# Shapes can be combined and separated (composed and decomposed) to make new shapes.

Opportunities to combine, rotate, and compare shapes will help children develop understanding of part-whole relationships within and among shapes (as  More →

# The flat faces of solid (three-dimensional) shapes are two-dimensional shapes.

As they explore three-dimensional solids, children will discover for themselves that the faces (or sides) of these solids look like  More →

# Shapes can be defined and classified according to their attributes.

Children need to go beyond the use of superficial shape labels to recognizing and specifying the defining attributes of shapes.   More →

# Spatial relationships can be visualized and manipulated mentally.

Learning how to hold a spatial representation in the “mind’s eye” can be challenging for young learners. They build proficiency  More →

# Our own experiences of space and two-dimensional representations of space reflect a specific point of view.

Practice in the classroom will cultivate an awareness of perspective: the understanding that spatial relationships look different when viewed from  More →

# Relationships between objects and places can be represented with mathematical precision.

A simple reminding remark such as “Where do we keep the paintbrushes?” is an opportunity for children to describe their  More →

# It is useful to compare parts of the data and to draw conclusions about the data as a whole.

Using the analysis we have done to learn something new is the final step and ultimately the purpose of data  More →

# Data must be represented in order to be interpreted, and how data are gathered and organized depends on the question.

With scaffolding and thoughtful guidance, young children can follow the steps involved in a simple data analysis process.  When they  More →

# The purpose of collecting data is to answer questions when the answers are not immediately obvious.

The most important thing young children can learn about data analysis is why we do it.  When they understand that  More →

# Quantifying a measurement helps us describe and compare more precisely.

Repeated, meaningful experiences with comparison will lead children quite naturally to understand that using their growing sense of numerosity results  More →