Expressions and equations: a learning progression
Translate situations, simplify expressions, and solve equations by preserving equality.
Before you begin
Use arithmetic properties, order of operations, and inverse operations.
Readiness depends on the ideas you can use, not only your age or grade. Start earlier in the sequence when an example feels unfamiliar.
How the skill develops
- Distinguish an expression from an equation.
- Use grouping, substitution, and the distributive property.
- Undo operations on both sides to solve one- and multi-step equations.
- Handle variables on both sides, inequalities, and systems; check solutions in the original conditions.
What grade is this taught?
Our catalog includes this progression from grade 5 through grade 9. That is a map of the practice available here, not a rule that every school uses the same schedule. Earlier grades may introduce models that later grades formalize.
The sequence is our teaching organization, informed by the published curriculum reference. High-school courses and calculus enrollment vary; check your school’s syllabus for placement decisions.
Build your next practice steps
Mark skills you already feel comfortable with. We’ll suggest the next unchecked skills in this sequence. This is a self-selected path, not a test score.
Grade 6
Grade 7
Grade 8
Common wrong turns along this path
- Doing every operation from left to right
- Changing only one side of an equation
- Using the same operation to undo an equation
- Dropping variable terms or forcing a solution