Types of Math Problems

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.