What is Numerical Fluency

Just as in the English language there exist multiple phrases to express the same concept, a mathematical problem can be approached in numerous ways. Numerical fluency is having the mathematical understanding to find the most efficient way of expressing, and then solving, a problem. Even addition can be approached in a multitude of ways. If an addition fact has not been memorized, many students will compute the answer through counting by ones. While this strategy works when performed correctly, more efficient techniques exist, such as decomposing to form a compliment of 10. Take the example of 8 + 7 – if the fact is not immediately known to be 15, it can be thought of as 8 + 2 + 5, or 10 + 5. Alternatively, 8+7=? can also be thought of as doubles +/- 1 so either 8+8=16-1=15 or 7+7=14+1=15. Further, when solving for an unknown such as in 8+ _____= 15 we can use the Facts Family concept to turn the problem into 15-8= ______.

Fluency doesn’t stop with addition. As the comfort level with multiplication families improves, the number 56 is no longer just 56 – it is also 2*28 and 4*14, and 8*7. Armed with this understanding, a mathematical statement such as 25*16 –- unfriendly and needing a pen and paper to solve -- can be rearranged to 25*4*4, or 100*4. A different route to the same answer.

Likewise, a quarter of a number becomes half of half or for example 1/4 of 230 is 1/2 of 230 = 115 and half of 115 is 57 1/2. No pencil and paper needed.

Though a student may favor one technique over another, true fluency is attained once a student can identify many routes to the solution and choose the optimal one. This power of choice that numerical fluency grants makes mathematics a friendlier discipline. Instead of a single answer to be found, a math statement becomes an expression to be understood.

Numerical Fluency is one of the key concepts we work on at Mathnasium of Littleton. Next up a discussion of Number Sense which works hand in hand with Numerical Fluency.