Pre-Algebra Basics for Seventh Graders

Pre-algebra is a critical foundation for all students who plan to take algebra in high school (and beyond). Though it may seem like a lot of work now, mastering pre-algebra concepts will give your seventh grader a leg up when he or she reaches algebra. Here are some basic concepts that your child should be familiar with before moving on to algebra.

Expressions, Equations, and Inequalities

An expression is a mathematical phrase that can contain numbers, variables, and operations (such as addition, subtraction, multiplication, and division). An equation is a mathematical statement that two things are equal. For example, the equation 3x + 5 = 13 is an equation because it states that the value of 3x + 5 is equal to 13. An inequality is a mathematical statement that two things are not equal. For example, the inequality 3x + 5 < 13 is an inequality because it states that the value of 3x + 5 is less than 13.

Solving equations and inequalities is a fundamental skill for all seventh graders. In order to solve equations and inequalities, students need to be able to use inverse operations. Inverse operations are operations that “undo” each other. For example, addition and subtraction are inverse operations because if you add two numbers and then subtract one of those numbers, you are left with the original number. Multiplication and division are also inverse operations—if you multiply two numbers and then divide one of those numbers, you are again left with the original number.

**Pre-algebra may seem like a lot at first glance**

Ratios, Proportions, and Percents

A ratio is a comparison of two values. Ratios can be written in different ways; for example, the ratio of boys to girls in a classroom can be written as “there are 2 boys for every 3 girls” or “there are 3 girls for every 2 boys.” A proportion is an equation that states that two ratios are equal; for example, the proportion 2/3 = 4/6 can be read as “two-thirds is equal to four-sixths.”

Percents are another way of representing ratios; specifically, they represent ratios out of 100. For example, 50% can be written as the fraction 50/100 or as the decimal 0.50; both of these representations mean “fifty out of one hundred,” or “half.” Mastering percent proportions will help your child understand how to calculate sales tax, tips, discounts, and more.

Pre-algebra may seem like a lot at first glance—but it’s worth taking the time to master these concepts now so that your child will be better prepared for high school (and beyond). By understanding expressions, equations, inequalities, ratios, proportions, and percents—and being able to solve problems involving these concepts—your child will have a strong foundation on which to build more complex algebraic skills later on.