*Investigations* is a complete mathematics program for grades K-5. Students using *Investigations in Number, Data, and Space* are expected to learn arithmetic, basic facts and much more. The focus of instruction is on mathematical thinking and reasoning. Students using the complete *Investigations* curriculum develop an understanding of:

- number, operations, and early algebraic ideas
- geometry and measurement
- data analysis and probability
- patterns, functions, and the math of change, which provide foundations for algebra

*Investigations* is based on our goals and guiding principles, years of work with real teachers and students, and research about what we now know about how children learn mathematics. It is carefully designed to invite all students into mathematics and to help them develop a deep understanding of fundamental mathematical ideas.

"Understanding refers to a student's grasp of fundamental mathematical ideas. Students with understanding know more than isolated facts and procedures. They know why a mathematical idea is important and the contexts in which it is useful. Furthermore, they are aware of many connections between mathematical ideas. In fact, the degree of students' understanding is related to the richness and extent of the connections they have made." (2002,

Helping Children Learn Mathematics, p. 10.)

As a natural part of their everyday mathematics work, *Investigations* students:

- explore problems in depth.
- find more than one way to solve many of the problems they encounter.
- reason mathematically and develop problem-solving strategies.
- examine and explain mathematical thinking and reasoning.
- communicate their ideas orally and on paper, using "clear and concise" notation.
- represent their thinking using models, diagrams, and graphs.
- make connections between mathematical ideas.
- prove their ideas to others.
- develop computational fluency - efficiency, accuracy, and flexibility.
- choose from a variety of tools and appropriate technology.
- work in a variety of groupings - whole class, individually, in pairs, and in small groups.