In this lesson, you used three different models to represent and solve equations.
The balance scale model uses the metaphor of a balance scale in order to represent the expressions on each side of an equation. Because the expressions must have equivalent values, the scale must be balanced. Any changes made to one expression must also be made to the other in order to preserve balance.
The cups and counters model uses cups to represent the variable and counters to represent numbers. Counters can be manipulatives such as color tiles, two-color counters, or objects such as beans. When solving equations using the cups and counters model, the goal is to determine the number of counters that go inside the cup in order to make the equation true.
The algebra tile model uses squares to represent numbers (units) and rectangles to represent variables (x). Green or yellow tiles are positive, and red tiles are negative. The algebra tile model allows you to visualize using zero pairs to solve equations and leads to the idea of using inverse operations to solve equations, which you will learn about in a future lesson.
