Counting and number sense: a learning progression
Connect number words, written numerals, and quantities before using numbers in calculations.
Before you begin
Start with small visible groups and one-to-one matching.
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
- Touch each object once while saying one number word.
- Keep the count unchanged when the same objects are rearranged.
- Compare groups, then connect more and less with movement on a number line.
- Build and break apart small numbers before introducing written equations.
What grade is this taught?
Our catalog includes this progression from kindergarten through grade 1. 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.