Understanding Teen Numbers Using Ten-Frames

Every once in a while, you teach one of those lessons you never forget. Years ago, I was working with a small group of first graders when my AP walked in for an observation. The students had been using two ten-frames to build and make sense of teen numbers, and I had several goals for the lesson. What I didn’t expect were the mathematical discoveries the students would make along the way—or how ridiculously excited my AP and I would be about them when the lesson was over!

My goals were for students to:

1. Recognize a full ten-frame as 10 without counting each counter.
2. Count on from 10 to determine a teen number.
3. Represent teen numbers as 10 and some additional ones—for example, $14=10+4$.

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Building Teen Numbers with Ten-Frames

As the students came in, a double ten-frame and a small pile of counters were waiting at each seat. I told them that I had meant to give each of them 20 counters, but I hadn’t had time to count them. I asked them to count their counters and give me any extras over 20.

That very quick exercise gave me a chance to check their one-to-one correspondence and counting skills. I was also able to coach one student that when counting objects, it helps to move each object aside as it’s counted. My first surprise of the lesson came when one friend decided to count by twos. I wasn’t expecting that!

To begin the lesson, I asked the students what they had discovered about filling a ten-frame. They told me that when it is full, it has 10 counters.

I asked if they had to count the counters one by one to fill the ten-frame, or if they could just fill it up fast.

Fill it up fast!

Good! We were ready.

I flashed the number 15, and counters started flying as the students built the number. As each student finished building 15, hands went up in the air in victory. Of course, if you’re counting from 1 to 10 every time you fill the first ten-frame, you’re not going to be nearly as fast—and they were beginning to figure that out.

Next, we practiced counting on from 10. Students put a whole hand over the filled ten-frame and said, 10. Then, pointing to each counter on the second ten-frame, they counted on: 11, 12, 13, 14, 15.

Finally, we wrote an equation to represent the number they had built. I had made a simple recording sheet that emphasized the value of the full ten-frame and the additional ones:

15 = 10 + 5

The ten-frame, the counters, the counting, and the equation were all representing the same number in different ways.

And Then the Really Good Stuff Happened

We practiced several more numbers using the same process. It was while we were working with 14 that the next surprise came.

When I asked whether they had needed to count to fill the ten-frame, one student said, No. Then he added that he hadn’t needed to count the 4 counters either.

Well, now I needed to hear more!

I asked him to explain. He told me he knew there were 4 because there was only one empty square in the row, and 4 and 1 make 5. We had recently been working on combinations for 5, and here he was applying that understanding in a completely different context.

A few numbers later, the same student announced that he had noticed something.

He pointed out that each of the numbers we had been building had a 1 at the beginning—13, 14, 15—and said that the 1 went with the ten-frame.

And there it was.

He wasn’t simply recognizing the numeral 15. He was beginning to understand its structure. The 1 in 15 represents one ten, and the 5 represents five ones. All of that work filling the ten-frame, counting on from 10, and writing $15=10+5$ had helped him connect the quantity, the visual model, and the symbols.

Just about that time, another young mathematician chimed in that the 5 was 5 ones.

Quickly, I captured their thinking on the whiteboard. I wrote 15 and labeled the tens and ones.

Why That Moment Mattered

Remember, these students were receiving additional math support, so watching them make these connections on their own was especially satisfying. Nobody had simply told them, The 1 is in the tens place and the 5 is in the ones place.

They had built the numbers.

They had seen that a full ten-frame represents 10 without having to count every counter.

They had counted on from 10 to determine the total.

They had written numbers such as $15=10+5$.

And from those experiences, they began noticing the structure of teen numbers for themselves: one ten and some additional ones.

That’s the kind of mathematical discovery we want students to make. The place value language and symbols aren’t arbitrary rules to memorize. They’re connected to quantities students have built, seen, and reasoned about.

A Lesson I Still Remember

When the students left the room, my AP and I had a little happy dance. We were both beaming and jabbering excitedly about the connections the students had made.

And then, when I checked Twitter later, I discovered that she had posted about the lesson. I still love having that little snapshot of the day.

How awesome that an administrator took a minute to make a teacher’s day!

And all these years later, I still think this lesson is a great reminder of how students develop an understanding of teen numbers. Build the quantities first. Give students opportunities to notice the structure. Then connect what they see to the symbols.

Try It With Your Students

his lesson doesn’t require anything complicated. Students need counters, double ten-frames, and a simple way to record the numbers they build. I’ve put together the double ten-frames and recording sheet I used for the activity so you can try it with your students.

Download the free double ten-frames and recording sheet here.

As students build each teen number, encourage them to recognize the full ten-frame as 10, count on to find the total, and record the number as 10 and some additional ones. Over time, those experiences help students develop mental images of teen numbers and understand the place value represented by the digits.

Once students begin seeing teen numbers as one ten and some more, you can extend that understanding into addition with my [Ten Plus Card Game]. Students use playing cards, counters, and a double ten-frame to find sums greater than 10 and match each sum to its 10+ representation.