Our set of Big Ideas map the key math concepts young children need to explore between the ages of 3 and 6. Big Ideas are foundational to lifelong mathematical thinking and can guide teaching and learning in the early childhood years. They are organized by topic here and in our book, *Big Idea of Early Mathematics: What Teachers of Young Children Need to Know.*

## Sets

Sets are basic to children’s thinking and learning. They are also basic to our number system. more →

## Number sense

Number sense is the ability to understand the quantity of a set and the name associated with that quantity. more →

## Counting

Counting is a part of young children’s daily life. They love to count everything from the stairs they climb to the crackers they eat. But what is counting? more →

## Operations

When children focus on what happens when we join two sets together or separate a set into parts, they learn about how quantities change. When they have lots of experience comparing amounts, they become familiar with thinking about differences between sets. more →

- A quantity (whole) can be decomposed into equal or unequal parts; the parts can be composed to form the whole.
- Sets can be compared using the attribute of numerosity, and ordered by more than, less than, and equal to.
- Sets can be changed by adding items (joining) or by taking some away (separating).

## Pattern

Pattern is less a topic of mathematics than a defining quality of mathematics itself. Mathematics “makes sense” because its patterns allow us to generalize our understanding from one situation to another. more →

## Measurement

Measurement is any process that produces a quantitative description of an attribute, such as length, circumference, weight, temperature, volume, or number. Measurement is an essentially mathematical procedure that we apply in many different contexts. more →

## Data Analysis

Data analysis can be very simple, like making a list of items and writing how many you have of each in parentheses, or creating and talking about a bar graph whose bars are higher for snowy than rainy days in the month of January. more →

- It is useful to compare parts of the data and to draw conclusions about the data as a whole.
- Data must be represented in order to be interpreted, and how data are gathered and organized depends on the question.
- The purpose of collecting data is to answer questions when the answers are not immediately obvious.

## Spatial Relationships

Children between the ages of 3 and 6 are more than ready to develop their skills at expressing directions from different locations and understanding relative positions. more →

## Shape

Everything in the material world has shape. In mathematics, the focus is very much on regular shapes, such as the two-dimensional circle, triangle, and rectangle and the three-dimensional solids known as spheres and polyhedrons. more →