For many years, primary teachers taught fact families. If you look carefully at either the CCSSM or the Texas state standards, the TEKS, you will not see fact families mentioned at all. Why is that?

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The CCSSM were published in 2010, and the updated TEKS followed two years later. In both sets of standards, we see a shift from curriculum focused almost entirely on procedures to one that is more balanced. Procedural fluency is still part of the equation, but it’s balanced with problem solving and conceptual understanding.

Which brings us to a discussion of what is meant by understanding. Richard Skemp defined two types of understanding—instrumental and relational. You can see the correlation between instrumental understanding and a focus on procedures, while relational understanding connects more closely to a balanced approach to teaching math.

So let’s get back to fact families. We typically taught fact families as a stand-alone skill. We did our “unit” on fact families. Students learned that a fact family is usually four equations—two addition and two subtraction—that use the same three numbers. Kids could rattle off a fact family, but did they truly have understanding? Often times, the answer was no. How did we know they didn’t understand? Because they used the three numbers in ways that didn’t make sense, such as 2 – 5 = 3. No understanding.

In the newer standards, fact families are gone. Instead we see standards in Kindergarten and 1st Grade for knowing all the combinations for numbers through ten, and references to the relationship between addition and subtraction. Both of these are very similar to fact families, but they stress conceptual understanding, rather than pure memorization. Enter number bonds.

Below you see representations for the number bonds for ten. As you can see, they look a lot like fact families. The difference is that with number bonds we focus on all the ways to make a number, in this case five. Throughout Kindergarten, students work on their own target number, moving from 5 to 6 to 7, etc.

Looking for ways to practice number combinations? I’ll give you two—one partner game and the other an online game.

Capture 4 Make 10

This partner game is super easy to prep! All you need is the game board and transparent discs. The goal of a Capture 4 game is to get four in a row horizontally, vertically, or diagonally. Player 1 places discs on any two spaces that make 10. In the picture below, you can see they have placed discs on 4 and 6, because 4 and 6 make 10. Play continues with players alternating turns until one player gets four in a row.

Download this game for free here.

Math Lines

There aren’t many only games for practicing the combinations for a number, but Math Lines from ABCya is one! It’s easier to see than explain how to play, so check out this video.

There you go! Fact families vs. number bonds. If you like this article, please share!