Grades 1–3
Concrete, Pictorial, Abstract: Teaching Math in Three Steps at Home
Concrete-pictorial-abstract, often called CPA, is a simple order for teaching any new math idea: real objects first, then pictures of them, then numbers and symbols. It is the backbone of Singapore-style math and works at a kitchen table.
Concrete: hold it
Start with things they can touch and move: blocks, coins, beads, pasta. For 8 + 5, they physically move objects into a ten-frame.
Pictorial: draw it
Once moving objects feels easy, draw them: dots in boxes, bars, number bonds. The picture keeps the meaning but is faster than the objects.
Abstract: write it
Only then write 8 + 5 = 13. Because the child has built and drawn it, the symbols describe something they already understand.
Moving between stages
Children do not move through the stages in a straight line. Going back to objects for a hard problem is normal and useful, even in Grade 3. The goal is understanding, not getting to the symbols quickly.
- New idea: start concrete, even if it feels too easy.
- Two or three good sessions: offer the picture version.
- Picture feels quick: try the written version.
- Stuck on paper: go back a stage for that problem only.