# Manipulatives and Other Math Tools

## Materials as Tools for Learning

Students of all ages benefit from being able to use materials to model and solve problems and explain their thinking. Encourage all students to use tools and materials and to explain how they use them. They should see how different people, including the teacher, use a variety of materials to solve the same problem. To make effective use of materials as tools for learning, teachers need to:

- Get to know the materials themselves.
- Organize the materials for classroom use.
- Introduce new materials thoughtfully.
- Make the materials accessible to students.
- Establish clear expectations about how materials should be used, shared, and cared for.

… continue reading about how to use materials effectively in the classroom (pdf).

## Array Cards in *Investigations*

Array Cards are rectangular arrangements of squares that help students develop a visual image of multiplication as equal groups (e.g. 6 rows of 8, or 8 rows of 6), and as area (e.g. a rectangle with dimensions 6 and 8). Used in Grades 3 and 4, Array Cards provide students with a way to practice and learn their multiplication combinations. They also help children develop an understanding of the operation of multiplication, its properties, and the relationship between multiplication and division. … continue reading about Array Cards in *Investigations *(pdf).

## Calculators in *Investigations*

*Investigations* sees the calculator as an efficient tool for many purposes in life, and aims to help students learn to use it sensibly, knowing that using it well depends on the user’s correct analysis and organization of the problem, comparing its results with reasonable estimates, understanding when they are appropriate to use and for double-checking. … continue reading about how calculators are used in *Investigations *(pdf).

## Software in *Investigations*

Computers are explicitly linked to one curriculum unit at each grade level through software that is provided with the curriculum. These pieces of software—*Shapes* at K-2 and *LogoPaths* at 3-5—are intended to support and extend the mathematics of the geometry and measuring units. While highlighted in these units, ideally students should have access to the software throughout the year.

Learn about the *Shapes* software (pdf).

Learn about the *LogoPaths* software (pdf).

Learn about using the computer as a tool for learning (pdf).