Pre-algebra

A visual proof of the Pythagorean theorem

Pre-algebra is a common name for a course taught in middle school mathematics in the United States, usually taught in the 6th, 7th, 8th, or 9th grade.[1] The main objective of it is to prepare students for the study of algebra. Usually, Algebra I is taught in the 8th or 9th grade.[2]

As an intermediate stage after arithmetic, pre-algebra helps students pass specific 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 may also learn how numbers, variables, and words can be used in the same ways.[3]

Subjects

Subjects taught in a pre-algebra course may include:

• Review of natural number arithmetic
• 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 (example: 340,000,000 in scientific notation is 3.4 × 10^8)
• Identifying Probability
• Solving Square roots
• Pythagorean Theorem[4]

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

Pre-algebra may also include subjects from statistics to identify probability and interpret data.

Proficiency in pre-algebra is an indicator of college success. It can also be taught as a remedial course for college students.[5]

See also

• Precalculus
• Mathematics education in the United States

References

1. In the Introduction to their book on prealgebra.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. "A Leak in the STEM Pipeline: Taking Algebra Early". U.S. Department of Education. November 2018. Retrieved May 13, 2023.
3. Linchevski, Liora (1995). "Algebra With Numbers and Arithmetic With Letters: A Definition of Prealgebra". Journal of Mathematical Behavior. 14: 113–120. doi:10.1016/0732-3123(95)90026-8.
4. "Gifted and Talented Honors Prealgebra | Johns Hopkins Center for Talented Youth". cty.jhu.edu. Retrieved 2021-02-10.
5. 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