代数 1: すべてを理解する! パート 1

Course Description: 
Algebra 1 introduces students to variables, algebraic expressions, equations, inequalities, functions, and all their multiple representations. In this class, students will develop the ability to explore and solve real-world application problems, demonstrate the appropriate use of graphing calculators, and communicate mathematical ideas clearly. This course lays the foundation for mathematical literacy that will help students be successful in every subsequent course in mathematics.

Prerequisite:
The student has obtained a grade of “C” or higher in Pre-Algebra or Basic Algebra.

Pre-requisites include	doing numeric computations with fractions (sum, difference,	 product, and quotient)	and converting to decimals or percents. Be able to work with	
percents and percent proportion. Be	able to	display/interpret data in graphs and tables.		
Be able to identify two-dimensional figures, find the perimeter and area of rectangles, and find	
the area and circumference of circles.

Objectives/Goals: 
By the end of this course, students will be able to… 
● Simplify or identify equivalent algebraic expressions. 
● Represent math relationships using symbolic algebra. 
● Differentiate between linear and nonlinear functions. 
● Model and describe slope as a rate of change. 
● Identify the slope from a graph, table, or equation. 
● Evaluate variable expressions and functions. 
● Identify an equation of a line from given information. 
● Recognize the general shape and properties of functions from graphs, tables, or 
   equations. 
● Interpret the role of coefficients and constants on graphs of linear or quadratic 
   functions. 
● Analyze functions by investigating domain, range, rates of change, intercepts, and 
   zeros.
● Model problems using functions and relations. 
● Create and connect representations that are tabular, graphic, numeric, and symbolic 
   from a set of data. 
● Represent quantitative relationships graphically and interpret the meaning of the graph
● Interpret and solve linear equations and inequalities. 
● Solve and interpret graphs of systems of equations and inequalities.

Semester 1: Table of Contents by Lesson
Unit 1: The Building Blocks of Algebra
Lesson 1: Rates, Patterns, and Problem Solving  
Lesson 2: Variables and Expressions  
Lesson 3: The Commutative and Associative Properties  
Lesson 4:  The Distributive Property  
Lesson 5:  Equivalent Expressions  
Lesson 6:  Seeing Structure in Expressions  
Lesson 7:  Exponents as Repeated Multiplication  
Lesson 8:  More Complex Equivalency 
Lesson 9:  More Structure Work  
Lesson 10:  Translating English to Algebra  
Lesson 11:  Algebraic Puzzles  
Unit Review

Unit 2:  Linear Expressions, Equations, and Inequalities 
Lesson 1:  Equations and Their Solutions  
Lesson 2:  Seeing Structure to Solve Equations 
Lesson 3:  A Linear Equation Solving Review  
Lesson 4:  Justifying Steps in Solving an Equation  
Lesson 5:  Linear Word Problems  
Lesson 6:  More Linear Equations and Consecutive Integer Games  
Lesson 7:  Solving Linear Equations with Unspecified Constants  
Lesson 8:  Inequalities  
Lesson 9:  Solving Linear Inequalities  
Lesson 10:  Compound Inequalities  
Lesson 11:  More Work with Compound Inequalities  
Lesson 12:  Interval Notation  
Lesson 13:  Modeling with Inequalities  
Unit Review 

Unit 3:  Functions  
Lesson 1:  Introduction to Functions  
Lesson 2:  Function Notation  
Lesson 3:  Graphs of Functions  
Lesson 4:  Graphical Features  
Lesson 5:  Exploring Functions Using the Graphing Calculator  
Lesson 6:  Average Rate of Change  
Lesson 7:  The Domain and Range of a Function  
Unit Review

Required Materials: 
● Binder 
● Pen/Pencil 
● Class notes and homework

Helpful Materials: 
● Free online calculator: ○ https://www.desmos.com/calculator 
● Algebra Resources: ○ http://mathbitsnotebook.com
● Algebra 1 textbook and Homework sets: ○ https://www.emathinstruction.com

Grading:
Assessments = 50%
Homework = 50%

Note: Homework is essential to determine if the student has understood the materials taught in class, thereby guiding the teacher’s instruction on the content understanding of the student.

Classroom expectations:
● Be on time
● Be prepared
● Work the problems 
● Ask questions, as needed
● Take notes
● Turn off/silence electronic devices
● Close all unrelated tabs and windows on your computer