Number Sense is a complex understanding of the meaning of a number. Number sense is not memorizing a sequence of names of numbers and reciting them, like an advertisement jingle. Number sense is not memorizing facts such as one plus four equals five. Let's think about the number five.
Five has character qualities like a person has personality. What do we know about five-ness? Being five means being half of ten, a very convenient thing! Being five means having parts such as two, three and four. Being five is like a four sided box with a dot in the middle like a domino or dice five. Five has one hand's worth of fingers and there are four fives if you include fingers and toes. Five multiples, such as fifteen, twenty, twenty-five, thirty...creates a wonder cadence and rhyme when spoken aloud. Five is odd. Five is prime. Five is a nickel. Five is wonderful.
The way we learn about five is by spending time with five, like a friend. We must see Five in a variety of situations before we realize all of the wonderful characteristics that Five has.
Children must understand number sense before they can mentally manipulate quantity. For example, without a clear sense of the quantity of five, mental addition will always be a matter of counting by ones. Once a child gains number sense, they can manipulate groups as though they were single units.
A great resource for developing number sense is Coming to Know Number by Reynolds and Wheatley. For children in grades 5 through 8, Developing Math Fluency continues with strategies for older kids. Check them out!