Equivalence and multiplicative reasoning help students see that mathematics is not a set of isolated topics but rather a web of closely connected ideas. Real-world contexts provide opportunities for students to connect what they are learning to their own environment. Students' experiences at home, at school, and in their community provide contexts for worthwhile mathematical tasks. In a fourth-grade class, students could make a map on a coordinate system of the various routes they use to walk to school. With the map, they could determine and compare the distances traveled.
Everyday experiences can also be the source of data.
Encouraging students to ask questions and to use mathematical approaches to find answers helps them see the value of mathematics and also motivates them to study new mathematical ideas. There are connections within mathematics, and mathematics is also connected to, and used within, other disciplines. Building on these connections provides opportunities to enrich the learning in both areas. For example, in a social studies unit, a fifth-grade class might discuss the population and area of selected states. They can investigate which states are most and least crowded.