# Manipulatives

In CMP, manipulatives are used only when they can help students develop understanding of mathematical ideas. For example, in Filling and Wrapping, students find all the different rectangular arrangements possible for a given number of cubes. They find the surface area of each arrangement by creating a net (covering) for the arrangement that exactly fits, with no overlap or underlap. They then identify the arrangements that require the least and the most material to wrap. This activity sets the stage for developing the ideas of surface area and volume of rectangular prisms. Most of the manipulatives used in CMP are commonly available, and many schools may already have them. Included are rulers, protractors, angle rulers, cubes, square tiles, counters, spinners, and dice.

The two manipulatives are unique to CMP.

### Polystrips

Polystrips are plastic strips that can be pieced together with brass fasteners to form polygons. These manipulatives are used in grade 7 to investigate the relationship among the side lengths of triangles and quadrilaterals. They also are useful in the eighth grade geometry Unit, Butterflies, Pinwheels and Wallpaper. A digital version of polystrips is available in the Student Activities.

### CMP Shapes Set®

The CMP Shapes Set® is a set of polygons used in grade 7 to explore sides, angles, and tilings. Labsheets are provided for teachers who do not have polystrips or the Shapes Set.