Algebra I Pre-AP; Laying the Foundation for Calculus AP.
This is a very rigorous, fast-paced, complete High School Algebra I course that provides in-depth coverage of all of the traditional Algebra I topics using functions, and solving of complex traditional and non-traditional real-world problems as the common threads. This class studies topics at the highest level of rigor, at a faster pace, and in more depth than "regular" algebra courses. The curriculum is designed to challenge the most talented math students. In addition to traditional Algebra I topics students in Algebra I Pre-AP will be exposed to topics that are not formally studied until later in the math sequence. Both linear and non-linear functions will be studied in depth in all of their forms, as will their applications. The types of functions we will investigate include linear, quadratic, variation, power, radical, rational, absolute value, exponential growth and decay, and trigonometric functions. Technology is used throughout the course to enhance learning, to help understand concepts, and as tools to help solve real-world problems. This includes use of the SmartBoard, and TI-84+ Graphing Calculators. The ChromeBook computers the boys have are used when Blended Learning is employeed as a teaching/learning technique. Students access specific websites that offer video presentations of pre-selected topics. This may be assigned as homework, or as directed class work. This is the "Flipped Classroom" method of providing students with a wider range of learning procedures that allow them to self-teach certain skills. It is also available as a source for remediation. Because of the nature of this course students are required to maintain an average of at least 85% to preserve eligibility to remain in the course. Any student who is unable to meet this requirement will be placed in a math course that is more appropriate for him. |
The 8th grade Pre-AP
Algebra course at the Academy ends the first semester grading period on
the date of the final class before the holiday break in December.
Students in this class will take their semester exam in December.
Because of the unique characteristics of this course, and because of the unique situations that traditionally arise that challenge the 8th grade for class time in the second semester, 8th Algebra Pre-AP will end its first semester on the final class day in December. The curriculum has been planned so that grading for the first semester can close in December without any negative impact on student report card grades. This procedure ensures sufficient time to complete the Pre-AP Algebra course while accommodating the class time interruptions inherent in the 2nd semester of 8th grade. |
ALGEBRA I Pre-AP CURRICULUM
Textbook: Algebra I; Addison-Wesley/Prentice Hall Publishing,
This class
will be taught using techniques that are being called, "Blended Learning".
This means that some homework requires
students to watch a video that is the lesson for the latest topic.
They are expected to learn the material
in the videos in the same way that they are expected to learn a lesson
when it is given live, in class.
Blended Learning techniques have been shown to be at least as effective
as in-person
lesson presentations and have been
incorporated in this class the past 2 years with great results.
The first semester includes lots of lessons on the Graphing Calculator.
It will also
include lots of supplementary material about functions.
There will be topics introduced throughout the year that do not appear
in the textbook.
They will be
covered at the appropriate times that they naturally fit.
Check the 100
Algebra Topics on this website to see what most of the topics are.
Chapter 1: Expressions and Equations; this is a review of 7th Grade Algebra.
1-1, Operations With Numbers---------------
1-2, Variables
1-3, Powers and Exponents
1-4, Order of Operations
These sections will be treated as a
1-5, Expressions From word Statements review.
They will be completed in
1-6, Introduction to Equations
2, or 3 days.
1-7, Solving Equations
1-8, Problems That Lead to equations----
1-9, Problems That Lead to Expressions and Equations (will be taught
using function language and will be completed in 2, or 3 days.)
Introduce the TI-84+ Graphing Calculator. 1 week.
Chapter 2: Operations With Negative Numbers; this is a review of pre-algebra.
2-1, Intro. to Negative Numbers-----------------
2-2, Adding Integers
2-3, Subtracting Integers
The first 7 sections will be
2-4, Multiplying Integers
completed in 3, or 4 days.
2-5, Dividing Integers
2-6, Commuting and Adding
2-7, Equations That Need Two Transformations-
2-8, Problems That Lead to Two Transformations
Chapter 3: Distributing Axioms and Other Properties; this is a pre-algebra review.
3-1, Distributing--------------------------------------------------
3-2, Distributing Multiplication Over Subtraction
Chapter 3 will be
3-3, More Distributive Properties
completed in 2, or 3 days.
3-4, Like Terms and common Factors
3-5, Field Axioms
3-6, Properties of Equality
Chapter 4: Harder Equations; this is a pre-algebra review.
4-1, Equations With Like Terms-----------------------------
4-2, Equations With Like Terms and Distributing
4-3, Equations With Variables in Both Members
4, or 5 days
4-4, Equations That Involve Decimals
4-5, Literal Equations and Formulas----------------------
4-6, Problems That Involve More Than One Expression.
