Relationships and Patterns

Relationships and patterns are significant in the teaching and learning of mathematics.  Students start to identify, recognize, and make sense of relationships at an early age in their education.  According to the Annenberg Learner, a website devoted to teaching and learning, "The youngest children begin simply by counting. They count by 1s, then by 2s, 5s, and 10s. These patterns give students a natural strategy to understand addition and multiplication. When considering a number pattern such as 2, 4, 6..., a young student will ask 'By what number can I count (add) to get to the next number in the pattern and the next and the next?'

As the student gets older, her knowledge of patterns advances from sums to products. When asked for the 50th number in the pattern, he or she will know to multiply 2 times 50.

High school students can start to understand functions, such as f(x) = 2x + 2, where x is the numerical sequence 0, 1, 2, 3,?. They begin with simple in-out machines and gradually adapt their understanding to the abstractions of algebra".