Pre-algebra is taught in either seventh or eighth grade as a precursor to the study of algebra. The Common Core Standards outline the math course that should be offered prior to algebra. General topics include the number system, expressions and equations, functions, geometry, and statistics and probability.
The Number System
Students should understand rational and irrational numbers, which includes whole numbers, fractions and decimals. To fully understand rational numbers, student should be able to use scientific notation, perform basic operations, convert between fractions and decimals, calculate percentages and use terminating decimals. Students should also understand exponents -- both in whole numbers and fractions -- and be able to perform basic operations using exponents.
Expressions and Equations
Students should understand that variables represent a numeric value, and they should be able to write both expressions and equations. Pre-algebra includes evaluation of expressions and the use of the order of operations to simplify expressions. Once students have mastered evaluation of expressions, they should be introduced to equations, which are mathematical phrases that include an equals sign. They should be able to solve simple one-step and two-step linear equations.
Students should use their understanding of equations to explore linear functions and should be able to graph the line the function represents. Students should also be able to define functions as lines or curves and compare them to each other. Functions should eventually be graphed and used as a way to solve word problems and model quantities.
The basic geometric concepts of congruence and similarity of polygons are introduced in pre-algebra. Students can develop this understanding through drawing and computer programs. The Pythagorean theorem is also introduced as pre-algebra students begin to study right triangles. Basic properties of cylinders and spheres are introduced and students learn to calculate the volume of these figures.
Statistics and Probability
The introduction to statistics and probability includes collection of data. Students learn to organize data in tables and charts and are able to represent data on a scatterplot. They learn to compare data sets and draw conclusions from given information. The pre-algebra curriculum should continue to develop the mathematical reasoning skills of students. Problem-solving is a key component in the development of skills for algebra.
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