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Algebra I has two big ideas that are threads throughout the course. The first big idea is that we can construct representations of relationships between two sets of quantities and that these representations, which we call functions, have common traits. The second big idea is that we can use these relationships between the quantities, which we call variables, to use our knowledge of the value of one variable to predict or determine explicitly the value of the other variable. In our formulation of the course, the first big idea is intended to inform students’ ability to use the second big idea.
It should be noted that there is a critical important prerequisite idea which is our abstraction from the idea of a specific set of quantities into a variable reference to these quantities. While this is an expected outcome of the middle school Common Core standards, this big idea is one that many high school students still do not completely understand.