Ratios, rates, and percent: a learning progression
Connect equivalent ratios and unit rates to proportional relationships and percent change.
Before you begin
Multiply, divide, and compare fractions and decimals.
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
- Keep ratio quantities in a consistent order with clear units.
- Find a unit rate by dividing the appropriate quantities.
- Identify whether a table, graph, or equation represents a proportional relationship.
- Calculate a percent of a base and distinguish change amounts from final values.
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.
Grade 6
Your next steps
Common wrong turns along this path
- Dividing x by y instead of y by x
- Using the new value as the percent-change base
- Reversing a unit-rate calculation