Rounding on an Open Number Line - Math Coach's Corner

Rounding on an Open Number Line

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

Rounding numbers is one of those skills that is often taught using “tricks” and “rules”. Don’t believe it? Google “rounding to the nearest 10” and take a look at some of the pages returned by the search. Let’s agree instead to teach rounding for deep conceptual understanding, and I have an alternate approach to offer.

First of all, students need to understand why we round numbers for the skill to make sense to them. We round numbers when a “close” number is good enough. It makes the numbers easier to work with. My favorite real-life example is shopping in a store. I am clothes shopping and I only have $50 to spend. I’m looking at a shirt that is $27 and pants for $19. Those numbers are not necessarily easy for me to work with in my head. But, $27 is really close to $30 and $19 is almost $20. And $30 + $20 I can do easily in my head. Looks like I’ll have enough to buy both with my $50!

Next, notice how I rounded. To round $27, I didn’t pull out a pencil and paper, underline the 7, tell myself that 7 is more than 5, so the 2 becomes a 3. Nope, I just know that $27 is closer to $30 than $20.

When we teach tricks, we often take the meaning out of the process. That’s why you see a student somehow round $27 to $40 or some other unreasonable number. They don’t remember how to do the “steps”, and that’s their only strategy. They’re not really thinking about what it means to round.

After setting the stage for why we round numbers, I move to the actual rounding process using a number line.

Teacher: I want to buy a shirt for $27. I wonder about how much that is? Let’s see if we can find out. Can you find 27 on the number line? (student uses a yardstick to point to 27) Good! We’re rounding to the nearest ten, so which two multiples of 10 is it between on the number line? (student points to 20 and then 30). That’s right. Twenty-seven is between 20 and 30. Which is it closer to? (student points to 30)

We practice this with additional numbers. The cool thing is that this approach can also be used with numbers over 100. If we’re rounding the number 131 to the nearest ten, it’s between 130 and 140 on the number line, and it’s closer to 130. Furthermore, the process is the same when we’re rounding to the nearest hundred–only now we’re asking which two multiples of 100 the number falls between.

So what do you do with that pesky 5? It’s not closer to either multiple of ten. That’s an interesting lesson, too. We start with the multiples of ten, and I ask what number falls right in the middle. They see that between 60 and 70 is 65. Between 90 and 100 is 95, between 130 and 140 is 135. And guess what? Between 100 and 200 is 150. And between 2,000 and 3,000 is 2,500. The kids see that the middle number always includes a 5, so they generalize the old traditional rounding rule. Then I just tell them that since it’s right in the middle–not closer to either one–somebody at some point made the decision that we would round those numbers up.

After the kiddos get lots of practice on a regular number line, move to an open number line. Now the kids write the two multiples of ten (or hundred), the number in the middle, and they place the number they are rounding.  It’s looks something like this:

Here’s a couple of rounding printables you can use for a little assessment.

  

Click here to grab yours!

44 Comments

  1. Storie

    I have taught and re-taught in as many ways as I can possibly think. I find that students who do not have a strong number sense foundation are the ones that struggle the most. I’m downloading the number line pages in hopes that it will help my students this year 🙂 Thank you!!
    Storie
    Stories by Storie

    Reply
    • Donna Boucher

      I have found working with number lines to be very effective. Just be sure to use the regular number line (with all the numbers) until they understand the concept. Then move to the open number line, like on the worksheets. Good luck!

      Reply
  2. Alison Hislop

    Hi Donna,

    Thanks for sharing. I have always used a roller coaster to demonstrate rounding (with 1 – 4 on the upslope – they roll backwards and 5-9 on the downslope so they go to the next ten) – I like your idea for older children!

    Alison
    mathswithmeaning.blogspot.com.au

    Reply
    • Donna Boucher

      Right, I know the roller coaster is popular. We typically begin rounding in 3rd grade, and I’d start right in with the number lines. I have also seen a 100 chart used, and I like that as well. The number lines and the hundred chart connect them to the bigger idea and strengthen their number sense.

      Reply
  3. Simone

    I had always used the rules bc that is how I was taught. Every year, I found that my students did not get it. Then I recently discovered the number line for teaching rounding and a light bulb went off. I was making real number lines with tick marks and found it overwhelming. I love your idea of using a simple open number line. I can’t wait to try it this year with my 6th graders. This will work great for large numbers too.

    Reply
    • Donna Boucher

      Exactly! We usually teach how we were taught until we find something different. I’m glad the number line was successful for you ans your kiddos. Yes, open number lines are an awesome tool! And you’re right–it works for numbers of any magnitude.

      Reply
  4. Anonymous

    Your ideas are very helpful. I will be teaching third grade this year- a move from kindergarten- and I have taken copious notes! Thanks for sharing so much:)

    Reply
    • Donna Boucher

      That’s quite a jump! I’m glad you’ve found my blog useful. 🙂

      Reply
  5. Justwright

    Thank you, Thank you. I have been looking for a “trick” that works for my students. This makes so much more sense!

    Reply
    • Donna Boucher

      It’s all about making sense of the mathematics! This should do the “trick”. 🙂

      Reply
  6. Dee Dee

    Thanks so much! We still have not adopted a math curriculum, and our “old” one does not target deep understanding. This week is ’rounding’ and ‘estimating’, so this came at the perfect time!

    Reply
    • Donna Boucher

      Great! I’m glad it was well-timed for you!

