The Simple & Effective Guide To Understanding Math Facts

Addition & Subtraction Strategies.

Fact Fluency.
Fact Memorization.
Three different sides of the same coin. Thinking about teaching math facts as being learned at each of these three levels will change your perspective on instruction altogether!

Addition & Subtraction Strategies

Counting on fingers, using manipulatives, using a number line, counting on, counting up, counting backward, etc.
Each of these are strategies you can teach your students so that they can accurately add and subtract numbers. When we are teaching strategies we are helping our students understand the operations of addition and subtraction, we are helping them to become more efficient when solving and we are giving them an opportunity to manipulate and practice with addition and subtraction.
At the end of the day, while strategies help to build understanding and may work towards fluency, strategies can end up looking a lot like procedures. While they are an important first step, you will need to move beyond strategies to build fluency.
Consider this example: I want to ultimately build towards fluency and memorization of +2 facts. At the strategy level, I may choose to review the counting on strategy with my students to connect the ideas that counting and addition are related. I mix together +1 and +2 facts and ask my students to use the counting on strategy to find the sums. 

Fact Fluency

Fact fluency is the idea that your students can quickly and accurately solve an addition or subtraction problem. They may be using a strategy that they learned above or they may be flexibly thinking about numbers in a way that will help them to arrive at their answer.
If you are thinking that the line between strategies and fluency is fuzzy, it absolutely can be. The biggest difference is that at the fluency level we are focusing on building efficiency.
At the fact fluency level, I am often looking to fold in number sense relationships to help my students move toward a more natural and fluent understanding of the facts they are working on.
Continuing the previous example, my students now know that counting and addition are related and can use the counting on strategy to find 1 or 2 more. I know that spatial reasoning is a number sense relationship I can use to move my students towards fluency in this case. I lay out a human-sized number line and ask my students to play a game where they spin a spinner to add 1 or 2 to a given number moving their counter along a number line. They are still building on the counting on strategy but by seeing the numbers on a number line my students are building their mental number line so that they are more efficient in “knowing” one or two more rather than having to employ the full counting-on strategy. 

Fact Memorization

The good news is that you don’t need to teach fact memorization at all. Memorization is simply the idea that your students have accessed these facts so many times that they don’t need to use a strategy or flexible thinking at all- they already know the answer.
You don’t need to teach memorization, repetition and time will move facts over to long term memory!
If you would like to help facilitate the process, allow your students the opportunity to access and recall these facts often as this will help the facts to move to long-term memory more quickly.
Following our example one final time, I may ask my students to play a simple board game. They flip a card, answer the math fact, and get to roll a dice to advance along the game board when they are correct. In the case of this example, I may only include cards with math facts involving adding one or two. In this way, my students will get an abundance of practice with these facts and their fluent thinking. As they play and have repeated exposure to this game, your students will stop using overt strategies and drawing on their flexible thinking- they will just KNOW the answers from memory and begin to answer much more quickly! 

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