How to teach addition

Teach addition in three stages: first counting all the objects in two combined groups, then counting on from the larger number, and finally recalling number facts from memory. Secure number bonds to 10 and 20 before two-digit addition, and only introduce regrouping once single-digit facts are fluent.

Most children begin addition in Pre-K and Kindergarten by combining small groups of objects, with formal written addition following through Grades 1 to 4. Early work is concrete and hands-on. The abstract column method with regrouping usually arrives around Grade 2, once counting on and number bonds are secure.

Counting all means starting at one and counting every object in both groups. Counting on means starting from the larger number and counting only the second group upward, so 8 plus 3 is 'eight, nine, ten, eleven'. Counting on is faster and is the bridge to recalling facts from memory.

The most common reason is still counting all from one instead of counting on, which is slow and error-prone. Weak number bonds to 10 force finger counting on every question. Regrouping errors, such as forgetting to carry, usually mean single-digit facts are not yet automatic, so practise those to recall speed first.

Number bonds are pairs of numbers that add to a total, such as 6 and 4 making 10. Learning the bonds to 10 and 20 by heart turns addition from counting into instant recall. That frees up working memory for harder, multi-digit problems and for mental strategies later on.

Regrouping, also called carrying, is what you do when a column adds to 10 or more: you write the ones digit and carry the ten into the next column to the left. For example 8 plus 5 is 13, so you write 3 and carry 1. Only teach it once single-digit facts are automatic.

Subtraction is usually taught alongside or just after addition, because the two are inverse operations linked through fact families. Once addition and subtraction within 20 are fluent, children move on to multiplication, which is repeated addition of equal groups. Secure addition facts make every later operation faster and less error-prone.