In solving generalization problems that involve figures and diagrams, I have always found working with the figures—constructing and deconstructing them—to generate the formula more interesting than working with the sequence of numbers directly that is, making a table of values and apply some technique to find the formula. Here’s a sample problem involving counting hexagons.
Problem: When making a cable for a suspension bridge, many strands are assembled into a hexagonal formation and then compacted together. The diagram below illustrates a ‘size 4’ cable made up of 37 strands. Continue reading “Generating Algebraic Expressions: Counting Hexagons”