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Developing Automaticity with Basic Math Facts

The standards, whether the CCSSM or the TEKS in Texas, definitively state that students should develop fluency with calculations, and that means automaticity with basic facts. Knowing math facts is similar to knowing sight words–it frees up the mind to solve real math problems. If a child has to struggle to solve 8 + 3, they have no mental energy (or desire) left to grapple with the types of problems that will increase their capacity as a mathematician. The difference is the approach we now take to teaching basic facts. Traditionally, the emphasis has been on memorization and speed, much to the detriment of countless students. For a great read on the problems with memorization, check out Jo Boaler‘s Fluency Without Fear.

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So the shift has been away from rote memorization of math facts and toward a strategy-based approach for learning math facts. There’s a big difference between memorizing and understanding. Sure, we want kiddos to have automaticity with their facts, but we want that fluency to be rooted in number sense–an understanding of how numbers are related. A great resource for strategy-based fact instruction is Mastering the Basic Math Facts in Addition and Subtraction: Strategies, Activities, and Interventions to Move Students Beyond Memorization. There’s one for multiplication and division facts, too.

To develop automaticity, students also need to engage in meaningful practice. Here are some suggestions for practice games and activities:

  • Provide concrete or pictorial support. The ability to create mental images of numbers and facts helps students make sense of numbers. A student who “guesses” that 7 x 9 might be a number in the 30s clearly does not have a mental image of 7 x 9. Tasks that either use pictures to represent facts or have students draw representations for facts help them develop the ability to form mental images.
  • Focus on strategies, not facts. When learning addition facts, strategies like Make a 10 and Using Doubles are very powerful. With multiplication, students learn that facts are related, for example by doubling. A game focusing on the 2s, 4s, and 8s highlights that doubling relationship.
  • Spotlight a specific number. In Kinder and 1st, students need lots of practice composing and decomposing the numbers to ten. Because of its importance in our number system, special emphasis should be given to making ten. Use a fun skip-counting game to practice all the multiples of a given factor.
  • Add a twist of strategy. Let’s face it, who doesn’t like a game of tic-tac-toe? The strategy that’s involved makes it almost addictive. Anytime you can incorporate a little strategy into a fact practice game, you’re golden.

And speaking of tic-tac-toe, I’ve created a little freebie for Making 10 (addition) and Making 24 (multiplication)! Click here to grab yours!

I’d love for you to share your comments about how you work with your students to develop automaticity with facts!

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    1. Honestly, I have not read the book. I do think there is great value in assessing students to determine the strategies they use when solving facts–usually we just give them a sheet of paper with a bunch of facts and time them, which is not productive. It’s my understanding that the running records book provides a means to do that. We have to keep in mind, however, that it’s only assessing a small part of a student’s mathematical understanding.

    2. Hi Lorie and Donna!
      I have been implementing Math Running Records for a couple of years now and love them. There are three parts to the interview no matter what operation. In Part 1 students answer one benchmark expression for each strategy in the progression of the operation. We get a reading on relative speed (the students don’t know it) and their accuracy. We take notes on any obvious behaviors like counting all or counting on with fingers or head counting. In Part 2, this is where we ask them probing questions about how they solve the fact in a strategy, asked them to solve more in that strategy and then have them describe how they figured it out. We keep track of whether they are using a counting strategy or derived facts, or have automaticity. In Part 3 we ask about their dispositions towards math.

      While this assessment is just about basic math facts, it does inform us about more than that. The very same strategies used for basic facts can be applied to larger numbers, fractions and decimals down the road. Setting the the foundation for strategic thought is crucial for our kiddos. I have found that the Math Running Record allows my teachers and I to have detailed discussions about our students’ abilities that have never happened before. It’s been very, very powerful. I’ve created a Facebook group called “Math Running Records” where I have shared resources and videos of them. Would love for you to add to the conversation!

  1. I ordered the book and will try this approach gladly. I had a terrible time with math as a child and still struggle at 60. My 7 year-old son struggles greatly with numbers and math. He even still struggles just counting on his finger correctly. I don’t like the memorization method at all because I know he isn’t learning math but I didn’t know how else to approach helping him. I look forward to some good insight and improvement over the pre-second-grade summer.
    Thank you.

    1. Try using a ten frame or MathRack as a concrete model for your child. These mathematical tools provide a built in structure that will promote thinking flexibly about number and lead to automaticity through understanding not memorization. Too often curriculums go straight to symbolic (numerals) and leave out the concrete and representational phases of instruction. This leads to learning procedures and memorization. We want kids to think like mathematicians … then they will succeed in all facets of mathematics.

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