Math fact fluency is much more than simply speed and accuracy. True fluency also includes flexibility and appropriate strategy use. When we take a mental math approach to math facts, we encourage students to be flexible thinkers who are able to build their own understanding and use that understanding to solve more complex problems.
We know that being able to think flexibly is more effective than memorization for math facts. This has been studied in depth by many different math researchers. But sometimes what happens when we begin to teach strategies, is that we “teach” the strategies for memorization. For example, “Whenever you see numbers that differ by 1, you can use the doubles plus one strategy.” Rather than “teaching” the strategies, ideally we want students to discover them and construct their own understanding. The best way to do this is through lots and lots of work with manipulatives. And yes, even if you teach upper grades your students should be using manipulatives!
However, sometimes it’s still nice to have a guide for what strategies to steer our students toward.
Below I have outlined seven different different mental math addition strategies that you can model in your classroom to help students build their understanding. I have also included videos for some of them.
Counting On – Counting On is a beginning mental math strategy. Counting on means that you start with the biggest number in an equation, and then count up. For example, in the equation 5+3, you want students to start with the “5” in their heads, and then count up, “6, 7, 8.” This is to discourage students from counting like, “1, 2, 3, 4, 5…..6, 7, 8.” Students also need to understand the commutative property of addition, where if an equation looks like this: “2+6,” they still should start with the bigger number (in this case, 6) and count up “7, 8.”
Here’s a video that will explain this strategy in more depth, or find a unit for teaching the counting on strategy HERE.
Make a Ten – Make a Ten is a mental math strategy where students use the number combinations that make ten to form connections and relationships to other facts. First, students must learn the number combinations that make 10. Then, they can confidently use those combinations. For example, to solve 8+5, a student might think, “I can take two from the 5 and give it to the 8 to make a ten, and then add the leftover 3 to make 13.” Ten frames are a fantastic way to illustrate this strategy.
Here’s a video that explains the make a ten strategy in more depth or find a unit for teaching make a ten HERE.
I hope this post has helped you make a plan for teaching math strategies in your classroom! I know that if you did not learn this way, it is not an easy transition.
If you’d like more support for teaching addition strategies in the classroom, check out this Mental Math Addition Strategy Bundle that includes units for all of the strategies that were discussed above.