Students apply the addition property of equality to solve equations. They are introduced to this property using a balance scale.
Up until this lesson, students have been solving equations informally. They used guess and check and reasoned about the quantities on either side of the equation in order to solve the equation.
In this lesson, students are introduced to the addition property of equality. As equations become more and more complicated, students will need to rely on formal methods for solving them. This property states that the same quantity can be added to both sides of an equation and the new equation will be equivalent to the original equation. That means the new equation will have the same solutions as the original equation.
To solve an equation such as x + 6 = 15, –6 can be added to both sides to get the resulting equation x = 9. However, since adding a negative number has not been introduced yet, students will consider both adding and subtracting a number (which is the equivalent of adding a negative number) from both sides to be an application of the addition property of equality.
Students will apply the addition property of equality to an equation with the goal of getting the variable alone on one side of the equation and a number on the other.
Goals and Learning Objectives
- Use the addition property of equality to keep a scale balanced.
- Use the addition property of equality to solve equations of the form x + p = q for cases in which p, q, and x are all non-negative rational numbers.