Algebra is the first and most basic of the mathematical languages. Algebra marks the transition from concrete arithmetic to symbolic mathematics and abstract reasoning skills. As such, it forms the foundation of other, more complex mathematics study. Success in algebra 1 requires a firm grasp of core skills and concepts of arithmetic.
Core Arithmetic Skills
Students of algebra 1 should have a good grasp of basic arithmetic. This includes addition, subtraction, multiplication and division. Beginning students should be able to work with positive and negative integers and solve equations with one variable. Many of the problems presented in algebra 1 can be simplified to arithmetic problems. Other pre-algebra skills should include an understanding of fractions, ratios and proportions and the ability to comfortably manipulate fractions in equations. Key to setting up and interpreting algebraic equations is the concept of the placeholder. Students should understand the role of placeholders in equations.
Basic Number Properties and Formulas
A good grasp of the associative, commutative and distributive properties is essential for simplifying and solving algebraic equations. Of the three, the distributive property is the one most often used in algebra. However, appropriate use of all of these properties is a basic math skill needed to solve algebraic equations successfully. The use of a formula as an algebraic expression is often introduced using geometry. Students should be familiar with basic geometric shapes and the concepts of perimeter, area, diameter and radius.
Students need to be able to translate word problems into algebraic expressions. The ability to read a simple story problem and then set up the arithmetic equation for the solution is a critical basic math skill. Students introduced to complex story problems and the concept of a placeholder or variable more easily develop an understanding of how to translate problems posed in text into an algebraic expression, which will produce the solution. Students should be able to incorporate the core skills and the basic number properties and formulas to set up an appropriate algebraic equation as the basis for solving the problem. This is a key skill and the pivotal step from concrete arithmetic to symbolic math.
Other Fundamental Concepts
Other basic math skills necessary for success in algebra 1 include an understanding of pictorial presentations, fluency in units of measure and familiarity with scientific notation. Students should be able to construct graphs -- such as bar graphs and pictographs -- to scale, read and interpret information from graphs and graph equations. They should also have some understanding of simple statistical concepts such as maximum, minimum, mean, media and mode. Success in algebra 1 is essential for students who plan to move on to algebra II, calculus and other higher math courses. For students who do not pursue higher math, algebra is an important skill in everyday life. Whether calculating how many hours it will take to drive somewhere, recalculating a recipe for twice the number of servings or trying to figure out how many gallons you need to paint the house, algebra is an important and useful tool for everyone.
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