Change in Quantity to 10
Before students meet the '+' symbol, they need to understand what adding and subtracting actually do: they change a quantity. Build-and-change tasks are the most powerful way to develop this understanding. 'Start with 4 cubes. Change your collection to show 6. How did you do it?' requires students to reason about the difference — to think 'I need 2 more' — without an equation in sight.
Change as a story
Change in quantity has a story structure: there is a starting amount, something happens (add or remove), and there is a result. Mathematical stories like 'There were 5 birds on a branch. 2 more landed. Now how many?' give change meaning before symbols are introduced. This narrative structure is the forerunner of word problems.
Build-and-change tasks
A build-and-change task gives students a starting quantity and an ending quantity and asks them to figure out what changed. 'Begin with 4 cubes. You need to end with 7. What will you do?' This requires reasoning about the difference (3 more needed) without being told to 'add.' It is more cognitively demanding — and more educationally powerful — than a straightforward addition prompt.
Generalizing the pattern of +1 and +2
Students can notice that adding 1 always gives you the next counting number, and adding 2 gives you the one after that. Similarly, removing 1 gives you the previous number. These are the first generalizations — the beginning of algebraic thinking.