Fractions: a learning progression
Progress from equal shares to fraction size, equivalence, and operations with fractions.
Before you begin
Recognize equal parts of the same whole; understand multiplication and division for later 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
- Name halves and fourths of a whole using equal shares.
- Treat a unit fraction as a number and locate it on a number line.
- Generate equivalent fractions and compare quantities using a common whole.
- Use common denominators for addition; interpret multiplication and division before applying procedures.
What grade is this taught?
Our catalog includes this progression from grade 1 through grade 6. 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 3
Grade 4
Grade 5
Grade 6
Your next steps
Common wrong turns along this path
- Adding or subtracting the denominators
- Counting number-line marks instead of intervals
- Changing only one part of a fraction