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= Welcome to F201, fall term 2010! =

This is our home page.
We will use this wiki to record our work in F203 this term; in effect, it will function like our textbook that we create as we go along.
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= Quantity = For responses to these question and more, click on "On Quantity" in the side navigation bar.
 * //Important Questions://**
 * What is a quantity?
 * What is not a quantity?

= BASE SYSTEMS = = Base Five = For responses to these questions and more, click on "On Base Five" in the side navigation bar.
 * //Important Questions://**
 * How do you count in base five?
 * How do you symbolize counting in base five? What does "10" mean in base five?
 * What patterns do you notice in base five counting?
 * For work on building a "complete" base five number system, click on "On Advanced Work in Base Five."**

= Base Twelve = The questions above are also important here! We'll use base twelve as well as base five this term for at least two reasons: (1) We get to make up names and symbols for numbers within a base! This puts us in a position of young children who learn about names and symbols for numbers within a base. (2) Base twelve has more numbers within a base. This means there are a lot more opportunities to build patterns and strategies, which is very important for understanding subtraction and multiplication well.

For more on base twelve, click on "On Base Twelve" in the side navigation bar.

= Strategic Additive Reasoning = For responses to these question and more, click on "On Strategic Additive Reasoning (SAR)" in the side navigation bar.
 * //Important Questions://**
 * How do students solve addition and subtraction problems by reasoning strategically?
 * How can we use these strategies--and more--to help us solve problems in base five and base twelve, and to extend our understanding of number, addition, and subtraction?
 * How do standard computational algorithms for addition and subtraction fit into the strategies that students develop?

=** Strategic Multiplicative Reasoning **= Strategic multiplicative reasoning includes most of the strategies we have been using to solve multiplication and division problems in base twelve. We are currently at work on "large" multiplication and division (multiplication and division of larger numbers). // **Important questions:** // ====For responses to these question and more, click on "On Strategic Multiplicative Reasoning" in the side navigation bar. For responses to the last two bullets, click on " On Large Multiplication " and " On Large Division ."====
 * What is whole number multiplication?
 * Is there more than one concept of whole number multiplication?
 * How do children--and ourselves--use counting and strategic additive reasoning to solve multiplication problems? We'll develop this largely in base twelve.
 * What other strategies can we develop for whole number multiplication?
 * What is whole number division? Is there more than one concept of whole number division?
 * What strategies can we develop for whole number division?
 * How can we reason through "large" multiplication problems (i.e., multi-digit)? How can we reason through "large" division problems (i.e., multi-digit)?
 * How do standard computational algorithms for multi-digit multiplication, and for division, fit into the strategies that students develop?