What is the Magnitude of Exponential Growth?

Summary:
On day two of our exponential relationship exploration we combined elements of practical notation with exploration designed to lead us to formal equations.

The Prime Time Problem reintroduced students to the terms, standard form, exponential form and expanded form as well as base and exponent. Students then had to contend with problems where they had to write numerical values according to these different formats.

For example:
2^5 is in exponential form
32 is in standard form
2 x 2 x 2 x 2 x 2 is in expanded form
when evaluating 2 to the 5th power, 2 is called the base and 5 is the exponent or power to which 2 is being raised

We then used a Cyberchase link online to look at a doubling activity and identified patterns and relationships that helped us to make predictions about future outcomes. The site can be found at http://pbskids.org/cyberchase/games/doubling/index.html

Finally, a few introductory pages of The King's Chessboard by David Birch were read to students to allow them to consider yet another exponential growth scenario and we once more explored the existence of formal math relationships.

Tonight's home nugget is the same as last night's, giving students a second chance to think about these new concepts, now armed with a clearer expectation given today's class lesson. An additional caution is included in the home nugget as well.

Home Nugget #30
Assigned on Tuesday December 12, 2006
Due on Wednesday December 13, 2006
From the new textbook Growing, Growing, Growing Page 10 and 11 problems 1, 2, 3
ASK YOURSELF: "If a classmate were to grade this lesson. will they find overwhelming evidence of quality work and effort?" THE ANSWER SHOULD BE AN EMPHATIC YES!!

Focus Correction Areas (FCAs)
2 points: all problems completed
2 points: there is evidence that considerable thought and effort were invested in the lesson.