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Graphing Inequalities, Connecting Meaning

tudents often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and my students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an inequality, students may lack a deep understanding of the relationship between the inequality and its graph. Hiebert and Carpenter (1992) stated that mathematics is understood “if its mental representation is part of a network of representations” and that the “degree of understanding is determined by the number and strength of the connections” (p. 67). I therefore developed an activity that allows students to explore the graphs of inequalities not presented as lines in slope-intercept form, thereby making connections between pairs of expressions, ordered pairs, and the points on a graph representing equations and inequalities.

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Students analyze items from the media to answer mathematical questions related to the article. This month's clips involve finding a mathematical error in an advertisement as well as working with ratios and proportions.

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Palette of Problems – April 2014

A monthly set of problems is aimed at a variety of ability levels.

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Lawn and Garden//Pulp Paper

Students analyze items from the media to answer mathematical questions related to the article. This month's problems involve reading slopes from graphs, finding average rates of change, and interpreting linear graphs.

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Learning Algebra from Worked Examples

Presenting examples of both correctly and incorrectly worked solutions is a practical classroom strategy that helps students counter misconceptions about algebra.

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March 2014 Calendar and Solutions

A set of problems of many types.

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Working the System

Two teachers discuss the planning and observed results of an introductory problem to help students nail a conceptual approach to solving systems of equations.

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February 2014 Calendar and Solutions

A set of problems of many types.

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Successfully Transitioning to Linear Equations

A multiphase lesson on selling T-shirts guides students from single-variable equations to linear relationships.

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Teaching Straight-Line Graphs Using Autograph

Students often have difficulty with the topic of straight-line graphs. Perhaps they cannot relate to the abstractness of the concepts involved. Perhaps the sheer number and complexity of the skills required—reading algebra, substituting values, rearranging formulas, dealing with negative numbers, understanding coordinates and fractions—magnifies any misconceptions or weaknesses that students may have in other areas of mathematics, rendering them unable to come to grips with the topic as a whole.