Vocabulary for Number Sense/Counting Unit:
- Number Sense: A person's ability to use and understand numbers,
· knowing their relative values,
· how to use them to make judgments,
· how to use them in flexible ways when adding, subtracting, multiplying or dividing
· how to develop useful strategies when counting, measuring or estimating.
- Counting/Natural Numbers: the numbers we count with.
- Whole Numbers: the counting numbers and zero.
- Rational Counting: students attach the correct number name to each object as it is counted (one-to-one correspondence).
- Numeral Principle: any group of objects can be printed.
- Stable Order Principle: counting in a fixed sequence (names of numbers and the order they come in)
- One-to-one Correspondence Principle: each object is counted once and only once (each object has a unique name)
- Cardinal Principle: the last number counted tells ushow many objects are in the set
- Order Irrelevance Principle: a set of objects can be countedin any order and any direction
- Abstraction Principle: objects of any kind can be counted.
- Counting On: counting forward from any number (foundation for addition)
- Counting Back: counting backward from any number (foundation for subtraction)
- Skip Counting: counting by a value other than one (usually start with 2's, 5's, and 10's -- foundation for multiplication)
- Classification: the ability to sort objects based on attributes. Simple Classification - the ability to sort objects into discrete groups.
Multiple Classification - the ability to sort a set of objects in more than one way with the understanding that sometimes objects can belong in more than one attribute category. Class Inclusion - the ability to sort a set of objects in ascending and descending hierarchies, understanding that major groups may have subclasses. - Seriation: the ability to arrange things in a sensible order, such as arranging a set of rods according to increasing or decreasing length.
- Subtizing (Sight Recognition): the ability to determine if two sets are equal in number, regardless of the size, arrangement, or order of the objects in the set. (definitions above from Dr. Stohr-Hunt's Notes for class, Content and Pedagogy for Elementary Math)
- Some Examples of Counting Manipulatives (Images below ):
1) Base Ten Blocks
2) Ten Frames 3) Cuisinaire Rods 4) Dominoes