Change in Quantity to 20
Change in quantity is addition and subtraction in story form before the symbols arrive. Start with 9. Make it 14. What changed? requires students to find the difference and describe it as an action. This verbal and concrete work makes formal equations meaningful: students write 9+5=14 because they understand what the symbols represent, not because they memorized a procedure.
Change as a story structure
Every addition or subtraction situation has three parts: a starting quantity, a change (adding or removing), and a result. In story problems, one part is unknown. I had 11 stickers. I got some more. Now I have 15. The change is unknown: 11+?=15. Recognizing the structure of a change problem is more important than memorizing a procedure.
Three types of change problems
Unknown result (8+5=?): the most common type. Unknown change (8+?=13): requires reasoning about what was done. Unknown start (?+5=13): requires working backwards. All three appear in real contexts and students benefit from meeting all three, not just the first. Naming them helps students recognize the structure when they encounter it.
From verbal to symbolic
The BC curriculum specifies that Grade 1 students should verbally describe change concretely and verbally. I started with 12 cubes. I added 4 more. Now I have 16. This sentence maps exactly onto 12+4=16. Language is the bridge to symbolic notation. The equation is a shorter way to write the verbal description, not a separate thing to be memorized.