A chart that shows the set of math fact family 5, 3, and 2 in Addition and Subtraction.

Learning Math by Fact Family vs One Operation at a Time

A Fact Family is an innovative way to group the learning of math facts. Some people are die-hard advocates of this way to learn facts. Yet students successfully learned math facts for decades without ever considering them as being composed of families. This blog discusses the pros and cons of learning with fact families. 


 What is a Fact Family


A fact family is a set of four math facts made with the same three numbers. The numbers 2, 3, and 5 can make a family of four facts: 2+3=5, 3+2=5, 5−3=2, 5−2=3. The numbers 2, 3, and 6 can make a different fact family: 2×3=6, 3×2=6, 6÷2=3, 6÷3=2.  


Why are Fact Families Important?


Fact families help children see that adding and subtracting are the opposite of each other. Multiplication and Division fact families do the same. Learning fact families may help students develop more flexibility in their number sense.   


Benefits of Thoroughly Learning a Single Operation at a Time


Rocket Math Addition Fact Family worksheet for students.

When it comes to memorizing math facts, students traditionally learn one operation at a time. They memorize only the Addition facts, typically in first grade. Not until later do students learn the concept of Subtraction, and then they begin memorizing Subtraction facts, usually in second grade. With Rocket Math, students will master Addition facts much better than most first graders. Students using Rocket Math will know Addition facts instantly without having to stop and think about them. When students have mastered Addition facts, an unusual thing happens when introduced to Subtraction. Students instantly recognize that the Subtraction facts are the opposite of those Addition facts they know so well, usually without even being told. This recognition does not typically happen in second grade with students who haven’t truly mastered Addition facts.  Therefore teachers think they need to teach in fact families to get students to recognize the reciprocal nature of Addition and Subtraction.   


Which Way is Better?


Only if students thoroughly master Addition facts, can they quickly recognize the reciprocal nature of Subtraction. Students find it easier when memorizing facts, to stick with Addition, rather than switching back and forth between adding and subtracting as is required by learning in fact families. They tend to memorize faster in single operations than they do in fact families.  However, if students memorize in fact families, they will learn the reciprocal nature of the fact families right from the beginning. They may learn it more thoroughly. That may help them develop more flexibility in their number sense. So that’s not a bad thing.


How to Learn Math with Fact Families and Single Operations


Teacher's directions worksheet for addition and subtraction fact families.Rocket Math offers separate Addition and Subtraction sequences, as well as fact family sequences. Both the Online Game and Worksheet Program provides these. If teachers (or their regular math curriculum) are wedded to fact families, they are available to use. Usually, the first fact families learned are Addition and Subtraction Fact Families through 10, then Fact Families from 11.  


I would recommend beginning with learning the operations separately: learning Addition facts (1s to 9s) first, followed by Subtraction facts (1s to 9s). For some students, this may be all they have time to learn.  If students have time, use Fact Families as a review. If the student has time, it would be beneficial and relatively easy for them to do Fact Families (+,-) to 10 and then Fact Families (+,-) from 11 afterward. Students will learn the facts more thoroughly, and the reciprocal nature of Addition and Subtraction will be deeply ingrained. This is quite simple in the Online Game, as it only involves switching the student to another Learning Track, and doesn’t require a new filing crate, as in the Worksheet Program.  


Using Rocket Math to Teach Single Operations & Fact Families


Rocket Math offers separate Addition and Subtraction sequences, as well as fact family sequences through the Online Game and the Worksheet Program. For teachers looking to teach Addition and Subtraction math fact families, Rocket Math offers two sequences of Fact Families; the first, Fact Families to10 and the second, Fact Families from 11. For teachers looking to teach in separate operations, Rocket Math offers separate sequences for learning Addition facts (1s to 9s) first, followed by Subtraction facts (1s to 9s). If the operations are learned separately, fact families can be used as a review. 



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