7th-Grade Algebra Pre-AP  Course Description

     7th Grade Pre-AP Algebra is a rigorous, fast-paced, first semester Algebra I course designed to prepare mathematically talented 7th graders for the rigors of the Algebra I Pre-AP course that they will be taking in 8th grade.  Functions and fundamentals of Pre-Algebra and Algebra 1 are the focus of this course.
     The curriculum is planned and delivered to challenge the most capable math students.  In addition to the curriculum outlined in the textbook students will be exposed to some math topics that are not traditionally studied in depth until future math and science courses.  Some time will be spent preparing for the SAT.
      Appropriate use of technology (TI-84+) graphing calculator) will be introduced during the year, but it will be limited, and concentrated in the 2nd semester.  Every effort will be made to help students master the skills that will ensure that they are prepared to make a smooth transition to the math courses with more sophisticated topics that they will encounter in the future.
     This course only is sequenced so the 1st Semester can be ended on the final school day in December.  Therefore the 2nd Semester grades begin accumulating on the 1st day back, in January.
     There are grade requirements that studens must maintain to ensure their continued enrollment in Pre-AP courses.  See the Curriculum Guide that can be found online for the specific requisites.

     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 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 since 2014 with great results.

                                       7th-Grade ALGEBRA Pre-AP CURRICULUM

     Textbook: Algebra I; Addison-Wesley Publishing,
 

     Textbook Overview:

     The first 7 chapters (the part of the book we will complete in 7th grade) consist of a tightly-sequenced series of topics leading as quickly as possible to a mathematically honest derivation of the Quadratic Formula.  This departure from the traditional sequence of topics is made possible by using a calculator to evaluate radicals.
     Chapter 5 introduces students to polynomials, including factoring.  This is done so that students have a solid grasp of how the process relates to completing the square.  One of the topics that will be presented later in the book will be introduced at end of Chapter 5.  That topic is Solving Quadratics by Factoring.
     Time will be spent developing the concept of a variable as a symbol that represents a value that really varies, rather than simply standing for an unknown constant.  To aid in this development, the book presents mathematical expressions as something to which one does two things: evaluates, when the value of the variable is known, and finds the value of the variable when the value of the expression is known.  The problem solving in this book has multiple parts in which students must write an expression representing a variable quantity, then do these two things with the expression.  This process helps students to understand that a variable can stand for a different number at different times in the same problem, depending on the situation.
     The properties of numbers are first presented as verbs.  These are the Field Axioms where students learn how to Commute, Associate, etc.  Use of the axioms will require justification in order to give students an introduction to the idea of proofs (deductive reasoning).  The concept of Closure will also be introduced in a formal way so students can begin to better understand the properties of the Real Numbers.

     The first semester includes  lessons on Pre-Algebra skills as well as SAT preparation.
     There will be some topics introduced throughout the year that do not appear in the textbook.  They will be covered at the appropriate times when they naturally fit.

Chapter 1: Expressions and Equations;

                 1-1, Operations With Numbers--------------\
                 1-2, Variables                                               \
                 1-3, Powers and Exponents                            \
                 1-4, Order of Operations                                  \    Three weeks, with SAT prep.
                 1-5, Expressions From word Statements         /
                 1-6, Introduction to Equations                        /
               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.)
                1-10, Chapter Review
 

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                                         \
                 2-4, Multiplying Integers                                          \   Two weeks, with SAT prep.
                 2-5, Dividing Integers                                               /
                 2-6, Commuting and Adding                                    /
                 2-7, Equations That Need Two Transformations-/
                 2-8, Problems That Lead to Two Transformations.
           2-9, Chapter Review

Chapter 3: Distributing Axioms and Other Properties; this is a pre-algebra review.

                 3-1, Distributing-------------------------------------------\
                 3-2, Distributing Multiplication Over Subtractio    \
                 3-3, More Distributive Properties                            \
                 3-4, Like Terms and common Factors                       \    Four weeks, with SAT prep.
                 3-5, Axioms for Adding & Multiplying                      /
                 3-6, Properties of Equality                                       /
                 3-7, Chapter Review-------------------------------------/

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   \    Four weeks, with Stanford prep.
                4-4, Equations That Involve Decimals                      /
                 4-5, Literal Equations and Formulas------------------/
                 4-6, Problems That Involve More Than One Expression.
                 4-7, Chapter Review

 ------------------------------  Chapter 5 begins polynomials -----------------------------

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                         \
                 5-5, Factoring Quadratic Trinomials - 3rd Term Neg.
                 5-6, Factoring Quadratic Trinomials, a   1                /     Five weeks, with Stanford prep.
                 5-7, Factoring the Difference of Two Squares        /
                 5-8, Squaring a Binomial                                        /
                 5-9, Factoring Trinomial Squares                         /
                 5-10, Radicals, Irrationals, and Closure            /
                 5-11, Chapter Review-------------------------------/
 

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        \
                 6-6, Completing the square                           /     Six weeks.
                 6-8, The Quadratic Formula                        /
                 6-9, Vertical Motion Problems                  /
                 6-10, The Discriminant                            /
                 6-11, Chapter Review----------------------/

Chapter 7: Linear Expressions/Equations That Contain 2 Variables

                 7-1, Evaluating Expressions With 2 Vriables--\
                 7-2, The Cartesian Coordinate System-----------\
                 7-3, Graphs of Equations With 2 Variables-------\
                 7-4, Intercepts and Rapid Graphing-----------------\
                 7-5, Slope and Rapid Graphing------------------------\
                 7-6, Finding the Equation From a Graph------------/     Six weeks.
                 7-8, Solve Linear Systems By Careful Graphing/
                 7-9, Solve Systems by Linear Combinations----/
                 7-10, Problem Solving Using Linear Systems-/
                 7-11, Chapter Review & Test-------------------/
 

                We will complete about half of Chapter 7 and return to it in 8th grade.

Semester 2 includes much more supplementary work with functions and graphing calculators.
It also includes time for a short review and the Algebra End of Year Test.