What is number sense?

Do you ever hear people talk about terms in education and wonder, “Hmmm…I THINK I know what that means…” or “That isn’t what I THOUGHT that was…”?
Me too.
I hear people say “reader’s workshop” and I wonder if they define it the same way I do.  I hear people say “project based learning” and “formative assessment” and “close reading” and I wonder if I really know what they mean.  Feel the same way?
I think the same can be said for “number sense”.  I know teachers are always talking about “number sense”–but I bet each one of us defines it differently and has different ideas about what it means.  So I’m curious…when you hear the term “number sense”–what thoughts go through your mind?  Here’s what a few “experts” say…
1. Number sense essentially refers to a student’s “fluidity and flexibility with numbers,” (Gersten & Chard, 2001).
Marilyn Burns describes students with a strong number sense in the following way: “[They] can think and reason flexibly with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different wayssee connections among operations, figure mentally, and make reasonable estimates.”
The National Council of Teachers in 1989 identified the following five components that characterize number sense:
Number meaning

Number relationships
Number magnitude
Operations involving numbers and referents for number
Referents for numbers and quantities

Using number lines can accomplish SO much of this…if the number line activities force students to think and reason.  I truly believe number line use can be one of the most valuable teaching tools we have available to us–and we can model how to use number lines on the fly OR can provide careful, scaffolded practice in small doses to really keep students thinking and analyzing.  Number line problems are very easy to create–but if you want a ton of great problems all ready to print and use, you might be interested in these!  I’d love to know what you think…