6.6 Expressions and Equations

In this unit, students learn to understand and use the terms “variable,” “coefficient,” “solution,” “equivalent expressions,” “exponent,” “independent variable,” and “dependent variable.” They begin to write coefficients next to variables without a multiplication symbol, e.g., \(10x\) rather than \(10 \boldcdot x\), and note that \(x\) is \(1 \boldcdot x\). They learn other situations in which the multiplication symbol can be omitted, e.g., \(6 \boldcdot (3+2)\) can be written \(6 (3+2).\) They work with expressions that have positive whole-number exponents and whole-number, fraction, or variable bases, using properties of exponents strategically to evaluate these expressions, given a value for the variable. They find solutions for linear equations in one variable and simple equations that include exponents, e.g., \(2^x = 32\) and \(100 = x^2.\) They use these terms and representations (including expressions with two variables) in reasoning about real-world and geometrical situations, understanding that some values of variables may not make sense in a given context. They represent collections of equivalent ratios as equations and use and make connections between tables, graphs, and linear equations that represent the same relationships.