### Math (K - 5)

TERC’s Investigations in Number, Data and Space is a K-5 mathematics curriculum designed to engage students in making sense of mathematical ideas.

Six major goals guided the development of this curriculum. The curriculum is designed to:

•  Support students to make sense of mathematics and learn that they can be mathematical thinkers.
•  Focus on computational fluency with whole numbers as a major goal of the elementary grades.
•  Provide substantive work in important areas of mathematics - rational numbers, geometry, measurement, data, and early algebra- and connections among them.
•  Emphasize reasoning about mathematical ideas.
•  Communicate mathematics content and pedagogy to teachers.
•  Engage the range of learners in understanding mathematics.

Developing computational fluency with whole numbers must be a lynchpin of the elementary curriculum. This development includes the building blocks of computation: understanding the base ten number system and its place value notation, understanding the meaning of the operations and their relationships, knowing the basic addition and multiplication number combinations (the "facts") and their counterparts for subtraction and division, estimating reasonable results, interpreting problems embedded in contexts, and practicing, and consolidating accurate and efficient strategies for computing. It also includes developing curiosity about the characteristics of numbers and operations and learning to articulate, represent, and justify generalizations.

One principle of the Investigations curriculum is that time and focus on the building blocks of computational fluency precedes practice and consolidation. Extended time across several grades is spent on each operation. Let's take subtraction as an example of this process.

• In kindergarten and grade 1, students solve subtraction problems by modeling the action of subtraction.
• By grade 2, students use the inverse relationship between addition and subtraction to add up to solve problems.
• During grades 2 and 3, they become fluent with the subtraction "facts" and model and solve a variety of types of subtraction problems, including comparison and missing part problems.
• In grade 3, they use their understanding of place value to solve problems with larger numbers.
• In grades 3 and 4, they articulate, represent, and justify important generalizations about subtraction. For example: if you add the same amount to each number in a subtraction expression, the difference does not change, as in the equation 483 - 197 = 486 - 200. They analyze and compare strategies for solving subtraction problems. They expand their command of computation procedures with multi-digit numbers. At this point, they are also in a position to appreciate the short-cut notation of the the U.S. "traditional" or "borrowing" algorithm for subtraction, analyze how it works, and compare it to other algorithms.

The account above gives only a glimpse of the work that helps students develop an understanding of subtraction. Each operation has similar complexity. When we think of entering first graders who are coordinating written and spoken numbers with their quantitative meaning, second graders who are uncovering the relationship between ten tens and one hundred, and fourth graders who are becoming flexible in their use of a number of algorithms to solve, we begin to get some sense of how much work there is to do in these grades.

In the revision of Investigations, as we strengthen the coherence and rigor of the number and operations strand, we are determined not to sacrifice the time and depth required for careful development of ideas in this strand. Maintaining a focus on depth and meaning requires us to make difficult decisions in which we navigated the morass of varying state standards, while keeping ourselves grounded in the experience of real students in real classrooms.

In order to give the attention needed to number and operations we had to make hard decisions about how much time can be spent on other important mathematical content: geometry, measurement, data, and patterns and functions. We also considered more carefully how work in these other content areas can connect to and support work in number and operations. For example, a greater emphasis on the foundations of algebra across the grades opens up important opportunities to strengthen work with number and operations. By creating a strong, coherent content strand in patterns and functions across grades K-5, we were able to connect the work primary students do with repeating patterns to the later work on functions. The work on functions provides interesting problem contexts in which students' work on ratio and on constant change connect to and support their work on multiplication.

Geometry and measurement provide contexts in which students revisit multiplication and fractions. Within the number and operations units themselves, articulation, representation, and justification of general claims about the operations (an aspect of early algebraic thinking) strengthen students' understanding of the operations.

Making choices about content in the Investigations curriculum is based on knowledge from research and practice, including our own extensive field testing. Choice, balance, sequence, and pace of content is based on: the centrality of number and operations for elementary school students, the importance of exposing all elementary students to a range of mathematics content, including work with geometry, measurement, data, patterns, functions, and the foundations of algebra the development of foundational ideas that students need in order to build understanding of mathematics what we learned from several years of in depth work with many, diverse students and their teachers.

This highly-acclaimed curriculum, developed in partnership with classroom teachers, provides a complete mathematics program for grades K-5.

Activity-based investigations encourage students to think creatively, develop their own problem-solving strategies, and work cooperatively. Students write, draw, and talk about math as well as use manipulatives, calculators, and computers. Mathematics content includes the number system; addition, subtraction, multiplication, and division; collecting, sorting, and representing data; probability and statistics; measurement; changes over time; 2-D and 3-D geometry; fractions; computation and estimation strategies; and tables and graphs. Assessment is embedded within the investigations.

Investigations is infused with teachers' practical suggestions and strategies, including actual student dialogues, lesson plans, teacher notes, and reproducible student materials. For more information about the curriculum and using Investigations to advance the teaching and learning of mathematics, click here.