Unit 10 in the SMSG's secondary school mathematics series is a student text covering the following topics in Algebra I: factors and exponents, radicals, polynomial and rational expressions, truth sets of open sentences, graphs of open sentences in two variables, systems of equations and inequalities, quadratic polynomials, and functions. (DT)

This twenty-fourth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 23. For each of the chapters in Unit 23, a time allotment is suggested, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, and answers to exercises are provided. In the appendix is a…

Graphs of exotic functions which can be defined using algebraic operations are discussed. (SD)

Examples of the presentation and solution of variations on a common projectile trajectory problem are presented. (BB)

The best predictor for success in Algebra I was found to be the grade in eighth grade math. (KR)

The patterns of the coefficients in the expansion of (x + y +z)n are discussed, and a recursive property is developed as a generalization of the Pascal triangle. (MP)

An alternative development of the quadratic formula via paper squares and rectangles is presented. A physical model is constructed to demonstrate the constant term needed to complete the square. (MP)

An algebra test was constructed within a Piagetian framework. Results of a selection of the test items are given and discussed. (MP)

Difficulties encountered when drawing the graphs of linear equations are discussed. Programs are developed to overcome these and worksheets are given for further practice. (MP)

Allowing students to discover a winning strategy for this game is suggested as a way to introduce modular arithmetic. (MP)

An account of student efforts to solve the problem of finding the equations for a pair of parabolas that intersect in exactly three points is given. The deceptively difficult problem leads to the rational root theorem and eventually to computer programs for locating roots and for approximating irrational roots. (MN)

The authors analyze student work in solving linear equations, categorize and discuss typical errors, and present resulting implications on instruction. (MN)

A sequence of ellipses and a sequence of hyperbolas, both graphically approaching some parabola, are expressed algebraically and then shown to approach the parabola. (MN)

Algorithms are developed and presented for the addition and multiplication of positive rational numbers using only their repeating decimal representation. (MN)

The action in a British sporting event (bumping races) was used to motivate a simple method of computing the correlation between starting and finishing positions. The method is generalized to other situations. (SD)