The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…

A geoboard-related extremal problem dealing with both concave and convex polygons is discussed and a proof is given of the solution. (MP)

The author shows how a rapid computational "trick" can lead to an investigation of Fibonacci-type sequences. (SD)

A familiar Christmas song described as a second-year algebra problem is presented in "The Twelve Days of Christmas". Five strategies for solving inequalities are discussed in "Solving Algebraic Inequalities". (JT)

Teaching ideas are shared in three separate articles titled, "Something Different for Middle School Mathematics,""A Discovery Approach for the Y-Intercept," and "How to Get Off the Track in One Easy Lesson". (JT)

Curiosities offer an interesting alternative to traditional methods of attacking problems. An illustrative situation is given, with graphical, computer, and analytical methods used to solve the problem. (MNS)

Presents several examples of investigations which demonstrate the following: (1) algebra is connected to other mathematical topics; (2) algebra is an effective tool for representing patterns and relationships; and (3) algebra is an effective tool for analyzing patterns. (DDR)

An algebra class asked: What is the smallest positive integer that is divisible by each integer less than or equal to ten? Students discovered factorials and a solution. Verifying the solution produced a series of numbers. Successive differences between entries, triangular arrays, and successive quotients finally led to Pascal's triangle. (KM)

Some activities are provided to help students develop a conceptual understanding of perimeter, area, and volume, as well as developing skills in spatial visualization and formulating generalizations. (MNS)

Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Briefly presented are suggestions on using exercises in number patterns in second-year algebra and factoring quadratics in a 10th-grade enrichment class. (MNS)

Students use a series of isosceles right triangles constructed on a geoboard to discover patterns and form generalizations. (MP)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Presents a brief definition and examples of residue designs while sharing some of the algebraic thought that a student used to form generalizations about the patterns discovered during the investigations of residue designs. (ASK)

Presented are problem-solving experiences with area, volume, and algebraic expresssions resulting from data collection. Three worksheets are included for students in grades 7-12. (MNS)