A renewed emphasis was placed on ratio and proportional reasoning in the middle grades in the Common Core State Standards for Mathematics (CCSSM). The expectation for students includes the ability to not only compute and then compare and interpret the results of computations in context but also interpret ratios and proportions as they are…

No person, place, or thing can capture the attention of a class of sixth graders like "man's best friend." To prompt students' interest in a series of lessons on proportional relationships, the authors brought in a unique teaching aid--a dog. A family dog was used to supply the measurements for scatter plots and variables so that students could…

An nth-term problem involves a sequence. Students must determine which expression will allow them to calculate the nth position of the sequence. To solve such problems, students are to find "a rule that determines the number of elements in a step from the step number." These types of problems help students develop concepts of functions, variables,…

Evolving technology has played an important part in a common quadratic-function lesson. Having been mentioned repeatedly in numerous reform documents, a recurring lesson has involved changing the parameters in f(x) = ax[superscript 2] + bx + c and studying the effects on the graph. In both NCTM Yearbooks and NCTM Standards documents, technology is…

Mathematics teachers can tap into students' curiosity about hurricanes to develop their understanding of mathematical ideas within a real-life context. This article discusses hurricane-based mathematics tasks involving cooperative learning that were found to help students enhance their understanding of patterns, graphs, and rates of change. For…

Sorting networks, used in graph theory, have instructional value as a skill- building tool as well as an interesting exploration in discrete mathematics. Students can practice mathematics facts and develop reasoning and logic skills with this topic. (Contains 4 figures.)

This article describes an activity in which students plot collections of ordered pairs according to prescribed set conditions. The coordinate plane sets can have rich variety, and their construction fosters critical thinking, attention to detail, and algebraic reasoning. (Contains 3 figures.)

Discusses mathematical thinking and problems posed by seventh- grade students as part of a unit on the study of algebraic ideas. The unit involves showing how variables cause changes and also incorporates the solving of systems of equations by constructing line-graph drawings and combination charts. (AIM)