Why Number Lines?

Last year, a friend brought this to my attention:

 

As an educator, I'm often asked my opinion of Common Core State Standards.  I can only speak for math, but in short, Common Core Math Standards are not much different than the standards Florida has used during my (going on) eleven years teaching.  Are the benchmarks more rigorous than when we were students?  Absolutely.  Does this require educators to use non-traditional methods to achieve deeper understanding?  Yes.  When gradually and reasonably challenged, do students rise to the occasion?  Indeed.

Enter my current favorite encouraging phrase:

Aren't most things difficult (or at least more time-consuming) when they're new or you've had little practice?  That's a natural consequence of learning, and fortunately, we often obtain the greatest results when we persevere through struggles.

So here's why number lines:

• We live in a visually-stimulating world.  Number lines allow students to visualize (see) real life situations that can be solved using mathematics.
• Numbers are flexible and interact with other numbers.  Number lines help students build number sense, understanding how numbers work:
• Numbers can be decomposed (taken apart) and composed (put back together).
• Landmark/Benchmark Numbers (familiar numbers that are easy to locate/recall) can be used on number lines to help efficiently compare numbers.  
• This helps us make reasonable estimates, because in some real-life situations, we don't always need exact numbers.  
• Modeling operations (addition, subtraction, multiplication and division) on number lines helps students understand operations' effects on starting and ending numbers.   Again, number lines are a terrific way to see these things in action.
• Number lines help students communicate their problem-solving process.
• Number lines are an excellent checking strategy--they help students find, understand, and correct computation mistakes.

And while we're at it, here are some misconceptions about number lines we'll address through using them this year:

• Number lines are always horizontal.
• Number lines always begin with zero.
• Numbers on number lines must be written least to greatest.
• Number lines are only useful for operations with whole numbers.

Bottom line: In real life, we find ourselves in situations where we have a problem, can solve it using mathematics, and need to do so quickly.  Sometimes we don't have paper handy and need to find an answer quickly in our head.  What students model on a number line, we adults often do mentally without much thought.  We're dealing with young learners who haven't had as much life experience/practice opportunities.  Using number lines provides meaningful experiences with numbers.  

Of course with with greater numbers (beyond 1,000), standard algorithms (procedures that always result in correct answers when performed correctly) are both appropriate and efficient.  And, yes, we'll eventually teach and use those. 

As the frustrated parent pointed out, everyone wants to do things efficiently, but do you really need to break out writing tools in daily life situations like comparing prices or figuring out how much of something is left?