Place Value: Understanding Numbers as Tens and Ones
What Is Place Value?
Place value is the idea that the same digit can represent very different amounts depending on where it appears in a number.
Take the number 2 — it might mean:
2 ones
2 tens (20)
2 hundreds (200)
2 thousands (2,000)
or even 2 million!
Kids don't learn this concept all at once. They build it gradually — starting with smaller numbers and working their way up. But for this understanding to truly stick, it's not enough to just see numbers on paper.
It’s much more effective when numbers are tied to something visual (like bundles of sticks, bead triangles showing 1+2+3+4=10, or classic base ten blocks) — and even better when they involve physical actions: tying real objects into groups of ten, stacking or arranging items, or building numbers with blocks.
Why Does It Matter for Kids?
When we look at the number 42, we don’t just read it as “four and two.” We understand it as four tens and two ones. But how do kids learn to make that leap? That’s where place value comes in. It helps kids grasp the deeper meaning behind the order of digits in a number.
Research shows that understanding place value is closely connected to skills like grouping objects, recognizing tens within numbers, and mentally breaking them into parts. Hands-on tools, such as base ten blocks, can make a big difference. When preschoolers build numbers using physical materials instead of just counting aloud, they develop a much stronger sense of how numbers are structured. Learning through concrete, visual actions — where numbers are not simply recited but built from tens and ones — helps kids grasp addition and subtraction within 100 more easily.
More importantly, early place value understanding sets the stage for future success in algebra. Kids who struggle to grasp how numbers are structured often face ongoing challenges in arithmetic and problem-solving in later grades. In this way, understanding place value lays the foundation for both numerical and algebraic thinking, which is essential for learning many other areas of mathematics.
How Do We Teach?
Kids explore place value through hands-on activities that let them see and feel how numbers work. To make counting easier, they tie sticks or matchsticks into bundles of 10. Each bundle represents "ten." If any sticks are left over, there can only be up to nine of them, because our digits stop at 9. As soon as a kid has 10 single sticks, they make another bundle.
Once all the sticks are sorted into tens, and fewer than 10 remain, kids can figure out the total. First they count how many full bundles there are — those are the tens. Then they count the leftover sticks — the ones. If there are no extras, the second digit in the number is zero.
Beads or berries can be arranged in a triangle: one in the first row, two in the second, three in the third, and four in the fourth. That adds up to exactly ten. These “triangle tens” are easy to check — kids know there are ten items, and nothing gets lost or skipped.
The same idea works with coins. Children learn to group them into tens too: ten 1s, five 2s, two 5s, or just a single 10-coin. First, they figure out how many full tens they’ve got. Then, any leftover coins become the second digit.
These activities help kids experience the idea that ten is a complete "set" — not just a number, but a whole group.
Once this concept clicks, kids begin to see numbers as having two parts: tens and ones. For example, 12 is made of 10 and 2. Fifty-two? That’s 50 and 2. To make this understanding stick, we use visual tools and playful activities — like base ten blocks, ten-frames, place value cards, or a hundreds chart. These give kids a concrete sense of how numbers are built.
Later on, when kids add or subtract 10, they start noticing that only the first digit changes — which makes counting much faster and more intuitive. As numbers get bigger, hundreds are added into the mix. And that’s when kids discover a key rule: no single digit can be greater than 9. If you have too many ones, you trade them for a ten. Too many tens? Trade them for a hundred.
First Steps
Tens and Ones Within 20
Around ages 5 to 6, kids start working with quantities that are too big to recognize at a glance. Take 12 objects scattered on a table — it’s hard for a kid to count them accurately. They might get one answer the first time, and a different one when they count again.
That’s when a familiar visual structure comes to the rescue: ten-frame thinking, built around two rows of five. If a kid sees 10 objects grouped neatly in a frame, with 2 more placed outside, they can quickly and confidently tell that there are 12 in total.
Place value (up to 20)
Numbers and quantities
Kids also learn about tens using special connecting cubes — 10 small blocks snapped together to make one stick. This helps them see what “ten” looks like, and makes it easier to count bigger numbers just by adding extra cubes.
When we say numbers like “fourteen” or “seventeen,” there’s usually a hidden structure behind the word: a ten and a few more ones. It’s important for kids to hear and understand that:
“Fourteen” means ten and four.
“Seventeen” means ten and seven.
Over time, they come to realize:
Single-digit numbers are less than 10, and two-digit numbers are greater than 10.
Place value shows up in real life too — like when kids count money. Sometimes a 10 is represented as one big coin. But in other cases, they might need to build ten out of two fives or five twos, set that group aside, and then count what’s left.
Once kids feel confident working with numbers up to 20 — seeing tens and ones, combining them, pulling them apart — they’re ready for the next step: counting by tens all the way to 100.
Base ten blocks
Count blocks (10–19)
Place value (up to 20)
Place value and comparison
Counting money
Count money (in 1s, 10s)
Base ten blocks
Count blocks by tens (10, 20, 30...)
Deep Understanding
Counting by Tens and Working with Numbers up to 100
Understanding place value becomes even more solid when kids start working with two-digit numbers. They begin to see that breaking numbers into tens and ones is a smart and efficient way to count larger quantities.
Place value
Tens and ones
It also helps to lay out groups of ten neatly — for example, lining them up in a hundred chart.
Over time, kids get used to the idea that every number can be split into tens and ones. For instance, they might picture the number 52 as two overlapping cards: one showing 50, and another showing 2 — covering the zero in 50.
When kids add or subtract 10 — like 10 glowing fireflies flying in or out — they often notice that the second digit stays the same. This insight becomes especially useful in games where, for example, they have to feed a hungry snake using numbers that skip count by tens, either forward or backward: 62 → 52 → 42 … or 10 → 20 → 30, and so on.
By playing, observing, and manipulating numbers this way, kids deepen their understanding of place value while also building confidence with numbers up to 100.
Hundred
Tens and ones
Place value
Tens and ones
Number line up to 100
Skip counting by 10s within 50
Number line & skip counting
Counting down by 10s
Confident Mastery
Moving on to Three-Digit Numbers
As kids move into the hundreds, their place value tools grow too. Along with unit cubes and tens rods, they begin using hundred flats — large square blocks that represent 100. Each type of block needs to be counted separately, and the result is written in its correct place value: hundreds, tens, and ones.
Base ten blocks
Count blocks (100–999)
One key idea becomes especially important at this stage:
No digit in a number can be greater than 9.
(There isn’t even a digit for “ten!”)
So when kids end up with more than 9 tens, they need to bundle them into a new hundred — and increase the digit in the hundreds place.
This mirrors how we count money, too. Kids may try to collect as many hundred-value bills or coins as possible, but often those hundreds are built from tens — and the tens, in turn, from smaller coins.
By learning to build numbers from hundreds, tens, and ones, kids are naturally preparing for place value-based operations — like adding and subtracting large numbers step by step.
Big numbers
Regrouping
Big numbers
Regrouping
Big numbers
Regrouping
Big numbers
Expanded form
Big Ideas
When we teach a kid to group objects — like putting cubes together to make tens — we’re introducing a powerful idea that has helped people across cultures and centuries:
It’s easier to count large quantities when you organize them into equal groups.
Most often, those groups are made of 10, like in our base-ten number system. But throughout history, other grouping systems have existed too — some based on twenties, others on sixties. Later in school, kids will explore different number systems, including the binary system that computers use today.
Another big idea is learning to sort and count things by type, instead of all at once — circles here, squares there. This skill comes in handy when kids begin working with charts, tables, graphs, and other ways of organizing data.
