Students become comfortable with new notations of multiplication and division and recognize their equivalence to the familiar notations of the prior grades. The expression 2 × 𝑏 is exactly the same as 2 ∙ 𝑏, and both are exactly the same as 2𝑏. Similarly, 6 ÷ 2 is exactly the same as 6/2. These new conventions are practiced to automaticity, both with and without variables. Students extend their knowledge of GCF and the distributive property from Module 2 to expand, factor, and distribute expressions using new notation. In particular, students are introduced to factoring and distributing as algebraic identities.
These include:
a + a = 2 · a = 2a
(a + b) + (a + b) = 2 · (a + b) = 2(a + b) = 2a + 2b
a ÷ b = a/b
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