In order to understand the mathematical relationships occurring in a problem or equation, students must understand the broad concepts involved. Some math relationships are spatial, they involve physical objects and/or physical space (e.g., the relationship between an object’s weight and its size or mass). Other math relationships are sequential, the order in which steps occur or elements act on each other is most important (e.g., the relationship between the equations ‘10x+4=24’ and ‘10x=24-4’).

To work effectively with math relationships, students must have a flexible approach to each problem, knowing that quantities may be represented in a variety of ways. For example, understanding the concept of place value (e.g., that 30 is the same as 3 tens) enables students to more easily deal with problems concerning money, just as understanding the concept of units and subdivisions (or parts and wholes) helps students divide a single candy bar into equal parts to share.

Finally, students must be able to store and retrieve concepts from long term memory, and to hold several symbols and concepts in their minds. For example, a problem requiring plotting information on a graph may involve multiple concepts, including collecting and organizing information, setting up ratios, finding averages, using the coordinate system, etc.

Here are some strategies to help develop and strengthen students’ understanding of relationships in math.