#### Spatial Thinking

##### What is Spatial Thinking?

Spatial thinking is an essential aspect of math. It involves understanding where different objects are located in relation to each other, visualizing and mentally rotating objects, and using representational maps or diagrams to solve problems.

This early math curriculum focuses on four aspects of spatial thinking:

*Spatial vocabulary:*using spatial words*Spatial reasoning*: understanding spatial relationships*Spatial navigation*: using maps and diagrams to plan, describe, and follow paths*Spatial representation*: connecting maps, diagrams, and models to their real-world locations or objects

##### Why is Spatial Thinking Important?

Spatial thinking skills provide a unique approach to mathematical problem solving. Advanced spatial thinking skills promote school readiness, indicate later academic success, and increase the likelihood of learners pursuing careers related to mathematics, science, engineering, and/or technology.

Spatial thinking activities will help children expand their knowledge, skills, habits of mind, ability to use representation tools (like maps), and reasoning processes when solving math problems.

#### Data Collection and Analysis

##### What Is Data Collection and Analysis?

Data collection and analysis is the practice of applying mathematical knowledge (counting, sorting, classifying, comparing, contrasting) and processes to find the answer to research questions they are investigating. Children become natural data collectors as they learn about and make sense of the world around them. More systematic collection and analysis helps children understand how data can help answer specific questions.

##### Why Is Data Collection and Analysis Important?

Preliminary evidence suggests that engaging in data collection and analysis (DCA) builds mathematics knowledge, computational thinking, and may broaden inquiry skills over time. This is important because the mathematics skills that young children build during their preschool years predicts their later academic success in both math and literacy. Children will also become more critical thinkers and more systematic in how they can find the answer to questions they ask about the world around them.

#### Subitizing

##### What Is Subitizing?

Subitizing is looking at a group of objects and instantly seeing how many there are. Subitizing happens quickly, it’s knowing "how many" without having to count. It’s also understanding that the type, shape, size, and positioning of the objects you are looking at does not matter, you can have five ducks or five beads, it’s still five.

##### Why Is Subitizing Important?

Subitizing is key to developing overall number sense. Number sense allows children to understand concepts, ideas, and problems concerning numbers. It is the beginning of children’s understanding of key mathematical ideas and a precursor for addition and subtraction and arithmetic. For example, children learn that 2 dots + 2 dots equals 4 dots. In later grades, this helps children to count larger numbers: count by twos or tens or hundreds. Subitizing also helps children to eventually be able to perform mathematical operations in their heads. This is called mental math.

In preschool classrooms, the goal is for children to **develop an understanding of whole numbers and the concept of quantity**, which includes:

- counting
- understanding one-to-one correspondence (knowing each item counted corresponds to a number)
- cardinality (determining the total number in a group and knowing that the last number counted tells "how many" there are all together. For instance, the number four can represent a set of objects such as four blocks or four plates or four crayons)
- comparison (comparing sets of objects to see if there "more than" and "less than")
- identifying parts of a group or of a whole object

Subitizing activities will help children master these concepts, and children will increase their ability to subitize as they develop each of the skills mentioned above.

#### Equipartitioning

##### What Is Equipartitioning?

Equipartitioning is also often known as "fair sharing" or "equal sharing." There are several types of equipartitioning:

- Equipartitioning collections is when children distribute a set of objects equally or when they distribute multiple sets of objects equally, such as giving two children five buttons each from a pile of ten buttons.
- Equipartitioning continuous wholes is when children split an object into equal-sized pieces, such as cutting a brownie into four equal size pieces so that each of four friends gets an equal share.
- Equipartitioning collections and wholes is when a child combines both equal sharing of collections and wholes. For example, if there are three crackers to share between two friends, a child is equipartitioning both collections and wholes when she gives each friend 1 1/2 crackers.
- Equipartitioning is also identifying whether or not a collection or continuous whole has been equally shared or divided. This happens when children look at two or more collections and say whether or not these collections have the same number of objects or when they look at two or more divided portions and say whether the portions have the same amount.

##### Why Is Equipartitioning Important?

The ability to equipartition or "equally share" builds children’s foundational understanding of fractions, ratios, division, and multiplication. It develops children’s number sense and helps them understand parts of a whole and the ways in which larger numbers are composed of smaller numbers. For instance, when a child divides a pile of eight rocks between two friends, she sees that eight is made up of four and four.

In preschool classrooms, the goal is for children to develop this foundation by:

- Understanding that making equal groups of objects means putting the same number of objects into each group
- Understanding that making equal portions means splitting a whole object into same-sized pieces
- Practicing dividing collections of objects into equal groups
- Practicing dividing whole objects into equal portions
- Identifying groups of objects as being equal or having more or fewer objects than other groups
- Identifying portions of a whole as being equal or being bigger or smaller / having more or less than other portions
- Redistributing objects in groups of unequal sizes to make the groups equal
- Repartitioning unequal-sized portions of wholes to make the portions equal
- Exploring and understand different methods of equipartitioning collections and wholes
- Understanding that wholes can be divided and distributed as collections
- Counting a collection of objects
- Learning and reinforcing number names and symbols
- Using comparative language such as the same, equal, more, fewer, less, bigger, smaller

Equipartitioning activities will help children master these concepts, and children will increase their ability to equipartition as they develop each of the skills mentioned above.