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yeongil

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I said this in the "Should calculus be taught in high school?" thread:

I mentioned in mathwonk's "Teaching Calculus Today in College" thread about some of the incredible errors that my precalculus students make, and these errors were in algebra. (I'm wondering if it's because our high school math books these days are so packed with material that in the teachers' attempts to cover as much as possible students aren't getting enough practice in many concepts.)

I've mentioned before that I'm a HS teacher (math and music) in a Catholic all-girls school in the US. This school year I taught Honors Algebra 1 and Honors Precalculus. Next year I'm dropping most of the music and will be essentially teaching Math full time, so I've been given 2 sections of Algebra 2, which I've not taught before. Here is the list of chapters and sections in our book, and as you can see, it's very long:

Chap. 1: Equations and Inequalities

1.1 Apply Properties of Real Numbers

1.2 Evaluate and Simplify Algebraic Expressions

1.3 Solve Linear Equations

1.4 Rewrite Formulas and Equations

1.5 Use Problem Solving Strategies and Models

1.6 Solve Linear Inequalities

1.7 Solve Absolute Value Equations and Inequalities

Chap. 2: Linear Equations and Functions

2.1 Represent Relations and Functions

2.2 Find Slope and Rate of Change

2.3 Graph Equations of Lines

2.4 Write Equations of Lines

2.5 Model Direct Variation

2.6 Draw Scatter Plots and Best-Fitting Lines

2.7 Use Absolute Value Functions and Transformations

2.8 Graph Linear Inequalities in Two Variables

Chap. 3: Linear Systems and Matrices

3.1 Solve Linear Systems by Graphing

3.2 Solve Linear Systems Algebraically

3.3 Graph Systems of Linear Inequalities

3.4 Solve Systems of Linear Equations in Three Variables

3.5 Perform Basic Matrix Operations

3.6 Multiply Matrices

3.7 Evaluate Determinants and Apply Cramer's Rule

3.8 Use Inverse Matrices to Solve Linear Systems

Chap. 4: Quadratic Functions and Factoring

4.1 Graph Quadratic Functions in Standard Form

4.2 Graph Quadratic Functions in Vertex or Intercept Form

4.3 Solve x2 + bx + c = 0 by Factoring

4.4 Solve ax2 + bx + c = 0 by Factoring

4.5 Solve Quadratic Equations by Finding Square Roots

4.6 Perform Operations with Complex Numbers

4.7 Complete the Square

4.8 Use the Quadratic Formula and the Discriminant

4.9 Graph and Solve Quadratic Inequalities

4.10 Write Quadratic Functions and Models

Chap. 5: Polynomials and Polynomial Functions

5.1 Use Properties of Exponents

5.2 Evaluate and Graph Polynomial Functions

5.3 Add, Subtract, and Multiply Polynomials

5.4 Factor and Solve Polynomial Equations

5.5 Apply the Remainder and Factor Theorems

5.6 Find Rational Zeros

5.7 Apply the Fundamental Theorem of Algebra

5.8 Analyze Graphs of Polynomial Functions

5.9 Write Polynomial Functions and Models

Chap. 6: Rational Exponents and Radical Functions

6.1 Evaluate nth Roots and Use Rational Exponents

6.2 Apply Properties of Rational Exponents

6.3 Perform Function Operations and Composition

6.4 Use Inverse Functions

6.5 Graph Square Root and Cube Root Functions

6.6 Solve Radical Equations

Chap. 7: Exponential and Logarithmic Functions

7.1 Graph Exponential Growth Functions

7.2 Graph Exponential Decay Functions

7.3 Use Functions Involving e

7.4 Evaluate Logarithms and Graph Logarithmic Functions

7.5 Apply Properties of Logarithms

7.6 Solve Exponential and Logarithmic Equations

7.7 Write and Apply Exponential and Power Functions

Chap. 8: Rational Functions

8.1 Model Inverse and Joint Variation

8.2 Graph Simple Rational Functions

8.3 Graph General Rational Functions

8.4 Multiply and Divide Rational Expressions

8.5 Add and Subtract Rational Expressions

8.6 Solve Rational Equations

Chap. 9: Quadratic Relations and Conic Sections

9.1 Apply the Distance and Midpoint Formulas

9.2 Graph and Write Equations of Parabolas

9.3 Graph and Write Equations of Circles

9.4 Graph and Write Equations of Ellipses

9.5 Graph and Write Equations of Hyperbolas

9.6 Translate and Classify Conic Sections

9.7 Solve Quadratic Systems

Chap. 10: Counting Methods and Probability

10.1 Apply the Counting Principle and Permutations

10.2 Use Combinations and the Binomial Theorem

10.3 Define and Use Probability

10.4 Find Probabilities of Disjoint and Overlapping Events

10.5 Find Probabilities of Independent and Dependent Events

10.6 Construct and Interpret Binomial Distributions

Chap. 11: Data Analysis and Statistics

11.1 Find Measures of Central Tendency and Dispersion

11.2 Apply Transformations to Data

11.3 Use Normal Distributions

11.4 Select and Draw Conclusions from Samples

11.5 Choose the Best Model for Two-Variable Data

Chap. 12: Sequences and Series

12.1 Define and Use Sequences and Series

12.2 Analyze Arithmetic Sequences and Series

12.3 Analyze Geometic Sequences and Series

12.4 Find Sums of Infinite Geometric Series

12.5 Use Recursive Rules with Sequences and Functions

Chap. 13: Trigonometric Ratios and Functions

Chap. 14: Trigonometric Graphs, Identities, and Equations

(I know that I'm not going to cover Chapters 13-14, so I didn't list the sections.)

Unfortunately, our school does not attract the strongest math students. In past years our students only got through the first six (!) chapters. I'm determined to cover more, maybe the first eight chapters. But in case I'm pressed for time, are there sections within the first eight chapters that could be skipped? Assume that the students who are interested in majoring in math/science in college would be taking the Honors Algebra 2 course, which covers chapters 1-9 and bits of chapters 10 & 12. Note also that our students use their graphing calculators a lot (too much, in my opinion). At the moment, the math sequence is Algebra 1-Algebra 2-Geometry, though I've submitted a proposal to change it to Algebra 1-Geometry-Algebra 2, though, if approved, this won't take affect until the following school year. TIA.01