Playing Your Cards Right: Integers for Algebra

The number and algebra strand of the "Australian Curriculum: Mathematics" (2015) advocates for holding together the study of number and algebra across years K-8--a position that mathematics educators have endorsed in many countries. This recommendation along with the report "Shape of the Australian Curriculum: Mathematics" (2009), which states that during years 7-10 students' understandings of mathematics, "include(s) a greater focus on the development of more abstract ideas," led the authors to ask the following questions about their instruction for year 7 students on integers (ACMNA, 280): (1) What models do we commonly use with students to teach them about integers and integer addition?; (2) Do these models support students for success in algebra?; and (3) How can instruction about integers and integer operations help students prepare for more abstract understandings of integers that are useful for algebra? The key issue in extending from addition with whole numbers (the positive integers) to addition with integers, generally, is the establishment of negative integers. This article outlines a card game that helps teachers develop a more abstract model for integers and integer addition with students in a fun and engaging context.