Resources and Tools for Elementary Math Specialists and Teachers

Good Strategies for Mastering Basic Facts

This discussion is part of a collection:Basic Operations

As a teacher of both intermediate elementary and middle school students, it often amazes me that students make it to 6th and 7th grade without mastering their basic math facts. I feel like once students get past 2nd and 3rd grades they are expected to know these facts and are therefore dismissed when they do not. Are there any good strategies to help students master their basic facts once they are expected to have mastered them and have not?


A teacher's role may vary among cultures. Teachers may provide instruction in literacy and numeracy, craftsmanship or vocational training, the arts, religion, civics, community roles, or life skills. Mathematics is one of the difficult subject to teach.

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By teaching the each topic a teacher should take the test of the basic concept that he/she taught in the classroom. If a student doesn't perform well in the test then a teacher should inform the student's parents about the performance of the student. Apart from this a teacher should provide 3 chances to a student to perform in the test of the basics.

I've developed a game to improve basic mathematical operations, too. You can check it out at,

Give it a try.. Great for kids

Check out "Mastering the basic math facts" series by Sangiovanni and O'Connell. They go beyond just memorizing the facts. Memorizing leads to fluency, and not understanding. This series leads to an understanding of the facts.

Mastering the Basic Math Facts is a wonderful resource. There is an older set of books called Facts that Last, by Larry Leutzinger that I have also found quite useful.

Mastering the Basic Math Facts is a wonderful resource. There is an older set of books called Facts that Last,by Larry Leutzinger that I have also found quite useful.

[This post has been modified by mathadmin]

I agree this is a great resource and it focuses on developing effective strategies to develop fluency. The book also has great literature connections for the different fact strategies.

These look like sensible thorough treatments. I've passed them on to our fact fluency cataloguer at ML. Much appreciated.

I can’t speak to teaching adding/subtracting facts, but I did get 5th graders in a middle school setting who needed work on multiplication, in some cases a lot of work. I used two techniques and had success with all but a couple of really hard cases.

First, the trouble with Flash card or similar electronic drills is the ‘Flash’ part. Memorization is a long-term learning task and that requires more energy and concentration than a quick run thru the deck. Also, these drills divorce the prompt from the response, encouraging guessing, and it’s a fact that people often remember their incorrect responses.

I put the fact, both prompt and correct product, on one side of the card in order to discourage guessing. To elicit the effort and energy needed for long-term retention, I have students try to memorize a set of five of their unmastered facts, reciting the prompt and the product together. You will see ‘brain strain’ during this activity, and that’s a good symptom. I demo with one student, teaching the others how to conduct this drill.

The second technique – require more memorization than you hope students will achieve. I have younger students pick an easily drawn and colored object to make an array of a fact. For example, 8 x 5 is 8 rows of five pine trees. I tell students they will be quizzed on ten of these facts and that they need to respond with the product and the associated object. This again steps up the required energy and, of course, we forget the pine trees after the products are mastered.

There is a new product, Math Bands for Multiplication, that help students understand the "building" concept of multiplication. These are silicone bands that have a skip counting sequence on them. They help transition from concrete to abstract, dealing more with written number problems. Great for helping those students who don't seem to get it the first time. I have seen a boost in test scores, as well as student confidence. They are at and on Facebook "Math Bands".

Thanks for the ideas relating to math facts. I have had much success using arrays with my fifth graders as well. By taking a daily number during the course of a month and creating arrays for it, students more easily understand math facts, prime and composite numbers, and square numbers for the numbers 1-30. They also begin to see patterns and are able to make predictions about numbers beyond 30.

I think it is crucial to "catch" these weaknesses in students during the transition from 5th to 6th grade. I have had experience with remediating a 6th grade class where we also worked with arrays and had students keep 5 facts on a key ring and practice them nightly. The program that we used was called Algebraic Foundations and provided us with a CD of facts set to music, many of our 6th graders were "too cool" to dance around the room singing their facts, this approach may have worked better in 4th and 5th grade.