Chapter 5: Some Operations With Polynomials and Radicals.
5-1, Introduction to Polynomials------------------------
5-2, Names of Polynomials
5-3, Products of Two Binomials
5-4, Factoring Quadratic Trinomials, a = 1
5-5, Factoring Quadratic Trinomials - 3rd Term Neg. Approx.
1 week.
5-6, Factoring Quadratic Trinomials, a > 1
5-7, Factoring the Difference of Two Squares
5-8, Squaring a Binomial
5-9, Factoring Trinomial Squares
5-10, Radicals, Irrationals, and Closure--------------
Chapter 6: Quadratic Equations.
6-1, Introduce Quadratic Formula-------------
6-2, Evaluating Radical Expressions
6-3, Equations Containing Absolute Value
6-4, Equations With Squares
6-5, Equations With Trinomial Squares
1 week
6-6, Completing the square
6-8, The Quadratic Formula
6-9, Vertical Motion Problems
6-10, The Discriminant----------------------------
------------------------------ Chapter 7 begins all new material -----------------------------
Chapter 7: Expressions and Equations Containing Two Variables.
7-1, Evaluate Expressions With 2 Variables
7-2, Cartesian Coordinate System
7-3, Graphs of Equations With 2 Variables
7-4, Intercepts and Rapid Graphing
7-5, Slope and Rapid Graphing
Approximately 4 weeksschool, beginning the 1st week of .
7-6, Finding an Equation From Graph
Done simultaneously with the reviews indicated, above.
7-7, Find Intersection of 2 Graphs
7-8, Solve Systems By Substitution
7-9, Solve Systems By Linear combination
7-8b, Solve Systems By Using Matrices
7-10, Problems Involving 2 Variables
Chapter 8: Linear Functions and Scattered Data.
8-1, Linear Functions ----------------------------------
8-2, Scattered Data and Linear Regression
Approximately 1 week.
8-3, Probability
8-4, Experimental Probability ----------------------
Chapter 9: Properties of Exponents
9-1, Prime Numbers and Prime Factors--------
9-2, Exponentiation
9-3, Exponents, Products and Powers
9-4, exponents and Quotients
2 Weeks
9-5, Negative and Zero exponents
9-6, Powers of 10 and Scientific Notation
9-7, Problems Involving Scientific Notation
10-1, Review Multiplying and Factoring Polynomials
10-2, Greatest Common Factor
10-3, Factoring Out Common Factors
10-4, Common Binomial Factors
2 Weeks
10-5, Factoring By Grouping
10-6, Factoring Harder Quadratics
10-7, Solving Quadratic Equations By Factoring-------
Chapter 11: Rational Algebraic Equations
11-1, Rational Algebraic Expressions and Equations----------
11-2, Simplify Rational Algebraic Expressions
11-3, Multiply and Divide Rational Expressions
11-4, Least common Multiple
11-5, Add and Subtract Rational Algebraic Expressions
3 Weeks
11-6, Combined Operations and Special Cases
11-7, Long Division
11-8, Fractional Equations - Extraneous Solutions
11-9, Problems With Ratio and Proportion
11-10, Problems With Probability and Rational Equations
Chapter 12: Radical Algebraic Expressions
12-1, Radical Algebraic Expressions----------------
12-2, Sums, Differences, Products of Radicals
12-3, Quotients of Radicals
12-4, Binomials With Radicals
12-5, Square Roots of Variable Expressions
2 Weeks
12-6, Radical Equations
12-7, Pythagorean Theorem and Applications
12-8, Higher Order Radicals
12-9, Rational and Irrational Numbers---------------
Chapter 13: Inequalities
13-1, Number Line Graphs--------------------------
13-2, Solving Inequalities
13-3, Compound Inequalities
13-4, Inequalities With Absolute Value
2 Weeks
13-5, Given x, Evaluate the Expression
13-6, Linear Inequalities With 2 Variables
13-7, Systems of Equations and Inequalities
Chapter 14, Functions and Advanced Topics
14-1, Functions------------------------------
14-2, Direct and Inverse Variation
14-3, Linear Functions
2 Weeks
14-4, Trigonometric Functions
14-5, Quadratic Functions---------------
Enrichment includes more function investigations
Semester 2 includes
much more supplementary work with functions. It also includes time
for a short review and
the Algebra End
of Year Test.