Integers and rational numbers: a learning progression
Extend arithmetic across zero using signed quantities, distances, and consistent operation rules.
Before you begin
Use number lines, fractions, decimals, 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
- Locate signed values relative to zero and compare their positions.
- Interpret absolute value as distance.
- Use signed movement for addition and subtraction.
- Apply multiplication and division rules, then check that contextual answers make sense.
What grade is this taught?
Our catalog includes this progression from grade 6 through grade 7. 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.