In the unit Get Ready for Algebra: Grade 7, we spend the first several lessons reviewing all of the sixth grade algebra topics and we also study some basic properties of the operations.
The main topics reviewed are the order of operations, expressions, and simplifying expressions in several different ways. The main principles are explained and practiced both with visual models and in abstract form, and the lessons contain varying practice problems that approach the concepts from various angles.
Next, students learn to solve one-step equations that involve integers. The lesson Solving Equations reviews the concept of an equation and how to model equations using a pan balance (scale). The basic principle for solving equations is that, when you perform the same operation on both sides of an equation, the two sides remain equal.
The unit presents two alternatives for keeping track of the operations to be performed on an equation. The one method, writing the operation under each side of the equation, is common in the United States. The other method, writing the operation in the right margin, is common in Finland. Either is adequate, and the choice is just a matter of the personal preference of the teacher.
The introduction to solving equations is followed by a lesson on addition and subtraction equations and another on multiplication and division equations. All the equations are easily solved in only one step of calculations. The twofold goal is to make the student proficient in manipulating negative integers and also to lay a foundation for later study of more involved equations.
In the next lesson, students write equations to solve simple word problems. Even though they could solve most of these problems without using the equations, the purpose of the lesson is to make the student proficient in writing simple equations so he/she will be able to move on to more complex equations from more difficult word problems.
In the lesson Constant Speed, we study solving problems with distance (d), rate or velocity (v), and time (t). Students use the equivalent formulas d = vt and v = d/t to solve problems involving constant or average speed. They learn an easy way to remember the formula v = d/t from the unit for speed that they already know, “miles per hour.”
Towards the end of the unit, we study two-step equations and practice solving them. There is also another lesson on patterns of growth, which may seem to be simply a fascinating topic, but in reality presents the fundamentals of a very important concept in algebra ― that of linear functions (although they are not mentioned by that name) ― and complements the study of lines in the subsequent lessons.