March 28, 29
Patterns are everywhere around us. We use patterns to organize what we see and hear and to make sense of data whether we are driving in a car, listening to music, or solving mathematical problems.
Finding, describing, explaining, and using patterns to make predictions are among the most important skills in mathematics. These skills allow users of mathematics to impose order, meaning, and understanding on situations that at first seem like collections of random facts.
Finding patterns is a subjective activity. Different people notice different things, so what one person sees is often different from what another perceives. That's why it's so important to describe patterns in language that everyone understands -- so others can see what you see. Algebra is a tool for describing patterns, and there are many others.
It's important to keep in mind, however, that algebra is much more than a language. Algebra is also a way to reason about things. In fact, "making sense" is what doing mathematics is all about.
I. Exploring Patterns:
Visit the first four sites, choose one to spend 10-15 minutes exploring patterns.
II. Name the Rule: Spend 10 minutes exploring the Function Machine and the Number Cruncher:
Discover the number pattern generated by the Function Machine to complete the table.
Enter numbers into the Number Cruncher, examine the output to discover the rule. Hint: Enter consecutive numbers to discover the table's pattern.
III. Complete the Quiz with a partner (hard copy handed out in class), everyone must hand in their own paper.
IV. Pascal's Triangle: View number patterns--and create your own.