## Count, Represent, and Recognize Numbers 0–31

Numbers and quantitative relationships are the first things that many people think of when they try to describe mathematics. Indeed, through the ages, people have devised systems of counting, recording numbers, and performing operations such as addition and subtraction of numbers.

In counting different objects, children must learn to represent and use numbers in different contexts. They might count other children in line, days on the calendar, or beads needed for a necklace. As they learn to say number names by rote, children learn that they must account for each item in a collection; however, they may start by counting any of the items. Children must learn to answer the question “How many are there?” The last number named when counting tells the answer. Children may also need many experiences to learn about number conservation, which means that no matter how a set of objects is arranged—close together or far apart—the set has the same number of objects. Finally, children learn how ordinal numbers such as first, second, fifth, and tenth tell about the positions of objects in a sequence.

Children must learn to represent numbers orally, with dot cards, drawings, snap cubes, and other manipulatives as well as with written numerals. Building from their knowledge of one and two, children develop ideas of numbers three through five. Just as they can show four counters and use one more to compose five, children also learn that five can be decomposed, or broken down, as four and one, three and two, and so on. Children also learn to use zero as the number that tells how many school buses are in the classroom or how many 100-year-old classmates they have.

**Teaching Model:** Count, Represent, and Recognize Numbers 0-31