Number Lines and Counting Lines Part 1

Number lines have been around forever. My teachers had a BIG one displayed at the front of the room and often a smaller one on everyone's desk. But I can't really remember ever being taught how to use it or if I even used it for that fact. Likewise, I've had them in my room and referred to them. I've shown the kids how to add and subtract on them. But to tell you the truth, it's just been another math tool the kids could use if they wanted to.

Not any more!

Some of you may be WAY ahead of me on this subject but I've been doing a little research on number lines and here's what I've found:

• Number lines are one of the most over looked tools in the classroom. When used properly it can help students improve number sense, operational proficiency, mental arithmetic, understand number relationships, and the position of numbers.
• In the Common Core, number lines are introduce in 2nd grade. (2.MD.6)
• The first way children encounter 'number lines' is as a line or row of numbers. This is NOT really a number line but is VERY useful and is called 'counting lines'. Some call it 'counting paths'.
• There are important differences between number lines and counting lines that PreK, K, and 1st grade teachers need to understand.
• Making a careful transition from counting lines to number lines is important. Number lines are not based on counting, but on measuring from a fixed point.
• The fixed point or origin is 0. The number that labels every point is the distance from the origin to that point. 
• A counting line does not have zero. So you can't show 5-5=0.
• Counting lines cannot show fractions or decimals or negative numbers.

My big 'AHA' was that in first grade, I'm not teaching number lines but I'm teaching COUNTING LINES and I'd better do it right so they can make the transition to number lines in 2nd grade!

This is an example of a counting line.

This is an example of a number line.

I found these great articles. You might want to take a look. (They are pretty short, not BIG research papers to muddle through.)

http://www.eduweb.vic.gov.au/edulibrary/public/teachlearn/student/mathscontinuum/readnumberlinewhole.pdf

http://bridges1.mathlearningcenter.org/files/media/rekenrek/numberline_overview.pdf

http://www.medindia.net/news/Research-How-Kids-Adapt-Their-Mental-Number-Line-Affects-Their-Memory-for-Numbers-73959-1.htm

http://riverdalemontessori.wordpress.com/2012/02/20/the-magic-of-the-number-line/

So what...? My daughter taught me that. She says, whenever she learns something new, she asks herself  "so what...should I do with this new piece of information? So what... should I change? So what... am I going to do differently? (Don't you LOVE it when your children become so wise and can teach YOU things!)

I don't want to make this post really LOOOOONG. So this is part one.
Come back tomorrow for my SO WHAT!!