Using a 5x5 geoboard or dot paper, students create various sized parallelograms. The students look for a relationship among the numbers in the three columns of their table, express this relationship as a verbal rule, and then write the rule in symbolic form. Students investigate how many stools with three legs and how many chairs with four legs can be made using 48 legs. They may use objects or draw pictures to make models of the solutions. They describe the pattern and how they found it in writing.
Students create their own designs using iteration.
They may use patterns such as spirolaterals or write a program in Logo on the computer. They use simple equations to iterate patterns. The resulting y value is 1. Using this as the new x value yields a 2 for y. Using this as the next x gives a 3, and so on.