The first step in our math program is to build what we call "Number Reasoning." In order to do this, we will go back through major concepts and rebuild them so that the kids have a much deeper understanding that will promote stronger reasoning and "number sense." Additionally, the deeper conceptual understanding will build a connection between arithmetic and algebra, providing a strong foundation for algebraic thinking.
Next week we will continue the work we did over these first two days. We will be looking into the concepts of addition and subtraction, moving through a "deductive lesson" structured to facilitate reasoning from simple representations, to progressively more complex ideas, to the algebraic or abstract representation of the concept. Your children will explore the multiplicative identity of a number, the meaning of "terms," how to combine like terms, and how to use properties such as associative, commutative, and substitution to create like terms that can be combined.
Additionally, we will soon focus on the concept of subtraction, rebuilding it from just an "operation" and expand it to a much deeper idea. We'll use a vertical number line to illustrate subtraction as the increase or adding of "debt" or "depth." Understanding subtraction from this perspective facilitates a connection to negative numbers (i.e. combining debts and losing debt ). We'll use the same foundation set up in addition --- "like terms", "substitution property," etc and the kids will soon be very facile with some very high level concepts that link directly to algebra.