##### (two semester course)

Key to Algebra is the fifth course offered in the sequence offered by Classic Math School’s Enrichment program, and is intended for students from 4th to 6th grade. The course prerequisites include  fluency with all operations on non negative rational numbers in any form ( i.e., fractions and decimals).  The scope and depth of the course may vary significantly depending on the actual students’ level and duration of the course.

Interactive Key to Algebra course is designed to be taught in a small group setting using a variety of instructional methods and materials. The main idea of the course can be described by the slogan 'Welcome to Algebra or have you already been there?’. Hands-on activities, math games and puzzles form an integral part of each class session to enhance student's understanding and retention.

The topics and problems that are studied in Key to Algebra course may include:

1. Understanding the point and need of elementary Algebra as a convenient tool for summarizing the very well familiar concepts (e.g. properties of arithmetic operations, family facts, parity, divisibility, etc.).
2. Refining the concept of divisibility. Developing formulas for even and odd numbers, as well as for any whole number divisible by another whole number with any given remainder. Reiterating the concepts of factors and multiples, GCF and LCM.
3. Refining the concept of prime numbers, relatively prime numbers, and prime factorization with exponential notation. Exploring Goldbach's conjecture.
4. Using algebraic notation for all the arithmetic properties and developing fluency in naming and applying them in different settings.
5. Reintroducing the concept of the order of operations as a convention rather than a math law. Scrutinizing PEMDAS and other common misbeliefs associated with order of operations. Incorporating exponentiation into the hierarchy of operations.
6. Introducing simple radicals as an application of the concept of inverse operations, emphasizing the essential restrictions.
7. Overviewing the Fractions/Decimals/Percents Concepts using algebraic notation.
8. Introducing negative integral exponents. Introducing scientific notation and expanded notation for decimals. Developing thorough understanding of decimals’ place value using expanded notation.
9. Mastering the concept of percent. Understanding fractions, decimals, and percents as different notations for the same number (with some exceptions to be considered), developing fluency in conversion process.
10. Solving multistep sophisticated word problems involving fractions, decimals and percents by any means (pictures, tape diagrams, systematic trial and error, etc.), but algebraic means. Further in this text those problems will be referred as ‘Problems Challenging without Algebra’.
11. Building on the concept of integers. Introducing the concept of opposites and absolute value, illustrating them with the number line.