## Growing math minds... Changing math mindsets

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Students recognize and distinguish measurable attributes (e.g., length, area, volume) from non-measurable attributes (e.g., big or bigger). Initially, many students will not be able to differentiate between these two types of attributes. Students will say one object is “bigger” than another without clarifying that it is longer, greater in area or volume, and so forth.

For students to accurately describe attributes such as length and weight, they need multiple opportunities to informally explore these attributes. Teachers encourage students’ conversations to extend from describing objects as big, small, long, tall, or high to naming, discussing, and demonstrating with gestures the appropriate attribute (e.g., length, area, volume, or weight).

For example, a student might describe the measurable attributes of an empty can or milk carton by talking about how tall, wide, and heavy the can is, or how much liquid will fit inside the container. All of these are measurable attributes. By contrast, non-measurable attributes include designs, words, colors, or pictures on the can.

As students discuss these situations and compare objects using different attributes, they learn to distinguish, label, and describe several measurable attributes of a single object. Kindergarten students connect counting and ordering skills and understandings to help them classify objects or people into given categories, count the number of objects in each category, and sort the categories by count.

Students identify similarities and differences between objects (e.g., size, color, shape) and use these attributes to sort a collection of objects.

Students compare the number of objects in one group (with up to 10 objects) to the number of objects in another group. Students need a strong sense of the relationship between quantities and numerals to accurately compare groups and answer related questions. They may use matching strategies or counting strategies to determine whether one group is greater than, less than, or equal to the number of objects in another group.

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