How Teaching About Tens Helps Kids Connect The Pieces In Math

I've always thought of learning math as putting a puzzle together. Some of the pieces seem fairly simple on their own, but until children understand how they fit together, the bigger picture can be pretty confusing.

Over the years, when I've worked with small groups of children, I've noticed many who haven't quite grasped the idea of ten and how important it is to their understanding of numbers. Some of these children can count. They recognize numbers. They may even know some addition facts. But when I ask them to show me what a number means or explain how they know an answer, I sometimes discover that an important puzzle piece isn't really in place yet.

They know the numbers, but they don't necessarily understand how they work together. It keeps coming back to ten.

Why ten matters

Think about this. Our number system is built around groups of ten. We have ones, but when we get to ten ones, we make a group and call it a ten. Ten tens make a hundred. Ten hundreds make a thousand. We use this system all the time, but that doesn't mean it is automatically obvious to children.

I've worked with children who can tell me that ten ones make a ten, but when I give them a number and ask them to show it with blocks or counters, they aren't sure what to do. That's why I know we need to slow down.
Before worrying about another worksheet or another set of addition questions, I want to give them opportunities to actually experience ten.

Making Ten

One of the activities I have used for years is making tens with dice and ten frames. It is a simple idea. Roll a die and figure out what number you need to make ten. Roll again and find another combination. But there is a lot happening as children play.

They begin to notice that 6 and 4 make ten. Then they see 7 and 3. Eventually they don't have to count on their fingers to figure it out.

I wrote about this in Making Tens With Dice and Ten Frames. One of the things I mentioned in that post was how quickly some children move from counting on their fingers to recognizing the combinations automatically. 

That's the kind of progress I like to see. Not simply remembering a fact because we practised it enough times, but beginning to see the relationship between the numbers. Once a child knows that 6 and 4 make ten, that relationship can become useful in many other situations.
What is 16 + 4?
What is 26 + 4?
What happens if we have 13 and need to get to 20?
The original idea of making ten is still there.

Ten Is Something Children Can See

This is why I like using concrete materials so much. If I ask a child to think about 8 + 2, they may know the answer. But if they can put eight counters into a ten frame and see the two empty spaces, the answer becomes visible.

They can see what is missing. They can fill the spaces. They can make ten. And then they can take it apart again.

That may seem very simple to an adult, but these are the experiences that help children develop an understanding of how numbers relate to one another.

I've written before about How Using Manipulatives With Numbers Helps With Abstract Use. I still believe very strongly in that progression from something children can see and manipulate toward the abstract numbers they eventually need to work with independently. 

Number Sense Is More Than Knowing the Answer

This is also why I think number sense is so important. I don't just want a child to tell me that 8 + 2 = 10. I want them to have some idea of why. I want them to know that 8 is two away from ten. I want them to recognize that if they have 8 and add 2, they have made a complete group of ten. And I want them to be able to use that knowledge somewhere else.

Number sense gives children ways to think about numbers rather than relying on one method every time.
I've written about How Developing Number Sense Impacts Student Confidence and Success before. I keep coming back to those ideas because I see them playing out when I work with children who are struggling. 
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Sometimes a child who says, "I'm not good at math," really needs more opportunities to make sense of what the numbers are doing.

Give Them More Than One Way to Make Ten

I also like giving children different ways to work with the same idea. Dice are one way. Ten frames are another.
Counters, cubes, fingers and base-ten blocks can all be used.

I might ask a child to find two numbers that make ten. Another time, I might ask them to start with ten and take some away. I might give them a group of objects and ask how many more are needed. The activity can change, but the mathematical idea stays the same.

That's important because I don't want children to associate a mathematical idea with just one worksheet, game or set of materials. I want them to recognize the idea wherever it appears.

When the Pieces Start to Connect

This is where the puzzle analogy comes back for me. Understanding ten is not the whole picture. But it is an important piece.

Once children understand that ten is a group they can make, break apart and use, they have something to connect to when they begin working with larger numbers. Ten ones become one ten. Ten tens become one hundred. The digits in a number begin to have meaning. Addition and subtraction can begin to make more sense. Money and measurement provide real-world examples.

Children have something to draw on when they are asked to solve a problem they haven't seen before. That's why I'm willing to spend time on these seemingly simple ideas.

Sometimes we need to slow down before we can move forward. If a child hasn't really internalized what ten means, giving them more complicated number work may only make the confusion bigger.

Instead, I would rather go back to the concrete. Roll the dice. Fill the ten frame. Build the number. Take it apart. Make ten in another way. Talk about what you see. Try it again.

Eventually, the hope is that the child doesn't need all those materials anymore because the understanding has become part of the way they think about numbers. And that's when I know another puzzle piece has finally found its place.

Looking back at those children I worked with who were struggling to make sense of math develop confidence because they finally understood how to use tens confirms my belief that this is an important puzzle piece and taking the time to make sure it is in place is worth it.

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