Curriculum Units – Level 5

This unit on algebra is devoted to the study of change, one of the overriding principles of mathematics. Chapter 1 focuses on analyzing change in situations from a qualitative perspective, giving students the opportunity of looking more globally at what is happening throughout the entire situation. To accomplish this, the x- and y-axes are not labeled with numbers; rather, students make sense of the situation by investigating the relationships between variables. In Chapter 2, students actually use quantitative data to create graphs and analyze the rate of change in more depth including examining slope, the y-intercept and points of intersection. In the lessons in Chapter 2, both the x- and y-axes are labeled with numbers.

In this unit, students learn about algebra as a set of concepts tied to the representation of relationships either by words, tables or graphs. They also learn about algebra as a style of mathematical thinking for formalizing patterns of change. They extend their notion of variable from a letter in an equation that represents a number to a more broad definition, that of a quantity that varies or changes. They will learn how to identify these quantities as variables, or things that vary, in different situations. They will use these variables to represent situations graphically and in tables. They will also analyze changes in the situations including the rate of change by looking at the relationships between the variables throughout the given situation. They will comprehend how to interpret the y-intercept in the context of a given situation and discuss how the steepness of the line or slope describes the rate of change. These experiences, discussions and written reflections provide opportunities for advancing mathematical understanding and are an important prelude to the more formal study of algebra students will encounter in middle school.