Addition and subtraction: a learning progression
Move from combining and taking away objects to flexible mental strategies and written regrouping.
Before you begin
Understand a total as two parts and count forward and backward.
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
- Represent joining and separating with objects or drawings.
- Use number bonds, fact families, and making ten.
- Align place values and exchange ten ones for one ten when needed.
- Choose operations in word problems and check by using the inverse operation.
What grade is this taught?
Our catalog includes this progression from kindergarten through grade 4. 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.
Kindergarten
Grade 1
Grade 2
Your next steps
Common wrong turns along this path
- Giving the total instead of the missing part
- Using the same addend twice when making ten
- Reversing subtraction in a fact family
- Forgetting the regrouped ten in addition
- Subtracting the smaller digit from the larger