You’re probably thinking about a carton of eggs or maybe your own fingers. It seems so basic, right? But ways to make ten is actually the "holy grail" of early numeracy, and if a kid misses it, they’re basically toast when they hit long division or multi-digit multiplication. I’ve seen it happen.
Ten is the anchor of our entire base-ten number system. It's the "home base." If you know that 7 and 3 make ten without having to count on your knuckles, you’ve unlocked a mental shortcut that makes all higher-level math significantly less painful. Honestly, it’s the difference between a student who feels confident and one who feels like they’re drowning in a sea of digits.
The Number Bond Obsession
Teachers talk about "number bonds" like they’re some mystical force. They aren't. A number bond is just a pair of numbers that join together to make a whole. When we talk about ways to make ten, we are looking for those specific "friends of ten."
Think about it this way: 1 and 9, 2 and 8, 3 and 7, 4 and 6, and the classic 5 and 5.
It sounds simple. It is simple. But the speed at which a brain can recall these pairs determines how much "cognitive load" is left over for the hard stuff. If you’re using all your brainpower just to figure out what 8 plus 2 is, you have zero room left to understand the word problem you're actually supposed to be solving. According to educational researchers like John Hattie, fluency in basic facts is a primary predictor of later success. It’s the foundation.
Why the "Make a Ten" Strategy Works for Big Numbers
Let’s say you need to add $8 + 5$.
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Most people who struggle with math will try to count up from 8: "9, 10, 11, 12, 13." It works, but it’s slow. And it’s prone to "finger slips."
The expert way—the way that uses ways to make ten—is to decompose that 5. You know 8 needs 2 to get to 10. So, you take 2 from the 5, turn the 8 into a 10, and you’re left with 3. $10 + 3 = 13$. Boom. No counting. No fingers. Just logic. This is what math experts call "bridging through ten."
It works for $38 + 5$, too.
$38 + 2 = 40$.
$40 + 3 = 43$.
If you don't have those combinations of ten hard-wired into your skull, you can't do that mental leap. You’re stuck in the slow lane forever.
Physical Tools That Actually Help
Don't just shout numbers at a kid. Or yourself. That’s boring and honestly doesn't work that well for long-term retention. Use "ten-frames."
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A ten-frame is basically just a $2 \times 5$ grid. It’s a visual representation of the number ten. When you put six red counters in it, you can instantly see there are four empty spots. That visual "gap" is what builds the mental image of $6 + 4$. Jo Boaler, a math education professor at Stanford, emphasizes that visual math is essential for all levels of learners, not just "visual learners." It creates more neural pathways.
You can also use a "Rekenrek."
It looks like an abacus, but it’s specifically designed with five white beads and five red beads. It forces the eye to see groups of five and ten.
Common Misconceptions About Learning These Pairs
- Rote memorization is everything. Wrong. If a kid just memorizes "7 and 3" but doesn't understand that 7 objects and 3 objects physically occupy the same space as 10 objects, the knowledge is brittle. It breaks the moment the problem gets slightly more complex.
- Flashcards are the best way. Kinda. They help with speed, but they often induce anxiety. Games are better.
- It’s only for kindergarteners. Absolutely not. I’ve met high schoolers who still count on their fingers because they never truly mastered their ways to make ten. It’s never too late to fix that foundation.
Real-World Applications You Already Use
You use this when you’re tip-calculating. You use it when you’re checking if you have enough change at a register. When you see a price like $7.99, your brain (hopefully) rounds it to $8.00 because you know that $.99 is just one cent away from a whole.
Subitizing is another big word experts use. It’s the ability to look at a group of objects and know how many there are without counting. Most people can subitize up to about five. Beyond that, we start "grouping." We see a group of 6 and a group of 4 and our brain shouts "TEN!" That only happens if you’ve practiced the combinations enough that they become second nature.
Tactile Ways to Master the Combinations
- Tens Go Fish: It’s exactly like regular Go Fish, but instead of asking for a matching card, you ask for the card that completes the ten. If you have a 3, you ask for a 7.
- The Rainbow Method: Draw a rainbow. Put 0 and 10 at the ends of the biggest arch. 1 and 9 on the next. 2 and 8 on the next. It’s a visual map of the pairs.
- Finger Folding: Put all ten fingers up. Fold down 4. How many are left? 6. It’s simple, but it connects the physical movement to the abstract number.
The "Zero" Problem
People always forget zero. But 0 and 10 is one of the most important ways to make ten. It sets the stage for understanding the identity property of addition later on. Plus, it’s just satisfying.
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We also need to talk about the Commutative Property. That’s just a fancy way of saying $3 + 7$ is the same as $7 + 3$. For a child, this isn't obvious. They have to discover it. Once they realize they only actually have to learn half the pairs, their confidence usually skyrockets.
Actionable Steps for Fluency
If you are trying to help someone (or yourself) get faster with these combinations, start with the doubles. $5 + 5$ is usually the easiest for the human brain to grab. Then move to the "neighbors." If $5 + 5$ is 10, then $6 + 4$ must also be 10 because you just moved one unit from one side to the other.
- Assess current speed: Give a random number between 1 and 9. See how many seconds it takes to shout back the partner. Under 2 seconds is the goal.
- Use "Target Ten" in the car: Spot a license plate. Try to find two numbers on it that make ten.
- Focus on the "tough" ones: Most people struggle with $7 + 3$ and $8 + 2$ more than the others. Spend extra time there.
- Connect it to money: Dimes and pennies. If something costs 4 cents, how many more pennies do you need to make a dime?
Mastering the various ways to make ten isn't just a school requirement. It’s a cognitive shortcut that stays with you for life. Once these pairs are locked in, the rest of the number system starts to look a lot less like a jumble of symbols and a lot more like a well-organized map. Stop counting and start grouping.
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