Assess the student's comfort level with basic arithmetic properties. Consider the commutative, associative, identity and inverse properties of addition and multiplication. Algebra introduces abstract variables into basic equations, and knowledge of these properties allows students to solve for the variable. Pre-algebra reviews these properties in depth.
Consider the student's ability to comfortably work with fractions, decimals and percentages. Especially consider her ability to translate numbers between the three forms. Algebra builds on these concepts, and a solid foundation is expected by most teachers.
Evaluate the student's flexibility in manipulating equations. Algebra requires students to assess problems, apply the best arithmetic equation, and reorder variables to find solutions. Pre-algebra will assist the student in identifying problem-solving strategies and strategically applying arithmetic concepts.
Write algebraic equations. Evaluate the student's comfort level with defining variables and translating verbal phrases into algebraic equations. Conversely, translate some simple algebraic equations into verbal expressions. For example, x + 1 = 6 translates into what numbers plus one equal six and vice versa.
Assess the student's ability to understand word problems. If he can easily identify the variable and translate word problems into mathematical equations, consider algebra - especially if he can easily reverse the process and write his solution both as a written answer and as an equation.
Consider the student's ability to communicate her solution. Algebra requires strong abstract thinking skills and the ability to translate abstract ideas into concrete solutions. Teachers use the ability to communicate this process both to evaluate student work and to assist with difficult concepts. Difficulty communicating in the language of math suggests that pre-algebra is the more appropriate choice.
Assess the student's logical thinking skills. If he can easily estimate answers and distinguish between reasonable and unreasonable results, consider algebra.
Determine if the student can logically determine what sort of data set is most appropriate for the solution. For example, some problems are better answered with data sets and others need a graph. If the idea that answers can take different forms is difficult, then consider pre-algebra.
Consider that algebraic thought requires both deductive and inductive reasoning skills. The flexibility to move between generalized to specific concepts and back forms the basis for abstract math. Students with a basic understanding of these ideas are ready for algebra.