Math Fluency

The following are the key shifts called for by the Common Core:

  1. Focus strongly where the Standards focus
  2. Coherence: Think across grades and link to major topics within grades
  3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity  
building fluency

Fluency does not require using one particular method over another. Rather, students should be able to work confidently and efficiently. Fluent in the Standards means “fast and accurate.” This is similar to when we say that somebody is fluent in a foreign language: when you’re fluent, you flow. Fluent isn’t halting, stumbling, or reversing oneself. 

However, speed and memorizing should not be the emphasis when we develop fluency.

One of the 8 Teaching Practices named in the NCTM Principles to Action isBuild Procedural Fluency from Conceptual Understanding: Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

For example, this Kindergarten standard, K.OA.4, says:
For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. 

While this 1st grade standard, 1.OA.6, says: 
... demonstrate fluency for addition and subtraction within 10 

If a first grader is struggling with fluency for addition and subtraction within 10, the focus on supporting is finding those combinations as described in the Kindergarten standard. 

Fluency is developed via routines such as Math Talks and counting routines. 


Back to Math Content Support

This table summarizes the required fluency in grades K–6:

K K.OA.5 Add/subtract within 5
1 1.OA.6 Add/subtract within 10
2 2.OA.2

Add/subtract within 20 (mental)

Add/subtract within 100 (paper & pencil)

3 3.OA.7
Multiply/divide within 100
​Add/subtract within 1000 
4 4.NBT.4 Add/subtract within 1,000,000
5 5.NBT.5 Multi-digit multiplication

6.NS.2 & 3

Multi-digit division  
Multi-digit decimal operations

Further Reading: Faster isn't Smarter - from Cathy Seeley. An explanation of the difference between Knowing from Memory and Memorizing from Graham Fletcher. The Best Way to Develop Kids’ Fact Fluency - a short ~7 minute video by Christina Tondevold In thi

Further Reading:

In this article, "Fluency Without Fear",  Jo Boaler discusses the damage that is caused by the practices that often accompany the teaching of math facts – speed pressure, timed testing and blind memorization – and summarizes the research evidence of something very different – number sense. High achieving students use number sense and it is critical that lower achieving students, instead of working on drill and memorization, also learn to use numbers flexibly and conceptually. Memorization and timed testing stand in the way of number sense, giving students the impression that sense making is not important. One way to do this is via games and tasks in which students learn math facts at the same time as working on something they enjoy, rather than something they fear.

This page was last updated on October 21, 2022