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Counting
Counting a collection by matching each member with exactly one number word, knowing that the last number said tells how many, and comparing collections by counting or by pairing.
math.number.counting
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Se basa en
Requisitos previos obligatorios, hasta el fondo: 1
Aprenderás a
- Count a collection of up to about 100 objects, saying exactly one number word for each object.
- Explain that the last number word said tells how many objects there are, whatever order they were counted in.
- Compare two collections by pairing their members one-to-one and by counting.
Definición
- Counting matches each member of a collection with exactly one number word, in order, without skipping or repeating.
- Two collections have the same number of members when their members can be paired up exactly, with none left over.
- Zero is the number of members of the empty collection.
Teorema
- The number of members does not depend on the order of counting or on how the objects are arranged.
- If the members of two collections can be paired with none left over, counting them gives the same number.
- Every counting number has a next one, so there is no largest counting number.
Errores frecuentes
- Thinking that spreading objects out makes more of them.
- Counting an object twice, or skipping one, when the objects are not in a line.
- Believing the last number word names only the last object rather than the size of the whole collection.
Conduce a
Descubrimientos opcionales
- Countability and Cantor's diagonal argument Pairing members one-to-one, rather than counting, is how mathematicians compare the sizes of infinite collections.
Itinerarios de aprendizaje
Lecturas complementarias
- Hung-Hsi Wu, Understanding Numbers in Elementary School Mathematics (2011)