Last week, we talked about subitizing, or recognizing how many objects are in a small group without having to count each one.
This week, we are going to build on that idea by looking at making a five and making a ten.
These may sound like simple skills, and they are. But they are also laying an important foundation for the math children will encounter later.
When children learn that numbers can be made from smaller groups, they begin to see numbers as quantities that can be put together, taken apart, and rearranged.
And one of the best ways to develop that understanding is to let them actually move the numbers around with their hands.
Start with Five
Give your child five small manipulatives. These could be counters, blocks, buttons, small toys, or just about anything you have available.
Ask them to count out five.
That's it.
Let them touch each one as they count. Let them move them around. Let them see that even though the objects change position, there are still five.
Once they have five, we can begin to play.
Ask them to split the five into two groups.
Maybe they make:
1 and 4
Then move them around and try again.
2 and 3
Then:
3 and 2
And:
4 and 1
We aren't asking the child to memorize these combinations yet. We are giving them the opportunity to discover them.
You might say:
“You made five! You put one here and four here. What equation could we make with those groups?”
You can write:
1 + 4 = 5
Then move the manipulatives again.
2 + 3 = 5
And again.
4 + 1 = 5
The child is physically building the equation before ever having to memorize it.
Let the Manipulatives Do the Talking
Sometimes I will simply put five manipulatives in front of a child and let them move them around.
Push some to one side.
Push the rest to the other.
Then talk about what we see.
“There are two here and three here. We still have five altogether.”
You can write the equation together.
Or you can simply say it:
“Two and three make five.”
If writing is part of the lesson, the child could write the equation on a dry erase board, on paper, or even practice writing it in a sensory material such as sand.
This is where you can adjust the activity based on what your child needs.
The goal isn't the worksheet.
The goal is understanding.
Now Let's Make Ten
Once children have had plenty of opportunities to explore making five, we can begin doing the same thing with ten.
Have your child count out ten manipulatives.
Then start playing.
“Let's split ten into two groups.”
Maybe they make:
1 and 9
Then:
2 and 8
Then:
3 and 7
Then:
4 and 6
And:
5 and 5
Each time, they are physically creating the two parts that make the whole.
You can talk about the equation afterward:
3 + 7 = 10
Or:
6 + 4 = 10
Or:
5 + 5 = 10
Again, the equation is simply a way to record what the child just did with the manipulatives.
Add a Ten Frame
A ten frame can be a helpful next step because it gives children a consistent visual for ten.
Put five counters on a ten frame.
How many spaces are filled?
How many are empty?
How many more do we need to make ten?
Now try six.
Then seven.
Then eight.
Then nine.
The child begins to notice something important:
The closer we get to ten, the fewer we need to add.
And because they have physically built these combinations over and over, they can eventually begin to recognize them without needing to count every single counter.
This connects beautifully back to our conversation about subitizing.
First, children learn to recognize quantities.
Then they begin to recognize how quantities can be combined.
Ready for the Next Step? Let's Play a Guessing Game!
Once your child is comfortable making five and ten, you can build on that understanding by asking them to figure out what is missing.
Start with three manipulatives and ask:
“I have three. How many more do I need to make five?”
Let your child use manipulatives to find the answer. They might count out two more, or they might recognize that three and two make five.
Now try the same activity with ten.
“I have seven. How many more do I need to make ten?”
As your child becomes more comfortable, you can turn this into a little guessing game.
Place five manipulatives on the table. Let your child see them, then cover them up. Uncover just a portion and ask:
“How many do you see?”
Then:
“How many are hiding?”
And:
“How many do we have altogether?”
You can do the same thing with ten, using a ten frame or a small cloth to cover some of the counters.
These activities encourage children to think about the quantities they cannot currently see, using what they already know about the whole number.
Now let's turn the activity around.
Place five manipulatives on the table and let your child count them. Cover them up, secretly take some away, and then uncover the remaining counters.
Ask:
“How many are left?”
“How many did I take away?”
“How many did we start with?”
Try it again with ten.
These simple games help children begin to understand the relationship between adding and taking away. They are learning that when we start with a whole, we can add to it to make a bigger group, or take some away and have a smaller group remaining.
Keep it playful, and let your child's understanding guide you.
If they need to uncover all the manipulatives and count them, that's perfectly fine. As their number sense develops, they may begin to figure out the missing quantities without needing to count everything.
From Hands-On to Thinking
Eventually, we want children to be able to think about these combinations without needing the manipulatives in front of them.
But we don't have to rush there.
There is value in letting children build it first.
They can:
touch it → move it → see it → say it → write it → eventually think it.
That progression is one of the reasons hands-on learning is so important in early mathematics.
We aren't just keeping children busy with counters.
We are giving them something concrete to connect to the abstract symbols they will eventually see on a page.
Try It at Home
You don't need special math manipulatives.
Use blocks, buttons, coins, cereal pieces, small toys, or anything else your child can safely count and move.
Start with five.
Make five.
Split five.
Move it.
Talk about it.
Write or say the equation.
Then do the same with ten.
As your child becomes comfortable, add the missing-number games.
“I have three. How many more do I need to make five?”
“I have seven. How many more do I need to make ten?”
“I started with five and now I have three. How many did I take away?”
Keep it short. Keep it playful. And repeat it often.
You may be surprised by how much mathematical thinking can happen with just a handful of objects on the table.
E3 Takeaway
Making a five and making a ten are much more than memorizing combinations.
They are opportunities for children to experience how numbers work.
When children physically separate and recombine quantities, they begin to understand that numbers are made of parts and that those parts can change while the whole stays the same.
Today, that might look like five counters being split into two groups.
Tomorrow, that understanding will help them make sense of addition, subtraction, larger numbers, and mental math.
Review. Reinforce. Grow.
From the Teacher's Desk
Sometimes the simplest math activities are the ones that give us the most information.
Give a child five counters and ask them to make five. Watch what they do.
Do they count each one carefully?
Do they recognize the group?
Can they split it into two parts?
Can they tell you how many are in each group?
Can they put them back together and explain that they still have five?
Those little moments tell us so much about what a child understands.
And that's one of the things I love about hands-on math. We aren't just teaching the skill. We are watching the thinking happen.
