Students in Kindergarten and first grade need to gain fluency with small numbers as a foundation for learning about larger numbers. Fluency means being able to visualize, combine and decompose small numbers. Small numbers are usually split into numbers up to 5, and then numbers up to 10.

Subitizing means that you can recognize how many are in a set without counting. Being able to recognize and estimate small amounts increases childrens ability to think about numbers flexibly. Almost everyone can subitize amounts up to 3--it's easy to see without counting how many 1, 2, or 3 are. Above 3, we rely on patterns we are familiar with to recognize amounts. You can probably easily recognize 4, 5, and 6 dots if they are arranged in the pattern you find on dice, but you'd have more trouble if it were just 4, 5, or 6 dots in a line. There are several ways to organize dots or amounts so that they can be readily recognized without counting. Some valuable skills are:

• Recognize dots on a die without counting
• Be able to hold up a given number of fingers without counting (if the teacher says--hold up 7 fingers, children should be able to put up 7 fingers without counting them)
• Recognize dots on a 10-frame in standard positions without counting

You can extend the dice dot patterns up to 10 in several ways. Think about this version for 7, 8, 9, 10: