Such problems are generally referred to as nonroutine problems. Students who are faced with nonroutine problems, and have no standard method for solving them, often simply give up, because they do not know how to get started. The ability to discover and analyze patterns becomes an important tool to help students move forward. When the students start to collect data and look for a pattern in order to solve a problem, they are often uncertain about what they are looking for. As they organize their information into charts or tables and start to analyze their data, sometimes, almost like magic, patterns begin to appear, and students can use these patterns to solve the problem.
Patterns help students develop an understanding of mathematics.
Whenever possible, students in grades 5-6 should be encouraged to use manipulatives to create, explore, discover, analyze, extend and generalize patterns as they encounter new topics throughout mathematics. By dealing with more sophisticated patterns in numerical form, they begin to lay a foundation for more abstract algebraic concepts. Looking for patterns helps students tie concepts together, gain a greater conceptual understanding of the world of mathematics, and become better problem solvers. Students in the middle grades should also continue to work with categorization and classification , particularly in the context of new mathematical topics, although much less emphasis should be given to these activities. For example, as students learn about fractions and mixed numbers, they must identify fractions as being less than one or more than one, as being in lowest terms or not.