Addition and subtraction are used to relate amounts before and after combining or taking away, to relate amounts in parts and totals, or to say precisely how two amounts compare. Story problems and situations that can be formulated with addition or subtraction occur in a wider variety than just the simplest and most common “add to” and “take away” story problems. Methods that young children can use to solve addition and subtraction story problems, again, rely on a fluent link between the number list and cardinality. Later methods (in first grade or so) also rely on decomposing numbers and on an initial understanding of the base 10 system, namely that the numbers 11 through 19 can be viewed as a ten and some ones.
Box 2-4 describes the different types of story problems or situations that can be formulated with addition or subtraction. Viewed from a more
Types of Addition/Subtraction Situations
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.
Change plus: Start quantity + change quantity = result quantity: “Two bunnies sat on the grass. One more bunny hopped there. How many bunnies are on the grass now?”
Change minus: Start quantity − change quantity = result quantity: “Four apples were on the table. I ate two apples. How many apples are on the table now?”
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