Visual Patterns
What are Visual Patterns?
A visual pattern is a rule or structure that shows up in designs, borders, or tiling. Most often, it’s about repeating elements like 🔵🔴🔵🔴, or ⏺️⏹️🔼⏺️⏹️🔼. Sometimes patterns include symmetry, where one part reflects the other. In tiling, the rule extends across the whole surface.
Patterns can also be growing: at each step, something new is added according to a rule. For example, a line of shapes that gets one more square every time.
Why Does It Matter for Kids?
Spotting patterns is one of the stepping stones to logical thinking. Patterns help kids form their first words (cat, dog, tree, car) and first concepts (blue, round, same, bigger). We also use them to explain changes and operations: swapping colors, adding or taking away objects, or noticing what stays the same. By recognizing shared features, kids learn to build concepts.
Research shows that recognizing patterns makes a unique contribution to early math growth, above and beyond general skills like fluid reasoning or working memory. In one study of 519 preschoolers from low-income families, strong pattern-recognition skills predicted better number knowledge and counting in 1st grade, as well as higher scores on high-stakes math tests in grades 4–6.
In another experiment, 140 first graders with low initial scores were divided into groups: patterning instruction, reading, math, and social studies. The group that practiced patterning achieved significantly higher results on the Woodcock-Johnson math concepts scale compared to the other groups.
How Do We Teach?
The world of patterns is all around us, from a simple border on the sidewalk made of repeating blocks to the intricate designs of Gothic cathedrals, mosques, and pagodas. When we introduce kids to the art of patterns, we are also touching on many big ideas in math.
The simplest sequences are made of identical elements. But once they flow into a continuous design, it is not always easy to pull the repeating unit out of the whole picture. More advanced patterns alternate elements every other step or every two steps. Kids not only practice continuing these patterns but also tackle challenges like predicting the color of the 23rd element in a sequence.
The same principle shows up in animation frames. Alternating phases of a walking person or a crawling caterpillar create the illusion of motion.
Necklaces arranged in a cycle also follow this idea. A fun challenge is to find the smallest fragment of the design that repeats. Quite often, there is more than one correct answer.
Tables can also form patterns. For example, imagine a grid where each row has the same shape and each column has the same color. Recognizing the rule for filling in such tables later helps kids make sense of the addition and multiplication tables, as well as something practical like reading a weekly class schedule.
Sometimes the colors in a grid are arranged like a Sudoku puzzle, where each row and column contains exactly one red square.
Another important math idea is tiling, or tessellations. These are designs that cover a surface completely without gaps or overlaps. The simplest tiling uses squares, like graph paper. A more complex one uses hexagons, just like honeycombs.
Mathematicians also study “patterns within patterns,” known as fractals. The same rule, such as removing the center, can be applied to both a large triangle and a smaller one, creating lace-like geometric designs.
First Steps
Repeat, Alternate, and Cycle
The simplest patterns are made of identical repeating elements. Kids come across repeats all the time. Walking and riding a bike involve repeating leg movements. Watering plants means tilting the watering can over one pot, then the next, and the next. Setting the table means putting a fork next to each plate.
But if you look closely, many of these are not just repeats — they are alternations. With the watering can, for example, you lift it, move it to the next flower, tilt it, then lift it again.
Serial reasoning
Reasoning by analogy
Counting objects works in a similar way. A kid points to the next item, says the next number word, and then moves their hand forward. Each step is a small alternation.
Some activities ask kids to notice alternations in a woven rug, for example, to figure out which piece of the pattern the cat is lying on.
In a game inspired by Egyptian gods, kids first see very simple repeats, like the same figure over and over (AAAA). Then the sequence becomes an alternation, such as ABABAB. Later, the patterns grow more complex, like ABCABCABC. Different parts of the figures can follow different rules. For example, the headpieces might change every other step while the lower parts stay the same, or they might form a three-step cycle.
