Solving different types of addition and subtraction problems allows students to think about the operations in different ways. There are four main types of addition and subtraction problems: joining, separating, comparing, and part-part-whole.
- A joining problem involves increasing an amount by adding another amount to it. The situation involves three amounts: a start amount, a change amount (the amount added), and a result amount. A joining problem occurs when one of these amounts is unknown.
- A separating problem involves decreasing an amount by removing another amount. The situation involves three amounts: a start amount, a change amount (the amount removed), and a result amount. A separating problem occurs when one of these amounts is unknown.
- A comparing problem involves the comparison of two quantities. The situation involves a smaller amount, a larger amount, and the difference between the two amounts. A comparing problem occurs when the smaller amount, the larger amount, or the difference is unknown.
- A part-part-whole problem involves two parts that make the whole. Unlike joining and separating problems, there is no mention of adding or removing amounts in the way that a part-part-whole problem is worded. A part-part-whole problem occurs when either a part or the whole is unknown.