初等代数学を楽しく学ぶ

This course will cover 13 units / topics in Pre-Algebra Grades (6 - 8)
1) Factors & Multiples: Weeks 1 - 3
2) Patterns: Weeks 4 - 6
3) Ratios & Rates: Weeks 7 - 9
4) Percentages: Weeks 10 - 12
5) Exponents and Order of Operations: Weeks 13 - 15
6) Variables & Expressions: Weeks 16 - 18
7) Equations & Inequalities: Weeks 19 - 21
8) Percent & Rational Number Word Problems: Weeks 22 - 24
9) Proportional Relationships: Weeks 25 - 27
10) One-step & Two-step Equations and Inequalities: Weeks 28 - 30
11) Roots, Exponents & Scientific Notation: Weeks 31 - 33
12) Multi-step Equations: Weeks 34 - 36
13) Two-variable Equations: Weeks 37 - 39
Final Exam: Week 40

This Pre-algebra course is designed to prepare students for a standard high school algebra course. Learners are introduced to integers, fractions, square roots, step equations, linear equations, and decimals. They will also learn how to solve basic equations using variables.

 This Pre-Algebra course serves as a bridge between elementary mathematics and Algebra.  This course will build a foundation of algebraic concepts through the use of technology, manipulatives, problem-solving, and cooperative learning.  Students will learn to utilize the graphing calculator in appropriate situations.  Concepts include algebraic expressions, linear equations, polynomials, factoring, inequalities, geometry, statistics, and graphing. Students will learn to utilize the graphing calculator in appropriate situations.  Problem-solving, reasoning, estimation, and connections between math and everyday applications will be emphasized throughout Pre-Algebra.  This course is designed to prepare students for Algebra I.

The competencies that will be covered in this course combine the content strands: 
* patterns/algebraic thinking
*  data analysis/prediction
* measurement
* geometric concepts
* number sense

This course will cover the process strands as well:
* problem solving/reasoning
* estimating
* incorporating technology
* communicating
* making connections/applications. 

The competencies may relate to one, many, or all of the mathematics curriculum strands and may be combined and taught with other competencies throughout the course.  Competencies are not listed in order of importance; rather the sequence of competencies relates to the broader K-12 framework.  Competencies provide a general guideline of on-going instruction, not isolated units, activities, or skills.

 COMPETENCIES and Suggested Teaching Objectives:

UNITS 1-2
1. Explain, classify, and perform basic operations on the set of real numbers. 
    a. Classify numbers as natural, whole, integer, rational, irrational, and real.
    b. Identify and apply the properties of real numbers (include the use of mental            
         mathematics and estimation methods).
    c. Model absolute value of real numbers as a measure of distance.
    d. Compare and order the real numbers and perform operations with rational   
         numbers. 
    e. Evaluate numerical and algebraic expressions using order of operations.
    f. Convert between repeating decimals and fractions.
    g. Recognize and evaluate perfect squares and approximate square roots.

UNITS 3-4
2. Solve, check, and graph linear equations and inequalities in one variable. 
    a. Relate the language of mathematics to indicate mathematical operations.
    b. Translate between verbal expressions and algebraic expressions.
    c. Given an algebraic expression, write a corresponding real-life situation.
    d. Simplify algebraic expressions by combining like terms and using the distributive 
       property.
     e. Solve, check, and graph one-step and two-step linear equations and inequalities.
     f. Solve and check multi-step linear equations and inequalities with variables on 
        both sides involving the distributive property.

UNITS 5-6
3. Recognize and perform basic operations on polynomials.  
    a. Classify types of polynomials.
    b. Determine the degree of polynomials.
    c. Simplify polynomials by combining like terms.
    d. Arrange polynomials in ascending or descending order of a variable.
    e. Use the rules of exponents to multiply and divide monomials.
    f. Use the rules of exponents to multiply monomials by polynomials.
    g. Model and use the distributive property and rules of exponents to multiply      
        binomials by binomials.
    h. Multiply and divide numbers involving scientific notation.
    i. Use manipulative models to demonstrate operations of monomials and polynomials.

UNITS 7-8
4. Use ratios, proportions, and percents to solve problems. 
    a. Represent, convert, and explain relationships among fractions, ratios, decimals,    
       and percents in problem solving.
    b. Use proportions and equations to find part, rate, or base in real-world situations.
    c.  Explain solutions and processes orally and in writing.

UNITS 9-10
5. Use concepts of probability and statistics to interpret information. 
    a. Model the Fundamental Counting Principle to determine possible outcomes of an 
        event.
    b. Use combinations and permutations in application problems.
    c. Calculate and apply basic probability.
    d. Collect, display, analyze, and draw appropriate conclusions from data.
    e. Interpret and construct stem-and-leaf, box-and-whisker, and scatter plots from 
        data.

UNITS 11-12
6. Solve, check, and graph solutions of equations and inequalities in two variables using the coordinate system.
    a. Given a set of ordered pairs, draw a coordinate system using an appropriate scale.
    b. Create a table to graph equations and inequalities that are presented in 
         slope intercept form.
    c. Use calculators/computers to check accuracy of tables and graphs as needed.
    d.  Identify slope as positive, negative, zero, or undefined from a graph.
    e. Calculate slope from two points graphically and algebraically.
    f. Identify x- and y- intercepts from a graph.
    g. Identify the solution of a system of equations from a graph.

UNIT 13
7. Use and apply properties and formulas to solve geometric problems. 
    a. Calculate perimeter, area, circumference, and volume using appropriate  formulas.
    b. Recognize the irrational number pi (?) as the ratio of circumference to diameter of 
        any given circle.
    c. Solve problems involving the use of the Pythagorean Theorem.
    d. Classify triangles by sides and angles.
    e. Use properties of similar triangles to solve problems.
    f. Recognize and determine degree measure of angles formed by parallel lines cut by 
       a transversal.
    g. Develop, extend, and model the relationships of faces, vertices, and edges of 
       three-dimensional figures.
    h. Perform transformations on plane figures.