How Base Ten And Place Value Activities Help Kids Make Sense Of Math

9/20/2026

One of the things I have come to appreciate even more through my work with small groups and tutoring is how much of elementary math comes back to understanding ten. Children may be ready to work with larger numbers, addition and subtraction, or place value on paper, but sometimes I discover that the foundation underneath those skills isn't quite as solid as it needs to be.

That's when I go back to something concrete. If a child can build a number, take it apart, trade one quantity for another and explain what is happening, I know we're getting somewhere.

For me, this is where base ten becomes so important.

base ten and place value activities build number sense

What Does the Number Actually Mean?

Take the number 246. A child may be able to read it and write it correctly. But can they tell me what the 2 means?
What about the 4?
What about the 6?
Can they build 246?
Can they show it another way?

This is where I like to use different representations of numbers.
246
200 + 40 + 6
2 hundreds + 4 tens + 6 ones
These aren't three separate math skills. They are three different ways of showing the same number.

When children can move between those representations, I have a better sense that they are beginning to understand place value rather than simply following a rule.

This is one reason I created resources that allow children to work with standard form, expanded form and base-ten representations. They give children a chance to see the relationship between the written number and the quantities it represents.

I've written more about this in How Using Manipulatives With Numbers Helps With Abstract Use

Base Ten Gives Us Something to Hold Onto

There is a reason I keep coming back to base-ten blocks and other concrete materials.
A child can look at 40 on a worksheet and see two digits. But four tens on a table are something different.
They can count them.
They can move them.
They can put them beside four ones.
They can add another ten.
They can take one away.
They can exchange ten ones for one ten.

The numbers become quantities rather than symbols. That is an important step. Eventually, I want children to be able to look at 46 and picture four tens and six ones without needing the blocks in front of them. But I don't think we should be in a hurry to get rid of the concrete materials. The materials are helping build the understanding that will eventually allow the child to work abstractly.

Let's Go to the Bank

One of my favorite ways to make regrouping more understandable is to use money.

Imagine that you have ten pennies. You take them to the bank and trade them for a dime. You still have the same amount of money. You haven't gained anything. You haven't lost anything. You have simply changed ten smaller units into one larger unit.

Then you can do the same thing with ten dimes and a dollar. This gives children a very concrete way to understand what happens when we regroup numbers.
10 ones → 1 ten
10 tens → 1 hundred
The amount stays the same. The way we represent it changes. That is a much more meaningful explanation than simply telling children that they need to "carry" a number when adding or "borrow" when subtracting.

What Are We Actually Doing When We Regroup?

Suppose we are adding and we end up with 14 ones. Rather than simply writing down the 4 and putting a 1 somewhere else because that's what the procedure says to do, I want children to understand what happened.

We had 14 ones. We can keep 4 ones and trade 10 of those ones for 1 ten. Now we have: 1 ten and 4 ones. The quantity hasn't changed. We've simply reorganized it.

This is the same idea they experienced when they traded ten pennies for a dime. That connection can be powerful.

The more opportunities children have to see the same mathematical idea in different situations, the more likely it is that they will recognize it when they encounter it somewhere new.

The Real World Gives Us More Opportunities

This is where I think mathematics becomes especially interesting. Base ten isn't something that only belongs in the math lesson.

We use our number system when we work with money. We use numbers when we measure. We use them when we compare prices, count objects, keep scores, record distances and solve everyday problems. Measurement is another area where children can see relationships between units.

Money is especially helpful because the idea of exchanging ten smaller units for one larger unit is so visible.
This is one reason I enjoyed developing my Money Lessons Unit with my Grade 3 class. We weren't just practising money facts. We were using money in situations that had a purpose. Children had jobs, earned classroom money, made choices about saving and spending, and had opportunities to use their mathematical thinking. The numbers had somewhere to go.

Understanding Before Memorizing

I'm not against children learning their basic facts. They need those facts. But I want them to have something underneath the facts.

If a child forgets 7 + 8, I want them to have some strategies for figuring it out. Maybe they know that 7 + 7 = 14 and can add one more. Maybe they make a ten. Maybe they think about 8 + 2 = 10 and then add the remaining 5.

The answer matters, but so does the thinking. This is one reason I've written about tips for helping math make sense and using games to develop place value and number sense.

Games and hands-on activities give children opportunities to use these relationships repeatedly without every experience feeling like another page of questions.

Sometimes Going Back Is the Best Way Forward

When I'm working with a child who is struggling, I sometimes have to remind myself that the answer isn't always to give them more practice with the skill they are having trouble with. Sometimes I need to go back.

Back to the counters.
Back to the ten frame.
Back to the base-ten blocks.
Back to the money.
Back to making ten.
Back to asking, "What does this number actually mean?"

That isn't going backward. It's finding the missing piece. Once that piece is in place, the next piece has somewhere to connect.

That's really what I want for children when they are learning math. I don't want them to simply learn a procedure well enough to get through a worksheet. I want them to understand what the numbers mean, how they relate to one another and how they can use that understanding when the situation changes.

Eventually, the blocks won't be there. The ten frame won't be there. The pennies and dimes won't be there. But the understanding will be. And that's when the math has really started to make sense.