Pre-algebra

Pre-algebra is a common name for a course in middle school mathematics. In the United States, pre-algebra is usually taught in the 7th grade or 8th grade.[1] The objective of it is to prepare students for the study of algebra.

As an intermediate stage after arithmetic, pre-algebra helps students pass certain conceptual barriers. Students are introduced to the idea that an equals sign, rather than just being the answer to a question as in basic arithmetic, means that two sides are equivalent, and can be manipulated together. They also learn how numbers, variables, and words can be used in the same ways.[2]

Pre-algebra includes several broad subjects:

Review of natural number arithmetic
New types of numbers such as integers, fractions, decimals and negative numbers
Ratios and percents
Factorization of natural numbers
Properties of operations such as associativity and distributivity
Simple (integer) roots and powers
Rules of evaluation of expressions, such as operator precedence and use of parentheses
Basics of equations, including rules for invariant manipulation of equations
Understanding of variable manipulation
Manipulation and plotting in the standard 4-quadrant Cartesian coordinate plane
Powers in scientific notation (Ex: 34 × 10^7 in scientific notation is 3.4×10^8)

Pre-algebra may include subjects from geometry, especially subjects that further understanding of algebra in applications to area and volume.

Proficiency in pre-algebra has been shown to be an indicator of college success. It can also be taught as a remedial course for college students.[3]

References

In the Introduction to their book on pre-algebra.Szczepanski & Kositsky (2008) say that "the math in this book should match what's taught in many middle school classrooms in California, Florida, New York, Texas, and other states". (p. xix)
Linchevski, Liora (1995). "Algebra With Numbers and Arithmetic With Letters: A Definition of Pre-Algebra". Journal of Mathematical Behavior. 14: 113–120. doi:10.1016/0732-3123(95)90026-8.
Gningue, Serigne Mbaye; Menil, Violeta C.; Fuchs, Eric (June 1, 2014). "Applying Bruner's Theory of Representation to Teach Pre-Algebra and Algebra Concepts to Community College Students Using Virtual Manipulatives". The Electronic Journal of Mathematics and Technology. 8. ISSN 1933-2823.

Szczepanski, Amy F.; Kositsky, Andrew P. (2008), The Complete Idiot's Guide to Pre-algebra, Penguin, ISBN 9781592577729

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[1] In the Introduction to their book on pre-algebra.Szczepanski & Kositsky (2008) say that "the math in this book should match what's taught in many middle school classrooms in California, Florida, New York, Texas, and other states". (p. xix)

[2] Linchevski, Liora (1995). "Algebra With Numbers and Arithmetic With Letters: A Definition of Pre-Algebra". Journal of Mathematical Behavior. 14: 113–120. doi:10.1016/0732-3123(95)90026-8.

[3] Gningue, Serigne Mbaye; Menil, Violeta C.; Fuchs, Eric (June 1, 2014). "Applying Bruner's Theory of Representation to Teach Pre-Algebra and Algebra Concepts to Community College Students Using Virtual Manipulatives". The Electronic Journal of Mathematics and Technology. 8. ISSN 1933-2823.