Place value and number forms: a learning progression
Build numbers from ones, tens, and hundreds, then extend the same structure to large numbers and decimals.
Before you begin
Count collections and recognize ten as a complete group.
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
- Trade ten individual objects for one bundle of ten.
- Write numbers in standard, expanded, and word form without losing empty places.
- Compare and round using the highest place that differs.
- Extend the base-ten pattern to tenths, hundredths, and scientific notation.
What grade is this taught?
Our catalog includes this progression from grade 1 through grade 5. 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 2
Common wrong turns along this path
- Adding digits instead of their place values
- Writing digits instead of expanded values
- Dropping a zero from a number