Early Math Big Ideas

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Big Idea One

• 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 when two identical right triangles are combined to make a rectangle).

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Big Idea 2

• 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 circles, rectangles, triangles and other common two-dimensional shapes.

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Big Idea 3

• 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. As children sort and classify shapes with knowledgeable others, they become aware of rules about shapes, such as that a triangle has three sides and three angles (corners), that a cylinder has a rounded form with two flat ends that are in the shape of a circle, or that a sphere has only one continuous curved side. That these sorts of precise distinctions can be made is not immediately obvious to young children; for this reason, it is important that teachers design activities to demonstrate this.

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Big Idea 4

• 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 in this skill when teachers provide concrete and pictorial experiences with spatial transformations, such as cutting an item in half, flipping it upside down, or rotating it to make it “fit.”

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Big Idea 5

• 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 different positions. It will take time before they understand that when they are face-to-face with their friend, something on their left appears to their friend on her right, but early experiences can prepare them for this type of sophisticated thinking.

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Big Idea 6

• 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 understanding of space. If the response is a gesture or a phrase such as “over here,” you can take advantage by saying, “that’s right, we keep them in the coffee can on the shelf by the window,” modeling a much more precise response. If your spatial language is rich and precise, over time, children’s language will become more specific, as will their understanding.

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Big Idea 7

• 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 analysis. Emphasizing this makes the entire process of analyzing data make sense to young children.

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Big Idea 8

• 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 have experience answering different types of questions, they begin to see that data becomes most helpful when it is visually depicted, and that these depictions will differ depending on the question at hand.

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Big Idea 9

• 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 it might be the most effective way to answer a difficult question, they have the piece of information that makes data analysis something they might want to know more about. Knowing the purpose of data analysis motivates children to try it and to try to understand how it works.

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Big Idea 10

• 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 in measurements that are more exact and ultimately more useful.

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