Fluency is “the efficient, appropriate, and flexible application of single-digit calculation skills and is an essential aspect of mathematical proficiency” (Baroody 2006, p.22).  A substantial amount of mathematics education research shows that children do not master their math facts through memorization alone. Instead, true mastery comes from being equipped with quick and effective strategies for finding the solution. By using these strategies, children will always have the mental tools needed to find the correct answer and the confidence to use them.  (Rinke and McAdam, 2014)

Students generally proceed through three phases as they develop mastery with any particular set of facts.

1.     . Modeling Phase: Modeling and/or counting all or counting on to find the answer:  For example, using fingers to help keep track of their counts to solve 5+7=?
2.     . Reasoning Phase: Deriving answers using reasoning strategies based on known facts, such a solving 5+7 by thinking, “Five plus five equals ten, and two more will make twelve.”
3.     . Efficient Phase: Mastery or efficient production of answers. For example, when asked, “What is 5 + 7?” a child might call out, “Twelve,” and explain, “I just knew it.”

While our ultimate goal is for all students to demonstrate fact fluency automaticity, it is important to first help them develop their understanding of facts and related unknown facts using reasoning and math strategies.

Listed below are fluency expectations by grade level, with accompanying fact strategies to use to build student understanding.