# Pre-algebra

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{{Short description|Middle-school math class in the U.S.}}
thumb|A visual proof of the Pythagorean theorem
'''Pre-algebra''' is a common name for a [course](/source/course_(education)) taught in [middle school](/source/middle_school) [mathematics](/source/mathematics) in the United States, usually taught in the 6th, 7th, 8th, or 9th grade.<ref>In the ''Introduction'' to their book on prealgebra.{{harvtxt|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)</ref> The main objective of it is to prepare students for the study of [algebra](/source/algebra). Usually, Algebra I is taught in the [8th](/source/Eighth_grade) or [9th grade](/source/Ninth_grade).<ref>{{Cite web |date=November 2018 |title=A Leak in the STEM Pipeline: Taking Algebra Early |url=https://www2.ed.gov/datastory/stem/algebra/index.html |access-date=May 13, 2023 |website= |publisher=U.S. Department of Education |language=en}}</ref>

As an intermediate stage after [arithmetic](/source/arithmetic), pre-algebra helps students pass specific conceptual barriers. Students are introduced to the idea that an [equals sign](/source/equals_sign), rather than just being the answer to a question as in basic arithmetic, means that two sides are [equivalent](/source/Equality_(mathematics)) and can be manipulated together. They may also learn how numbers, [variables](/source/Variable_(mathematics)), and words can be used in the same ways.<ref>{{Cite journal|last=Linchevski|first=Liora|date=1995|title=Algebra With Numbers and Arithmetic With Letters: A Definition of Prealgebra|url=|journal=Journal of Mathematical Behavior|volume=14|pages=113–120|doi=10.1016/0732-3123(95)90026-8}}</ref>

== Subjects ==
Subjects taught in a pre-algebra course may include:
* Review of [natural number](/source/natural_number) arithmetic
* Types of numbers such as [integer](/source/integer)s, [fractions](/source/Fraction_(mathematics)), [decimal](/source/decimal)s and [negative number](/source/negative_number)s
* [Ratio](/source/Ratio)s and [percents](/source/Percentage)
* [Factorization](/source/Integer_factorization) of [natural number](/source/natural_number)s
* Properties of operations such as [associativity](/source/associativity) and [distributivity](/source/distributivity)
* Simple (integer) [roots](/source/Nth_root) and [powers](/source/Exponentiation)
* Rules of evaluation of expressions, such as [operator precedence](/source/operator_precedence) and use of [parentheses](/source/parentheses)
* Basics of [equation](/source/equation)s, including rules for invariant manipulation of equations
* Understanding of variable manipulation
* Manipulation and plotting in the standard [4-quadrant Cartesian coordinate plane](/source/4-quadrant_Cartesian_coordinate_plane)
* Powers in [scientific notation](/source/scientific_notation) (example: 340,000,000 in scientific notation is 3.4 × 10<sup>8</sup>)
* Identifying [Probability](/source/Probability)
* Solving [Square roots](/source/Square_root) 
* [Pythagorean Theorem](/source/Pythagorean_theorem)<ref>{{Cite web|title=Gifted and Talented Honors Prealgebra {{!}} Johns Hopkins Center for Talented Youth|url=https://cty.jhu.edu/online/courses/mathematics/prealgebra.html|access-date=2021-02-10|website=cty.jhu.edu|language=en}}</ref>

Pre-algebra may include subjects from [geometry](/source/geometry), especially to further the understanding of algebra in applications to [perimeter](/source/perimeter), [area](/source/area), and [volume](/source/volume).

Pre-algebra may also include subjects from [statistics](/source/statistics) to identify [probability](/source/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, particularly in [community college](/source/community_college)s.<ref>{{Cite journal|last1=Gningue|first1=Serigne Mbaye|last2=Menil|first2=Violeta C.|last3=Fuchs|first3=Eric|date=June 1, 2014|title=Applying Bruner's Theory of Representation to Teach Pre-Algebra and Algebra Concepts to Community College Students Using Virtual Manipulatives|url=|journal=The Electronic Journal of Mathematics and Technology|volume=8|pages=|issn=1933-2823}}</ref>

==See also==
{{Portal|Education|Mathematics|United States}}
* [Precalculus](/source/Precalculus)
* [Mathematics education in the United States](/source/Mathematics_education_in_the_United_States)

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==References==
{{Reflist}}
*{{Citation |last1=Szczepanski |first1=Amy F. |last2=Kositsky |first2=Andrew P. |year=2008 |title=The Complete Idiot's Guide to Pre-algebra |publisher=Penguin |isbn=9781592577729 |url=https://books.google.com/books?id=wLA2tlR_LYYC }}

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Category:Elementary mathematics
Category:Algebra education

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Adapted from the Wikipedia article [Pre-algebra](https://en.wikipedia.org/wiki/Pre-algebra) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Pre-algebra?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.