Kids also learn to carry the sequence forward in their minds and predict what a later element will look like, for example the eighth figure in the pattern.
Alternation can happen not only in a line but also in a loop. Kids may be asked which small piece of the design can be repeated to form the entire cycle.
Patterns
Patterns in geometry
Patterns
Add missing figure fragments to a 3-part pattern (2–3 fragments each)
Patterns
Properties and attributes
Patterns
Patterns with beads
Deep Understanding
2D-Patterns
A key skill for kids is learning to picture in their minds what a cut-out piece of a pattern would look like. For example, what happens if you cut a pentagon-shaped piece out of a flag?
Patterns
Complete visual patterns
Regular tilings of a surface with polygons are called tessellations. Kids notice them not only on floors but also on tiled walls and other everyday surfaces.
Two-dimensional patterns where one feature changes vertically and another changes horizontally — for example, the same shape down a column and the same color across a row — prepare kids for reading and understanding tables. Another fascinating type of 2D pattern involves choosing one element from each row and each column. The simplest way is to follow a diagonal line, but there are many other possibilities.
These kinds of tasks often combine several rules at once. For instance, each row might need to include 1, 2, and 3 pencils, all in different colors. Kids learn to juggle overlapping patterns and spot how multiple features can interact at the same time.
Patterns
Complete visual patterns
Serial reasoning
Visual patterns
Serial reasoning
Reasoning with tables
Serial reasoning
Visual patterns
Confident Mastery
Cartoons and Growing Patterns
Some patterns can imitate motion, just like the frames of a cartoon.
For example, the illusion of walking can be created with just two phases: one figure with legs together and another with legs apart.
Serial reasoning
Order the steps
It gets even more interesting when two characters with different movement cycles appear on the screen. One caterpillar might raise its head and then curl into an arch, then raise its head again and curl once more. Another caterpillar might move in a different rhythm, alternating between one arch and two arches.
The phases of the moon also form a pattern: full moon, three-quarters, half moon, quarter moon, new moon, and then back again.
Sometimes a pattern does not return to its starting point but keeps changing. For instance, kids might look at a picture being colored step by step, or a chessboard growing larger and larger: first 1×1, then 2×2, 3×3, and so on.
Fractals are another fascinating kind of pattern. Take the Sierpinski triangle: first the middle triangle is cut out, leaving 4 smaller triangles. Then, at the next stage, the middle is cut out of each of those, and the process repeats again and again, creating an increasingly intricate lace-like design.
Serial reasoning
Order the steps
Serial reasoning
Reasoning by analogy
Patterns
Patterns in geometry
Patterns
Patterns in geometry
Big Ideas
If a kid can predict the color of the 100th bead in a sequence like blue-red-yellow-blue-red-yellow, they are already practicing the same thinking that helps with divisibility and remainders when dividing by 3. Remainders and skip-counting naturally lead to the idea of an arithmetic progression.
Tables also play an important role. In a table, some properties stay the same across a row while others change down the columns. Understanding how a table works is useful far beyond math: it helps with reading schedules, browsing products online, and even accounting. In mathematics, tables show up as matrices. Choosing one element from each row and column is a bit like Sudoku and, in math, becomes part of calculating a determinant.
Patterns on a plane lead us to the concept of tessellations, where a surface is covered with shapes that leave no gaps or overlaps. Simple tessellations use squares, equilateral triangles, or regular hexagons. Floors can even be tiled with irregular pentagons, sometimes called “houses.” Other tilings are more unusual: for example, the Penrose tiling never repeats in a regular way.
Fractals are “patterns within patterns.” Inside a large design you can find smaller versions of the same design, and inside those, even smaller ones, continuing endlessly. This idea connects to the concept of infinitely small numbers. In the real world, chemistry and physics have shown us that matter is made of tiny indivisible particles. Yet in mathematics, many models work differently. For instance, no matter how small a segment is, it can always be divided into ten parts, and those parts can be divided again.
