Number Names, Counting Forward and Backward
What Is the Topic?
When kids first start learning about numbers, the concept can feel a bit like a puzzle with too many pieces. Take the number five: it’s the written digit “5”, the spoken word “five”, the idea of five objects (like five fingers on a hand or five dots on a domino), and also the fifth position in a number sequence. Somehow, children have to connect all these versions into one complete understanding of what “five” means.
At first, kids memorize the names of digits from 0 to 9 like a song. Then comes number 10 — and after that, number names begin to follow a regular pattern. This pattern helps kids count forward from any number, which is essential for understanding how to add 1, 2, or 3. But it’s just as important to know how to count backward, especially when it comes to subtraction — that means knowing which number comes before and being able to take a few steps back.
You can see this in action in our lesson:
Why Does It Matter for Kids?
Understanding the number sequence and how to count isn’t just a nice-to-have — it plays a key role in helping kids build strong math skills and succeed in school.
Studies show that thinking clearly about numbers is the foundation for learning how to add, subtract, and build more advanced skills over time. Kids who understand that numbers follow a logical order, and that each one connects to others, are better prepared to tackle more complex math later on.
Seeing numbers as part of a sequence, and understanding how they relate to one another, is a central part of number sense. Strong number sense is one of the most important building blocks for long-term success in math.
Preschoolers who get comfortable with counting and number order early on are more likely to thrive in math once they enter elementary school.
Counting forward and backward also helps strengthen focus and working memory. Kids have to keep track of where they are and what comes next, which boosts their overall thinking and problem-solving skills.
And just as important, when kids understand that numbers are connected and that they can move through them step by step, they start to feel more confident. This growing sense of control helps reduce math anxiety and makes new challenges feel less intimidating.
How Do We Teach?
Kids begin learning about numbers through all the different ways they show up in real life — as digits, words, quantities of things, and places on a number line. Our job is to help them bring these pieces together.
At the same time, we link number words to finger movements. For example, when a kid hears “four,” they hold up four fingers. This physical connection makes numbers feel more real and helps kids understand addition and subtraction as moving forward or backward along a number path.
Next comes learning how to count on and count back — not from the beginning, but starting from any number and taking steps forward or back. As they grow more confident, kids move into the next ten (11–20), then master round numbers like 30, 40, and so on, all the way to 100. We encourage them to notice the patterns in number names — and not be afraid of mistakes like saying “thirty ten.” That kind of experimenting shows that kids are thinking deeply about how numbers work.
Eventually, they start using these same strategies with larger numbers, relying on their understanding of number neighbors and how each number connects to the next.
First Steps
Introduction to Number Names and Counting Sequence
At around 3 or 4 years old, kids often learn to recite “one-two-three-four-five” like a favorite rhyme. This simple number chant becomes their first tool for counting objects or figuring out what’s missing in a sequence.
Number line
Counting sequence (up to 5)
It helps to connect number words with finger movements. When a kid hears “four,” they hold up four fingers.
If they add one firefly, they move to the next number. If they take one away, they go back to the previous one. Little by little, kids start to match number words with quantities, and the number sequence begins to settle in their memory.
Counting up to 5
Make four
Number line up 100
Counting up and down within 5
Quantities & addition
Matching equal quantities up to 5 (objects only)
Counting up to 5
Number sequence (up to 5)
Deep Understanding
Moving Beyond Counting to Flexible Number Use
Around the age of 5 or 6, they begin to connect counting forward with addition. Instead of starting from scratch to add two numbers, they learn to “count on” from the first number. So, if a kid wants to add 3 to 7, they don’t need to count all the way from 1. They say “seven,” then take three steps forward in the number sequence: “eight, nine, ten.” That gives the answer 10.
The same approach works for subtraction, too. To subtract 3 from 10, they count backward: “nine, eight, seven.”
Basic subtraction (up to 10)
Subtracting part-by-part
Once kids feel confident with numbers up to 10, they begin to explore the next set of numbers. The teens (11 to 19) are tricky because their names don’t always follow the same pattern as the first ten. Then come the round numbers like twenty, thirty, forty, and so on, which help kids count all the way up to 100.
The biggest challenge at this stage? Knowing when to stop! That’s how we sometimes get funny number names like “thirty ten”.
Number line
Counting sequence (up to 10)
Place value (up to 20)
Numbers and quantities
Counting money
Count money (in 1s, 10s)
Base ten blocks
Count blocks by tens (10, 20, 30...)
Confident Mastery
Applying Counting Strategies with Larger Numbers
The same “counting on” method works well with bigger numbers too. Let’s say a kid needs to add 5 to 58. They fold down five fingers, then open them one by one as they count: “fifty-nine, sixty, sixty-one, sixty-two, sixty-three.”
Addition
Counting up
Having a strong sense of number neighbors — the numbers that come just before and after — is especially helpful when kids start adding and subtracting bigger numbers. For example, if a kid knows what comes right before 200, they can quickly figure out 200 minus 1. And when they understand what comes after a big number like a million, it’s much easier to add to it.
Big numbers
Counting up
Number line & skip counting
Skip counting by 10s
Big numbers
Regrouping
Big numbers
Place value
Big Ideas
One of the most powerful ideas kids discover is that numbers never really end. No matter how big a number is, there’s always another one that comes after it. This is their first step toward understanding the concept of infinity.
Later on, kids learn that the number line doesn’t just go forward — it stretches backward too. That’s where negative numbers come in.
And when they start exploring decimals, things get even more interesting. They find out that between any two points on the number line, there’s an endless number of smaller parts. You can divide each section into 10 pieces, and then divide those again into 10 more.
Eventually, in middle and high school, kids learn about irrational numbers — the ones that go on forever without repeating. And yet, even with all these new ideas, the number system still keeps its familiar structure of tens. That early understanding of counting and number order lays the foundation for everything that comes next.
