SSDS Boston 8th Grade Algebra Web Site

E Block Algebra

Calculator

The calculator we will use in class is a TI-84+ (click here to go to the TI-84+ web site).

There is an on-line booklet called "Calculator Notes" that you can get at the Calculator Notes and Programs web site. This 60-page booklet explains how to use the calculator to do many things we do in class. The booklet was designed for the "Discovering Algebra" book used in one of our other classes, but you may still find it useful.

You will need Adobe Acrobat Reader to read it. You can get that for free (legally!) at the Adobe Acrobat web site.

Units of Study

Here is a summary of the topics we will study during this term.

Problem of the Week (POTWe)

Students solve a variety of puzzles and problems. Student must write about each problem: restate the problem, choose and describe a strategy, describe the solution to the problem and justify it. The main goal is for students to learn how to write about mathematical problems. Problems of the week will be graded based on

Understanding the problem

Describing a method for solution

Finding a correct answer

Submitting a write-up that is neat, legible and easy to follow.

Find out more, including how POTWe's are graded, by viewing the materials handed out in class in PDF or Microsoft Word format.

Geometer's Sketchpad (GSP)

Self-paced study using Geometer's Sketchpad Software. Students complete weekly assignments. Assignments consist of guided investigations that require the use of GSP software on a home computer or computers in school. There are four units: Points Lines and Angles, Triangles, Quadrilaterals, and Symmetry.

Assessment is based on

Completing all assignments

Giving thoughtful, correct responses to questions in the worksheets

Occasional quizzes (one or more per unit)

Prerequisites

There are several topics presented in the beginning of the textbook we use that were taught in seventh grade. Students are responsible for reviewing the topics in chapters one to three of the textbook before the beginning of the class. The class will begin with a brief review (perhaps a few days) of the main topics of these chapters followed by a test on them.

Students are responsible for the following topics:

	Chapter 1: A Preview of Algebra: This provides a general review of basic topics such as expressing numbers (approximating, rounding) and the place value system, working with variables, expressions, equations and inequalities, graphing, matrices, word problems and probabilities. Section 1.3 on order of operations is particularly important and should be reviewed carefully.
	Chapter 2: The Rules of Algebra: This chapter focuses on the basics of simplifying expressions, solving equations and on the formal properties (or rules) that we use when simplify and solve. You need to know the names of the properties, what they mean, and how to use them to simplify and solve.
	Chapter 3: Signed Numbers: Main topics of this chapter include use of number lines, number sets (natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers), working with signed (positive and negative) numbers, and special relationships (reciprocal, opposite), and matrix operations. Also included are a few new properties (most notably the Closure Property).

Chapter 4: Working with equations

Solve equations with variables on both sides. Solve matrix equations using matrix multiplication. Solve equations involving squares and absolute value. Describe solutions to equations as solution sets. Use the Pythagorean Theorem. Collect, graph and interpret data. Progress will be assessed with a test at the end of the chapter.

Chapter 5: Working with inequalities

Solve inequalities using properties of inequality, boundary and distance methods. Use inequalities to classify angles and solve geometric problems. Solve compound inequalities. Use properties of order and inequality. Progress will be assessed with a test at the end of the chapter.

Chapter 6: Graphing

This unit connects three ways of modeling real-world situations: graphs, tables and equations. We study several different forms of linear equations (point-slope, intercept, general linear), and we learn how to graph non-linear equations (quadratics and absolute value). Graphing calculators are used to support learning. Progress will be assessed with a test at the end of the chapter.

Chapter 7: Formulas and Functions

We review how to apply familiar geometric formulas, and are introduced to the quadratic formula and its use. Students learn what functions and relations are, and are introduced to function notation, f(x). Progress will be assessed with a test at the end of the chapter.

Chapter 8: Systems of Equations

Students learn how to find solutions to systems of equations and inequalities using three methods: multiplication/addition, substitution, and graphing. Techniques are applied to real-world problems. If time permits, students will be introduced to matrix methods (row reduction, Cramer's rule) for solving systems of linear equations. Progress will be assessed with a test at the end of the chapter.

Chapter 9: Exponents and Radicals

In this unit, students learn how to simplify and solve algebraic expressions and equations that use exponents and radicals. We review scientific notation, and learn key properties of exponents. Study of radicals includes rationalizing and interpreting expressions with fractional exponents. Progress will be assessed with a test at the end of the chapter.

Chapter 10: Polynomials

Students learn what polynomials are, and how to add and multiply them. They learn how to recognize perfect square trinomials and the difference of squares patterns, how to multiply and simplify expressions using these patterns. Finally, they apply the quadratic formula to a wide variety of problems and will learn how to prove the quadratic formula. Progress will be assessed with a test at the end of the chapter.

Chapter 11: Quadratics

This is a formal study of quadratic equations and parabolas. Students review the basics of graphing parabolas. They learn how to rewrite a general quadratic in vertex form. They apply knowledge of factoring, the quadratic formula and vertex form to problems of projectile motion. Progress will be assessed with a test at the end of the chapter.

Chapter 12: Proportion and Rational Equations

This unit begins with a review of ratio and proportions. Students then solve more sophisticated algebraic problems using proportions. They solve a variety of problems including simplifying complex rational expressions, and solve problems involving rates, and direct and inverse variation. Progress will be assessed with a test at the end of the chapter.

Extension Units

One or both of these extension units will be included, time permitting.

Extension Unit: Exponential Growth and Decay

A one-week unit focusing on exponential growth and decay. We solve problems involving compound interest, depreciation, and population growth. This unit is not assessed.

Extension Unit: Probability

A one-week unit focusing on the basic concepts of discrete probability. We learn how to determine number of combinations and permutations, probability of random events and conditional probability. The final problem involves computing the probabilities associated with medical tests for a fictitious disease.

This web site was developed by and is maintained by Mr. Srebnick for use in the 8th grade math program at the Solomon Schechter Day School of Greater Boston.