@article {MATHEDUC.06079401, author = {Yun, Jeong Oak and Flores, Alfinio}, title = {Algebra from chips and chopsticks.}, year = {2012}, journal = {Mathematics Teaching in the Middle School}, volume = {17}, number = {6}, issn = {1072-0839}, pages = {324-331}, publisher = {National Council of Teachers of Mathematics (NCTM), Reston, VA}, doi = {10.5951/mathteacmiddscho.17.6.0324}, abstract = {Summary: Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving a problem and appreciate the joy of finding various solutions. The activities also allow students to think about how to find patterns, express the patterns in numerical forms, and generalize the patterns into algebraic forms. Students work with chips to represent triangular, square, pentagonal, and hexagonal numbers; use chopsticks to break polygonal numbers into components; and represent each part and the total with an algebraic expression. In so doing, they are establishing relations between different algebraic expressions. This article focuses on the approaches that students used to break pentagonal and hexagonal numbers into lower polygonal numbers. (ERIC)}, msc2010 = {H23xx (D43xx U63xx)}, identifier = {2012e.00644}, }