the number of toothpicks in each figure. Find the perimeter and number of two picks for figure 10 and 25.

Toothpick Patterns of Triangles

Questions?