Counting Objects vs Saying Numbers
Saying numbers in order is not the same as understanding quantity. Children build number meaning by matching number words to real objects, one-to-one. This is how numbers stop being sounds and start being tools.
Developmental research shows that understanding grows from doing before representing. Counting objects gives the brain reliable feedback, which helps numbers stick.
How and when to do this?
First of all, counting is about how many objects. It’s not about a rhyme or a song, so do as much counting objects as you can.
How many cakes, how many sandwiches, how many knives, how many forks.
There are lots of opportunities to count. When you count in their presence, count out loud. Show them you use it.
Counting the steps as you go up, 1, 2, 3, 4 may be okay. But just reciting numbers without carrying a meaning isn’t really supporting their sense of maths.
If a child can count but struggles with quantities or changes, it’s rarely about effort. It usually means the foundations are still organising.
Developmental research shows that understanding grows from doing before representing. Counting objects gives the brain reliable feedback, which helps numbers stick.
How and when to do this?
First of all, counting is about how many objects. It’s not about a rhyme or a song, so do as much counting objects as you can.
How many cakes, how many sandwiches, how many knives, how many forks.
There are lots of opportunities to count. When you count in their presence, count out loud. Show them you use it.
Counting the steps as you go up, 1, 2, 3, 4 may be okay. But just reciting numbers without carrying a meaning isn’t really supporting their sense of maths.
If a child can count but struggles with quantities or changes, it’s rarely about effort. It usually means the foundations are still organising.
Use Zero
This isn’t a counting trick. It’s about how number meaning is organised. When zero is part of a child’s number system early, later maths becomes easier because the structure is already there.
Get them used to the concept of zero, because they’re going to need that as soon as they start hundreds, tens and units. If you teach them zero now, it’ll be easier then.
Developmentally, children move from handling quantities to representing them mentally. Zero supports that shift by anchoring the idea that “nothing” is still a number.
How and when to do this?
We’re sure you know some variations to this song: Five little speckled frogs sitting on a log… then four, then three, then two, then one.
And then people often say, no frogs. Or something like “and then there were none”. Don’t do that. That is a missed opportunity. Use the word zero.
Get them used to the concept of zero, because they’re going to need that as soon as they start hundreds, tens and units. If you teach them zero now, it’ll be easier then.
Developmentally, children move from handling quantities to representing them mentally. Zero supports that shift by anchoring the idea that “nothing” is still a number.
How and when to do this?
We’re sure you know some variations to this song: Five little speckled frogs sitting on a log… then four, then three, then two, then one.
And then people often say, no frogs. Or something like “and then there were none”. Don’t do that. That is a missed opportunity. Use the word zero.
Beginning Beginners’ Maths: How Many Are Under My Hand?
If your child sees three sweets on the plate, and you take one away when they’ve turned around, they know one is missing. Or at least, they know they’ve lost out.
So how can we build on that to build mathematical concepts?
Well, get three sweets (or better yet, three gems or other items that don’t involve sugar). Count them together: one, two, three.
Ask them to close their eyes. Cover two with your hand. Ask, “How many are under my hand?”
If they can’t immediately tell, you go ahead and count: Count the one that’s out, “one”, then tap twice with a finger on the back of the hand that is on the table, “two, three. I wonder how many are under my hand.” Your child will guess. Then together you will look. “I covered two of them!” You can reinforce by repeating: “One, two, three, I covered two”.
Keep doing that until they’re consistently right. Then you can build up to four and to five. Don’t go beyond five and do let them have a turn.
And sometimes look a little puzzled and take a while to work out what’s under their hand.
There’s a point where they may find it boring and they may tease you so that you’ll get it wrong, by hiding one of the gems under the table or in their pocket. That’s when you know they are ready for another math game altogether.
Helping Young Children Build Number Sense: How Many Are In the Box?
What we want is for children to know how many, to form a mental picture of numbers in their head. This is the foundation for later math skills like addition, subtraction, and problem-solving.
A simple, hands-on activity can make this concept clear and fun for young learners—and it only takes a few toys and a box.
- Start with an empty box
Use a small box, basket, or pot with a lid. Gather five toys that fit inside. - Ask, “How many are in the box?”
Look together and decide there are zero. Say out loud: “There are zero toys in the box.” - Add one toy at a time:
Ask: “How many toys will there be when this one goes in?” One. Put the toy in the box. “Let’s look and see”. Open the box. Check it. Yes, one toy in the box. Close the box. Pick up another toy. “How many toys will there be in the box when I put this toy in? In it goes!” Check together. - Vary the task
You can add one toy at a time or two toys at a time. Sometimes the toys can get out of the box.
Tip: Make it fun, make it silly, make it giddy.
Tip: Always pretend you’re checking because you’re unsure — this makes it fun and reinforces the concept of counting and verifying.
Why Number Lines Matter
Number lines help children understand numbers as related to each other, not isolated facts. They show direction, distance, and order in a way the brain can map visually.
This supports the shift from concrete handling to mental representation. Without this map, subtraction and estimation feel unpredictable.
If number lines feel confusing, it often means the internal number map is still forming.
This supports the shift from concrete handling to mental representation. Without this map, subtraction and estimation feel unpredictable.
If number lines feel confusing, it often means the internal number map is still forming.
Why Counting Backwards Is Unsettling
Counting backwards reverses the usual number pattern. This disrupts the internal number map unless it’s well established.
If a child becomes anxious or stuck, it’s not resistance. It’s instability in the underlying structure.
If a child becomes anxious or stuck, it’s not resistance. It’s instability in the underlying structure.
Why Subtraction Feels Harder Than Addition
When you are subtracting, much like when you count backwards, you’re traveling backwards on the number line. And backwards is much less familiar than forward. Activities that familiarize the child with their body structure, and specifically with the back are often helpful with subtraction.