Ensure all learners have opportunities to engage deeply in meaningful intellectual work. In "Ambitious Instruction," author Brad Cawn offers a blueprint for how to make rigor visible, accessible, and actionable in grade 6-12 classrooms. The resource guides readers toward using the twin tenets of problem-based learning and synthesis to…

Transform mathematics instruction with the comprehensive mathematical competencies (CMC) framework--a research-based model that integrates seven essential competencies: conceptual and procedural integration, problem solving, logical reasoning, communication, tool use, pattern recognition, and student engagement. Through practical classroom…

The book that inspired millions of educators to refine their approach to teaching returns for an all-new third edition. Built on a more rigorous research base and updated to emphasize student diversity, equity, and inclusion, "The New Classroom Instruction That Works" offers a streamlined focus on the 14 instructional strategies proven…

This problem deck contains over 150 problems related to the module "Using Tables to Solve Problems." The problems are presented at five levels of difficulty and contain four basic types of two-dimensional tables: (1) constant sum; (2) constant differences; (3) constant quotient or ratio; and (4) constant product. (MP)

Several examples are given of a variety of nonstandard problems, not ordinarily found in texts or courses, now accessible to students who have programmable calculators. These include: (1) finding limits; (2) evaluating infinite series; (3) calculating finite series; (4) computing variable length products; (5) solving equations; (6) searching for…

This teaching guide presents six lessons on using tables to solve problems. For each lesson, the guide gives the purpose, the rationales, materials, and detailed teaching procedures. The six lessons involve making a table, completing a table, using tables to solve problems (lessons 3 and 4), reading tables, and solving problems. Each lesson opens…

The message of this article is that there are many types of problems ordinarily requiring advanced techniques or special insight to solve which can now be done as simple programming exercises on inexpensive programmable calculators. Several examples appropriate for the secondary school curriculum are given. These are: (1) evaluating polynomials;…

Examples are given of problems which can be solved pictorially, thus aiding in the general development of geometric intuition and in developing some of the basic ideas of probability. (MP)

This pamphlet is designed to give help in developing problem solving by examples of techniques at grade levels one through six. A number of illustrations are presented of problems that are typical of the types appropriate at each grade level. For each problem, a suggestion of a solution appears with alternative methods suggested in several cases.…

Detailed is a strategy for teaching the transformation of word problems into equations, equation systems, or inequalities. Classroom experiments using the method are described and are favorable. The underlying philosophy of the method is that the transformation will be accomplished by means of comprehension at first, but in the second stage the…

Increased interest in mathematical problem solving and in the development of problem-solving ability have demanded that mathematics educators give greater attention to problem-solving instruction. A four-step model for solving problems is followed by sets of suggestions for instructional use. (MP)

The demise of mathematics of finance as a subject is discussed and a resurgence is seen as possible, but the traditional instructional presentation is seen as in need of modernization. Financial mathematics is referred to as a beautiful subject when inflation is incorporated, provided that calculators are used in computations. (Author/MP)

It has been found that students gain much greater insight into routine calculations with business formulas when such work is viewed in the light of graphing concepts. Ten problems are presented that illustrate how three specific objectives in a unit on graphing in a business mathematics course have been met. (MP)

These materials were developed in response to the Utah State Board of Education's new high school graduation requirements, particularly as they relate to the identification, teaching, and assessment of certain basic functional competencies. The document has been compiled as a guide and aid to mathematics teachers. Thirty competencies have been…

The Weight Problem of Bachet de Meziriac is described, which looks for four integral weights to measure every amount between one and forty kilograms. Discussed are generalizations of the problem and analogous problems, solutions of particular cases, and a solution of the general problem. (MP)