Understanding Patterns In Mathematics
In mathematics, patterns are arrangements of objects, numbers, shapes, or symbols that follow a specific rule or structure. For example:
A repeating pattern alternates shapes to create a predictable sequence.
Recognizing and working with patterns is a foundational skill for understanding mathematics. Patterns help students see relationships, identify predictable sequences, and understand how numbers and operations connect. Whether a students is copying a pattern, describing it, or using it to solve a problem, they are engaging in important problem-solving processes that develop logical thinking.
Patterns are deeply woven into all areas of math. Early on, they help students develop essential skills like counting, ordering, and sequencing. For example, recognizing patterns in skip counting (e.g., 2, 4, 6, 8) helps build number sense and lays the groundwork for understanding multiplication. Patterns are also a key part of prenumber concepts, as students learn to classify, compare, and sort objects by attributes—skills that form the foundation for recognizing and creating patterns.
As students progress, patterns become key to developing strategies for basic facts, such as doubles (e.g., 5 + 5 = 10) or adding ten (e.g., 8 + 10 = 18). Understanding repeated groupings (like tens and hundreds) helps students grasp place value and the foundation of our base ten number system. Later, patterns play a significant role in algebraic thinking, where students identify relationships, explore sequences, and solve for unknowns.
How Are Patterns Organized?
Patterns can be organized in various ways to highlight repetition or growth. In elementary grades, students often encounter repeating patterns, such as ABAB or ABCABC, where elements alternate in a predictable way.
The part of the pattern that repeats is called the pattern unit. For example, in the above ABAB pattern, the pattern unit is one red square and one blue square.
Students may also work with growing patterns, where each step adds more, such as increasing by one (1, 2, 3, 4) or doubling the previous value (1, 2, 4, 8). These patterns are essential for developing number sense, as they highlight relationships between numbers and help students recognize structures they’ll encounter in multiplication, place value, and algebra. For example:
A growing pattern increases incrementally, introducing the idea of numerical relationships.
Patterns, whether repeating or growing, are built on predictable rules. Understanding these rules and identifying the pattern unit are essential steps for students as they work with increasingly complex mathematical ideas.
Teaching Strategies For Patterns
Helping Students Explore Patterns
Teaching patterns involves more than simply identifying what comes next. Helping students explore patterns should involve a wide range of experiences that allow them to see patterns in different contexts and forms.
Copying a pattern is often the first step in recognizing structure and repetition. This can include recreating designs with pattern blocks, modeling figures on a geoboard, or mimicking rhythmic sequences like stomps and claps. Patterns also exist in movement, such as dance steps, and in language, where repeating phrases, rhyme schemes, or rhythms in poetry and text provide rich opportunities for exploration. Patterns in counting, like skip counting or counting backward, can also be incorporated to strengthen numerical understanding.
Building on these experiences, students can practice finding the next part of a pattern or extending it to see how it continues. For example, a growing pattern like 1, 2, 3, 4,__ encourages them to predict the next number, while a repeating pattern like ABAB challenges them to think about repetition and consistency. As students become more comfortable with these ideas, they can create their own patterns. Encouraging students to explain the rule behind their pattern helps deepen their understanding and strengthens problem-solving skills.
