Patterns appear everywhere in your daily life. In mathematics, a pattern refers to distinct similarities between numbers. You begin to learn number patterns in kindergarten through counting. At first, you learn how to count by ones, but as you grow older you will identify more patterns by counting by twos or threes. The next step in learning about number patterns is through addition and then multiplication. Once you reach high school, you use your knowledge of number patterns to help you solve complex functions in calculus.
Patterns are an important area of mathematics because they help us recognize similarities and make number predictions. For example, when learning multiples of 10, students often see a pattern in that all multiples of 10 end in zero. Learning basic number patterns helps a student learn about functions, because functions describe relationships between different quantities. Learning about patterns is also important in problem-solving. Students who are able to look for and identify number patterns are more likely to use the pattern to generalize and solve the problem at hand.
In mathematics, a sequence refers to the order of a specific number. You first learn sequencing when you start learning how to count by ones. For example, you learn that one comes before the number two, but after the number three. Once students have learned to count, they will be able to predict the next number in a sequence by counting forward or backward. Sequences of numbers not only refer to counting by ones, but they are also used to depict the sequence when counting by twos, threes or more.
Sequencing is used to teach students how to identify larger numbers from lesser numbers. Once students can identify number differences, they will be able to subtract a larger number from a smaller number, or add two numbers together. Number sequences are also helpful to understanding the basics of multiplication and division. Understanding the order of numbers is essential to solving even the most complex mathematical problems.