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Response to Marcy's request regarding how to teach problems involving ratio and proportion is the link entitled Unit Rate versus Matching. Looking forward to reading your responses.

Please let me know if I forgot to respond to any of your requests made during our first workshop on October 13.

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Here is my copy of Geometry by Moise/Downs. Copyright 1982. I taught out of this book from 1988-1990. Back then California had a "Golden State Exam". My 55 9th graders all received High Honor (52) or Honors (3). This book is awesome!

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Response to Dave's request:

My webpage's URL is: http://www.math.ucsd.edu/~harel/

Just click on publications. If you wish to read DNR papers, I suggest you begin with the paper, "What is Mathematics? A Pedagogical Answer to a Philosophical Question". It is one of the papers appearing in bibliography of the CCSSM.

My webpage's URL is: http://www.math.ucsd.edu/~harel/

Just click on publications. If you wish to read DNR papers, I suggest you begin with the paper, "What is Mathematics? A Pedagogical Answer to a Philosophical Question". It is one of the papers appearing in bibliography of the CCSSM.

This is a partial response to Kelly’s request. The problems below aim at helping students sorting out the meaning of the phrase “the value of each share increased by 11.85%”, and in general with the notion of percentage increases/decreases. I suggest that before starting the investment problems, the class do some problems such as:

(1) A pair of jeans costs $130. The store selling the jeans decides to have a 20% off sale. What is the sale price of the jeans? (percentage decrease by 20%)

(2) The price of the jeans is further reduced by 15%. What is the new price of the jeans? (percentage decrease by 15% after decrease by 20%)

(3) You decide to buy the jeans. The sales tax on the jeans is 8%. The cashier computes the sales tax before taking the discounts. Should you complain? (percentage increase by 8% followed by two percentage decreases)

In working through these examples, the class should observe that percentage increases and decreases are multiplicative, i.e. increasing a quantity P by a% and then b% gives the same result as increasing first by b% and then a%.

I will make up a few problems in line with the JJJ Investment Problem, where students come to realize that percentage deals with “portions of a quantity” (i.e., hundredths of a quantity), rather than the quantity itself.

(1) A pair of jeans costs $130. The store selling the jeans decides to have a 20% off sale. What is the sale price of the jeans? (percentage decrease by 20%)

(2) The price of the jeans is further reduced by 15%. What is the new price of the jeans? (percentage decrease by 15% after decrease by 20%)

(3) You decide to buy the jeans. The sales tax on the jeans is 8%. The cashier computes the sales tax before taking the discounts. Should you complain? (percentage increase by 8% followed by two percentage decreases)

In working through these examples, the class should observe that percentage increases and decreases are multiplicative, i.e. increasing a quantity P by a% and then b% gives the same result as increasing first by b% and then a%.

I will make up a few problems in line with the JJJ Investment Problem, where students come to realize that percentage deals with “portions of a quantity” (i.e., hundredths of a quantity), rather than the quantity itself.

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nixthetricks.com describes many different tricks that kids learn. Since conceptual understanding is important, this is big for us.

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