Change Plus and Change Minus Situations

Change situations have three quantitative steps over time: start, change, result. Most children before first grade solve only problems in which the result is the unknown quantity. In first grade, any quantity can be the unknown number. Unknown start problems are more difficult than unknown change problems, which are more difficult than unknown result problems.

Put Together/Take Apart Situations

In these situations, the action is often conceptual instead of physical and may involve a collective term like “animal”: “Jimmy has one horse and two dogs. How many animals does he have?”

In put together situations, two quantities are put together to make a third quantity: “Two red apples and one green apple were on the table. How many apples are on the table?”

In take apart situations, a total quantity is taken apart to make two quantities: “Grandma has three flowers. How many can she put in her red vase and how many in her blue vase?”

These situations are decomposing/composing number situations in which children shift from thinking of the total to thinking of the addends. Working with differ