Describes how students develop proportional reasoning through problem solving. Identifies the essential components of proportional reasoning and includes recommendations for instruction. (YDS)

Presents an activity that connects area with cutting brownies which are in different shapes for different numbers, uses algebraic equations, and fixes the exact dimensions of brownies. Concludes with four different solutions from six people for the class of 16 and a trapezoidal brownie. (ASK)

Presents building-up strategies and activities for preservice teachers to help students move from using informal strategies to expressing proportional relationships in algebraic terms. (ASK)

Introduces an activity, Equation Telephone, designed to improve students' ability to interpret written information and recognize equivalent forms of an equation. Discusses the activity in detail and presents examples of student responses. (KHR)

Describes a hands-on, guided-learning activity that forges vertical connections among grade levels and relies on physical models in the investigation of algebraic concepts. This lesson helps students discover that a given value can have multiple representations. Includes a sample student activity log. (AIM)

Describes how various projects helped middle school students build mathematical conclusions through algebraic thinking as they used number patterns and verbal rules to explore the interrelationships of representations. Suggests some topics for projects. (AIM)

Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)

Presents a modified version of the Wheel of Fortune game for mathematics classrooms that engages students in solving equations by using formal and informal methods. Encourages mental computation and estimation. (ASK)

Describes a project incorporating movies, literature, games, and other resources into mathematics instruction. Focuses on cultural differences. (Contains 10 references.) (YDS)

Discusses the importance of toys in improving students' motivation and understanding of scale, proportions, and ratios by connecting toys with their real-life counterparts. Presents a unit that includes measurement activities in order to teach these topics by comparing toys and actual measurements for known and unknown scale toys. (ASK)

Uses SimCalc MathWorlds, which is downloaded from the World Wide Web, to engage students in algebraic problem-solving activities. Uses software to animate characters by creating graphs of position and velocity. (YDS)

Middle-school students were asked to determine the dimensions of a hotel atrium so that guests could enjoy the maximum area of scenic view, given that 650 feet of brass railing could be used around each floor. Several solution approaches are described. (MKR)

Presents an alternative method to teaching percent problems which uses a 10x10 grid to help students visualize percents. Offers a means of representing information and suggests different approaches for finding solutions. Includes reproducible student worksheet. (MKR)

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…

Describes how graphing calculators can be used to explore different functions, from linear to higher degree polynomials. "Globs" (circles) are drawn around randomly plotted points on the screen, and students devise functions that pass through as many of these globs as possible. Variations on the game are also mentioned. (DPM)