Number Combinations Through 10

Learning all the number combinations through ten is a big math goal in Kindergarten. I’d even say it might be the most important one, because it lays the groundwork for fact fluency.

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What is this standard?

Regardless of the standards you follow, you’ll likely find some version of this skill. In Texas, it’s K.2(I).

K.2(I) compose and decompose numbers up to 10 with objects and pictures.

If the words compose and decompose are new to you, compose means to put smaller numbers together to make bigger ones and decompose means to break numbers apart.

All the combinations for 5 would look like this:

And students need to know all the combinations for the numbers up through 10. Here you see the combinations starting from 3.

Why is it Important?

Knowing the combinations for numbers up to ten helps students develop part–whole thinking, build flexibility with numbers, and lay the foundation for strong computational fluency. It’s a skill that supports nearly every other area of math they’ll encounter.

Consider what happens in First Grade. A student is working on her basic addition facts and doesn’t know 8 + 5. But she does know her combinations for 10.

She sees the 8 and remembers that 8 and 2 make 10. She also knows she can break apart 5 in different ways—and 2 and 3 is one of them. She uses the 2 with the 8 to make 10, which means she’s now thinking of 8 + 5 as 10 + 3—a much friendlier fact.

With time and practice, she’ll know 8 + 5 instantly. But for now, she can reason her way to the answer. And trust me—it took her way less time to do it in her head than it just took me to explain it to you!

Now let’s jump to Second Grade. This friend is working on multi-digit addition and doesn’t know the standard algorithm yet—and that’s totally fine. He remembers that if 8 and 2 make 10, then 38 and 2 make the next 10, or 40—a nice, friendly number.

He also knows that 25 can be broken apart in different ways, and one of those ways is 2 and 23. So, he uses the 2 with the 38 to make 40. Now he can solve 38 + 25 by thinking 40 + 23, which is a much easier mental calculation.

How do we develop the Skill?

Kindergarten students need differentiated practice throughout the year to develop fluency with the number combinations. Students are assessed to determine their target number and then practice the combinations for that number using differentiated tasks, such as this Shake and Spill game using teddy bear counters.

Ten is Special

Because ten is so important in our number system, the combinations that make ten have a special place in early math learning. As students work on their target numbers throughout the year, they can also be practicing these combinations. The combinations for ten—often called the “friends of ten”—should be posted and visible in your classroom all year for students to reference.

As with the other combinations, it’s important to have plenty of games for students to practice the combinations for ten. Initially, they should use objects or pictures before moving to abstract numbers.

This bump game uses ten frames to support their learning. Players take turns rolling a ten-sided die and use the ten frames to find the number that, combined with the roll, makes ten. They then mark that space.

If an opponent’s piece is already on the space, a player can bump it off. If their own piece is there, they can place another piece on it to lock the space.

Linking cubes work well as playing pieces.

The first player to use all of their pieces wins.

You can download a free copy of the Bump game here.

Bring This Approach to Your School!
If you’re an administrator looking for ways to make math instruction more meaningful and engaging, I offer professional development sessions that show teachers how to move beyond worksheets and build real problem-solving skills. Teachers will leave with practical strategies they can use right away—and students will develop deeper understanding and confidence. Interested? Let’s connect!