初等代数の概念 - サマーブートキャンプ

When students understand the conceptual foundations of Algebra, learning problems and formulas becomes logical and students tend to progress at a faster pace with greater confidence.  This course provides an in-depth overview of key foundational concepts needed to be successful in Pre-algebra.  It is designed as a preparation course for students entering a Pre-algebra.  The class meets for eight 45 minute sessions offered in a consolidated 2-week time frame.  The camp focuses on learning and understanding the underlying concepts that define Pre-algebra.   We will focus on the “why” of equations, formulas, and properties, as well as spend time “proving” them.  

Week 1 - 
Session 1 - Prealgebra
Students will get an overview of Pre-algebra including what it is used for and why they are learning it.  We will also discuss  algebraic equations and the rules that govern them.  At the end of the session, students will be asked to write their own equation, and we will solve them together as a class.

Session 2 - Properties
Students will be introduced to the 5 properties that are common when working with algebraic equations (Commutative, Associative, Distributive, Identity, and Inverse).  The instructor will introduce, define, and demonstrate each property.  The students will have an opportunity to work with each property by working together to create a 'proof' and explain to the class.  

Session 3 - Real Numbers
This session will focus on the types of numbers included in the real number system and the rules that govern them.  By the end of the session, students will be able to identify and explain the differences between rational, irrational, integers, natural numbers, and whole numbers.  The instructor will teach the different types of numbers and show examples of each.  During the lesson, the students will derive numbers through various calculations, and identify the number type. 

Session 4 - Order of operations
In this session, students will start learning about numerical expressions.  The lesson will focus on the different ways mathematical actions are represented, e.g. multiplication can be represented by parenthesis, a dot, or an "x".  We will also learn how the order of operations applies to algebraic equations and have hands on practice interpreting them.

Week 2 - 
Session 5 - Fractions, addition and subtraction
After a review of week 1, the students will learn about fractions as they relate to algebraic equations.  Students will learn and review fractions, equivalent fractions, improper fractions, and mixed numbers.  The class will have hands-on practice solving problems with like and unlike denominators.  At the end of this session, students will be asked to create their own fraction problems for their classmates to solve.

Session 6 - Fractions, multiplication and division
This session will continue the discussion of fractions and add the concept of multiplying and dividing rational numbers to the skills the students already learned.  Again, students will be asked to create their own fraction problems for their classmates to solve.

Session 7 - Ratios and proportions
This session will discuss the concept of ratios and proportions.  After a conceptual overview, students will be given some tips and keywords for solving ratio and proportion problems, whether in the form of an expression or a word problem.  Students will be asked to solve ratio and proportion word problems both on their own and together as a class.

Session 8 - Inequalities
In this final session, students will learn about inequalities as they compare and contrast them with equations.  Students will be taught the rules that govern inequalities, and will develop "proofs" to better understand and validate the rules.  Finally, in this last session, students will be given a certificate of completion for the "Pre-Algebra Summer Boot Camp" and will be officially ready to take the full Pre Algebra or Algebra 1 course with an expectation of success!