Addition Fact Fluency

When I began my teaching career as a second grade teacher, there was one mathematical standard that frightened me the most. “By the end of second grade, know from memory all sums of two one-digit numbers.” (CCSS 2.OA.B.2) I approached this standard in the same way in which I was taught my addition and subtraction facts by drilling my students with facts. I incorporated flashcards, games that required quick recall of the sum like knock out and around the world as well as weekly fact quizzes into my math lessons, but as the year progressed, there were two problems that surfaced. 

1. My students were not engaged during fact practice time. To be frank, they were bored. 

2. My students were not making progress on their weekly fact quizzes. 

Needless to say, I was feeling quite defeated. My second grade students were not going to know the addition facts to 20 from memory by the end of the year if I continued to employ the same strategies. Luckily, around this same time, I was able to attend some professional development at my local university’s STEM Education office. Through this training, I learned about the concept of fact fluency, which is “the skill in carrying out procedures flexibly, accurately, efficiently and appropriately.” I further learned that fact fluency is developed over the course of three stages.

Stage One: Counting

When a student is solving facts at the first stage of fact fluency, they are solving facts by counting with objects, tools, manipulatives or mentally. And yes, fingers are tools! 

What stage one looks like:

In this photo, we can see that the mathematician solved this equation using objects, in this case, colored pencils. They took out two colored pencils to represent the first addend and three to represent the second addend. To determine the sum, the mathematician counted the number of colored pencils.

In this photo, we can see that the mathematician solved this equation using a numberline. They started at the first addend, 5, and jumped forward two. They landed at the number seven, which was the sum of the equation. 

 Stage Two: Deriving

When a student is in the deriving stage, they are using strategies to solve unknown facts. Stage two is perhaps the most important to develop fact fluency, and it was the stage that was missing in my instruction.I was trying to take my students from stage one to stage three without teaching them explicit strategies. The problem was, I had no idea what these strategies were, much less how to teach them! Through some learning ( I highly recommend reading Math FactFluency by Jannifer Bay-Williams and Gina Kling for learning the specific strategies and how to teach them), I learned that there are 7 addition strategies, which are broken down into foundational and derived strategies. Mastery of the foundational fact sets must be achieved prior to moving on to the derived strategies. 

The foundational strategies are: 

1. Counting On 0, 1 and 2 

2. Doubles Combinations of Ten

3. Adding Ten 

The derived strategies are: 

1. Near Doubles 

2. Making Ten 

3. Pretend a Ten 

Proficiency of these strategies is crucial for students to move onto the third and final stage of fact fluency. 

What Stage Two Looks Like:

Stage Three: Mastery

When a student is in the mastery stage, they are able to efficiently and accurately solve facts. They may solve from memory, or they may have become so efficient at using a specific strategy, that they do it mentally within seconds (sometimes without even recognizing they are using the strategy!). 

What Stage Three Looks Like: 

This is the simplest of the three stages to identify. A student has achieved mastery when you are able to ask them a fact, and they are able to solve it mentally within 3-6 seconds. Alright, so I now knew and understood the three stages of fact fluency, but I was still left with a problem. How do I move my second grade students from stage 1 to stage 3 by the end of the year? 

Moving from Stage 1 to Stage 2: 

In order for students to progress from stage one to stage two, teachers must spend time explicitly teaching each of the strategies. Teachers also must provide ample practice opportunities for utilizing the strategy with objects, tools and manipulatives. 

Moving from Stage 2 to Stage 3:

 After you have taught the strategy and began to provide practice opportunities, you will notice that students will slowly stop reaching for the objects, tools and manipulatives. This is a sign that the student has moved to stage two! At this point, it is of utmost importance that you nurture the student’s confidence, efficiency and proficiency with the strategy you have taught. I previously thought this should be done through flashcards and timed games and quizzes. But as we already know, that was ineffective. My students were not moving to stage 3 with those activities. Through my professional development and reading, I discovered that the best way to nurture my students’ confidence and efficiency is to incorporate strategic games play into my math block. Games increase student engagement and efficiency without stress and anxiety that can be a product of tests and timed games. I began developing games that targeted specific strategies for my students to play. You can purchase the games individually or by the bundle in my store - learn more about them here! 

Some of my students’ favorites are: 

Race to the Top In this game, students have a game board (that I laminate) with equations on it. They place the race cars on the bottom of the board. To start the round, they play, “Rock, Paper, Scissors!” The winner of the game solves the equation above their race car. If they correctly solve the equation, they move their race car up the board. The first player to reach the finish line wins! My students love playing these games (seriously, I get cheers when they are in my math stations!), and I love how they get ample strategy practice without anxiety. I also can track data so well with the record sheets, which lets me know when a student may be ready to learn another addition strategy!

Go Fish! In this game, students have a mix of cards with equations and sums. If they have an equation card and are looking for the sum card, they ask a fellow student for the sum of the equation. If they have a sum card and are looking for the equation card, they ask if a student has a card with the specific equation on it.

I hope that this has been both informative and actionable for you. I would love if you left a comment with something you took away from this blog post! Happy teaching! Sources: Bay-Williams, J. M., & Kling, G. (2019). Math fact fluency: 60+ games and assessment tools to support learning and retention. ASCD. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics.Washington, DC: Authors. 

 Bio

Hi, I’m Gretchen from Learning with Miss G! I believe that all people are Math people, and I currently work as a Math Interventionist for students in Grades 3-8. I am passionate about fact fluency, color by number worksheets, national parks and a good rom-com. Check out my Teachers Pay Teachers store and Instagram for more resources and tips!