Thursday, December 27, 2012

Number Lines, Number Sense

Well...it's time to start thinking about upcoming units in my fourth grade studio--and I wanted to share with you something I have been doing more and more of this year with great results.  I challenge you to think about how you can incorporate this simple strategy into your math instruction over the upcoming months.

As you all know, number sense is critical for students as we work to develop well rounded mathematical thinkers.  It isn't enough to be able to DO math, students need to be able to UNDERSTAND math, to reason about math, to talk about math, to explain about math, and to be able to apply math.  One thing that I have noticed is that my fourth graders (even my mathematically best and brightest) are very computation based.  They quickly learn algorithms and solve problems but sometimes the trickiest questions trip them up. consider the following number line I presented to my students earlier this year.




My question--"What number would go by the blue line?"  Trust me, I truly thought this was an easy one...a "no brainer"...a "warm up".  What happened was astonishing!  My students (especially the mathematically best and brightest!) all started yelping about how easy it was, blah blah blah.  When I asked for the answer, I got the following:

It's so easy!  It's 2,000 because 5,000 - 1,000 is 4,000 so you take half of that!

and

It's so easy!  It's 2,500 because the number line goes to 5,000 and the blue line is halfway!

Fascinating, right?  So...needless to say...we changed our course for the day and tackled number lines and thinking about numbers.  We created all sorts of similar number lines...we changed the starting and ending numbers, we changed the "blue line", we tried fractions and decimal, we tried adding in negative numbers.  Most importantly, we LOOKED CLOSER (see earlier post!!!) and really started paying attention to number lines.  We have amazing discussions--truly amazing discussions, and I am convinced many of my students are changed because of it.  We have continued to work regularly with number lines, and I can honestly say that simple problem has dramatically deepened students' mathematical understanding.

 So...my challenge to you is this:  How can YOU incorporate number lines into what you teach in math?  What other ways can you use them?  I actually use number lines as exit slips...I give problems similar to the one above and ask students to explain their thinking.  I'll even give problems as open ended as "Design a number line that accurately shows me where 0.35 and 2.5 would be. Explain your thinking."  Another favorite--have students build a number line with a "mystery blue line" and exchange it with a partner.  Have the partner write the missing number and explain their thought processes.  The two students need to come to agreement about what number should be there.

What do you think?  Do you use number lines?  How do you use them?  Let's share our best ideas here!

(NOTE:  Try these problems with your teacher friends...you can learn a LOT about their own mathematical understanding!  We had a teacher who had her eyes really opened about number sense when we tried these at our team time!)


One kiddo working on finding "equal parts" on a number line moving from 0 to 1.







10 comments:

  1. I just LOVE your blog and gave you a RACK (random act of kindness) in my recent post! You can choose any item from my TPT store. Thank you for the number line post today. I really enjoyed it:) Check out my post at the link below and send me your choice from my store!
    ~Holly
    Fourth Grade Flipper

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    1. Wow! Thanks, Holly! I appreciate your kind words...I have fallen in love with blogging, and it makes me happy to think that others might be getting something out of my little piece of "Cyberland"!

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    2. It is addicting helping others and in turn getting inspired, isn't it? I can't find your email (comment is the no-reply blogger). Can I send you the fraction centers or something else from my store?
      Send me your email and I will get it out to you:)
      Thanks!
      Holly
      Fourth Grade Flipper

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    3. Hey there Holly...I sent you a message with it on your TpT page. ;)

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  2. Fascinating how some kids' (and adult) minds work isn't it? I can totally believe their thinking pattern having had the same experience in my classroom. I've also had my co-teachers coming in with a logic problem to explain to me that it "doesn't work" (it did!) and needing to have it explained to them :) We've used number lines for fractions, negative numbers, skip counting and we designed an interactive number line display for parent night. (That was my first inkling that some of my little ones didn't have a clue about number lines when I saw how they labeled them!) :) We went back to the beginning as well.
    Lynn

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    1. Thanks, Lynn! I would love to see the interactive number line you designed!

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  3. You never posted an answer to the half way point between 1,000 and 5,000.
    answer: 3,000

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  4. I found your blog through Pinterest. Your blog is so wonderful; I will be back often to check it out. Thanks for sharing.

    Janna
    Fabulous Finch Facts

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    1. Thank you so much for your kind comments! I hope you DO come back often! :)

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