Patterns in Quantities: Growing Patterns
What Are Patterns in Quantities?
Many math ideas start with noticing simple examples. Take odd and even numbers. You could explain it logically: 1 is odd, every odd is followed by an even, and every even is followed by an odd. But before kids grasp that rule, they usually spot the pattern first: odd–even–odd–even. These rhythms are easy for kids to catch, just like skip counting by 3s or following any repeating pattern.
But patterns aren’t only about alternation. There are also growing patterns — sequences where numbers increase by a rule. For example:
In the sequence of odd numbers 1, 3, 5, 7, 9, … each number is 2 more than the one before it.
In the sequence of powers of two 1, 2, 4, 8, 16, … each number is double the one before it.
Why Does It Matter for Kids?
Understanding spatial and numerical patterns is a key step in developing mathematical thinking. By observing and reproducing patterns, kids learn to notice, predict, and describe changes. This builds the foundation for counting, number order, and understanding relationships between numbers.
Research shows that the ability to recognize patterns at an early age is closely linked to later success in arithmetic, logical reasoning, and even learning algebra. Kids who feel confident working with repeating and growing sequences find it much easier to grasp ideas like “2 more,” “double,” or “every other one.”
Working with patterns also nurtures flexible thinking: a kid begins to see the same number in different ways — as a group of objects, as a design, or as a point on a number line. This shift from concrete images to abstract concepts is what prepares kids for more advanced math in the future.
How Do We Teach?
For little kids, numbers often look like a staircase: 1, 2, 3, 4, 5 — “getting bigger and bigger.” They start by lining up groups of objects and spotting simple patterns. Bit by bit, their number sense grows: dots on a page, fingers on a hand, or random groups showing the given number of dots.
Want to know more about how kids quickly recognize the number of dots? Check it out!
Soon, kids begin to play with numbers in new ways — skip counting, telling even from odd just by looking, counting by tens, and finding number patterns in everyday situations.
As they go, the patterns get more exciting: square numbers, powers of two. Kids fill in missing numbers and figure out the rules behind these sequences.
All of this isn’t just fun — it’s preparing them for bigger math ideas like progressions, algebra, and even the concept of functions.
First Steps
From Simple Stairs to Number Sense
For 3- to 4-year-olds, it all begins with the simplest staircase: 1–2–3–4–5 objects. At this stage, kids start to understand ideas like “higher and higher” or “more and more things.” Ordering groups by size is an important activity that connects the order of numbers with their quantity.
Monotone behaviors
Order by height
Other sequences quickly appear. The staircase can climb up (1–2–3), then go back down (3–2–1), or even repeat itself (1–2–3, and then 1–2–3 again).
In later activities, the number of dots keeps growing, but they’re no longer lined up neatly as a staircase. Numbers can show up in many different forms — as longer rows of objects, as the familiar dots on a dice face, or as fingers on a hand.
Sometimes a growing or shrinking sequence comes with an extra twist: alternating colors.
Number patterns
Number patterns
Number patterns
Number series
Number patterns
Number Sequence (up to 5)
Number patterns
Number Sequence (up to 5)
Deep Understanding
Rules Behind the Numbers
Once kids feel confident with the number line, they can start skipping every other number — counting by twos, evens, or odds.
The sequence of even numbers often shows up in real-life situations, like arranging chairs around a longer and longer table.
Patterns
Geometric patterns
Kids also learn to predict whether a number will be even or odd just by looking at it.
Counting by tens can be seen as another kind of pattern: we simply add a zero to the numbers from 1 through 9. The structure of our base-10 system is actually made of two overlapping patterns — the digits 0 through 9 repeating in the ones place, and the same pattern repeating in the tens place.
Patterns
Number patterns
Number line
Odd and even numbers on the number line
Number patterns
Find the missing number
Number patterns
Skip counting by 10s
Confident Mastery
Playing With Patterns and Predicting What Comes Next
As kids grow older, they begin to explore more fascinating number sequences — like square numbers:
1 dot in a 1×1 square
4 dots in a 2×2 square
9 dots in a 3×3 square
16 dots in a 4×4 square
25 dots in a 5×5 square
Number patterns
Number series
They also discover sequences where numbers keep doubling: the flowers on a cactus multiply each day — 1, 2, 4, 8, 16. Or the opposite can happen: the number of nuts gets cut in half day by day.
Kids enjoy guessing the missing number in a sequence of odds, or predicting the “color” of a number in a repeating pattern like blue, green, pink, blue, green, pink, and so on.
Tricky counting
Recognize the pattern
Halves and multiples
Halves
Number patterns
Number series
Seeing patterns
Patterns in quantities
Big Ideas
A number sequence is often the very first example of a function that kids encounter — a rule that tells us which number comes in the 1st, 2nd, 3rd, or 4th place. Sequences show up everywhere in math: from prime numbers to pentagonal numbers to the famous Fibonacci sequence. Later on, in high school, kids will even learn how to find the sums of arithmetic and geometric progressions.
At first glance, figuring out the next term in a sequence feels more like solving a riddle than doing math. But by the end of the 20th century, mathematicians gave this problem a precise definition: the task is to find the shortest possible description of the rule that fits the known terms. The length of that description is called its Kolmogorov complexity.