      Reply
  7. TC Booth

    Thank you Donna. 🙂

    Reply
    • Donna Boucher

      It’s my pleasure!!

      Reply
  8. Anonymous

    I also teach the number line. I draw it oustide on the sidewalk with chalk. Each student gets a number and has to find their spot on the number line. Discussion is then held about how they knew where to stand and how close theys atnd to the multiple of 10. This would then bring that right inside. Love it!

    Reply
    • Donna Boucher

      Oh, that’s a great activity! Love the kinesthetic approach. 🙂

      Reply
  9. Anonymous

    Thanks, Donna! You explained it beautifully!

    Reply
    • Donna Boucher

      Glad it was helpful! 🙂

      Reply
  10. Anonymous

    I have done that number line for years and I have been teacher over 30 years. The kids really understand and for those who are visual learners it is really great!

    Reply
    • Donna Boucher

      Right! This is not a new idea, but it definitely one that kiddos get!

      Reply
  11. Anonymous

    I am working with my third graders this week on rounding. I was trying to get them to “see” where the numbers fall on a number line to decide whether to go up or down. I teach at a Montessori school, so I got out the cards for 10, 20,30 etc and laid them down with a space between them. Then I wrote numbers on other cards, like 57 and we placed it between the 50 and 60 and then decided on whether it rounded to 50 or 60. The part they were having trouble with was what 2 numbers should the number in question go between, ie some were confused what their choices were! These sheets will be perfect as we move on to rounding to hundreds. We can place the numbers between the hundreds on the floor, then they can do the sheets later in the day.

    Reply
    • Donna Boucher

      Ooh! I love the kinesthetic approach! You’re right that kids have trouble determining which tens a number falls between. Having a full number line in the room helps support that, but I also ask, “If I was counting by 1s, which two tens would I hear this number between?”. So if the number is 54, they might try counting by ones starting at different tens (maybe 40, 50, or 60, because those are closest to their number), but they’d only hear it when counting from 50 (51, 52, 53, 54!).

      Reply
  12. Fontenot's Firebreathers

    I used to teach the roller coaster way…then I still had students not grasping the concept, but they did not….when I use the number line…. I simply ask what is 27 closer to? 20 or 30? Then I give them a number and let them brainstorm with a partner. I have heard some good discussions this way! I try to tie it to money or food or something they are into (pokemon cards for example—yes that is a bit out of date, but only thing I could think of!). They do understand it…then we talk about rounding and compatible numbers…etc.

    Reply
    • Donna Boucher

      You are so right about connecting it to a real life example! Money is great, because it’s something they are all familiar with. So nice to hear how you “teach” it, too. You basically pose a problem and let the kiddos talk it out. Hooray for problem solving!

      Reply
  13. Mary

    I would love to find number lines that help with various ways to round a large number. I find that my 4th graders have trouble rounding 456,375 to different place. They like to round to the largest place only.

    Reply
    • Donna Boucher

      That’s the beauty of the open number line, Mary! If, for example, you want them to round 456,375 to the nearest thousand, they would make a number line with 456,000 on one end and 457,000 on the other. What’s right in the middle? 456,500. Is 456,375 closer to 456,000 or 457,000? Well, it’s not to the halfway point (456,500), so it’s closer to 456,000.

      Reply
    • Anonymous

      Donna, I want to piggy-back on Mary’s statement/question. My fourth graders also struggle with rounding and I would really like to use the open number line approach. I’m trying to get away from the tricks! The problem I see with the larger numbers is that they have trouble identifying which “thousand” the number 456,375 is between. I read an earlier comment that you responded to by saying “if you were counting by ones which two tens would this fall between?” Do you have any suggestions as to how to help students identify them when the number is too large to count? I’m going to give this a try but let me know if you have any advice. 🙂

      Krista

      Reply
      • Karen

        I am working with a group of 4th graders and this is exactly the problem we are having with the larger numbers as well. Any advice?

        Reply
        • Donna Boucher

          Open number lines work for any magnitude of numbers! I would start smaller and let them see the patterns, and then just let them put larger numbers on their open number lines.

          Reply
      • Denise

        I’ve found this method helps some of students to look at chunks of numbers:
        If they are rounding to the tens place in the number 4,567 I would have them underline the tens place and everything to the LEFT, then make a box around that number. Sometimes I have them use a sticky note to cover up everything to the right of the place they are rounding. So they would have 456 boxed in. Replace the other digits with a zero for the placeholder. 456(0) This would be their ‘lower’ ten and if they are counting on, the next ten would be one more than their boxed number and their ‘upper’ ten would be 457(0)

        Reply
  14. Leah Routley

    Great post! But I have to nitpick. “Between 90 and 100 is 95, between 130 and 140 is 145.” Between 130 and 140 is 135, not 145.

    Reply
    • Donna Boucher

      Thanks for catching that, Leah! Fixing it now. 🙂

      Reply
  15. Anonymous

    I like to use measuring tapes with my resource students. I have them highlight the tens with a marker. For kids who don’t have the number sense to use an open number line, this is a great visual lesson.

    Reply
    • Donna Boucher

      Ooh, I like that! Anything that adapts to the kiddos’ needs is good. 🙂

      Reply
  16. Nikki F

    Just a couple if years ago I finally heard a “reason” for why rounding the 5 goes up. When numbers 5-9 are added to each other they make a number with ten or more. Numbers 1-4 when added to each other do not make a ten.

    Reply
  17. Julie

    Hi Debbie – Love your number line lesson! Do you a free printable number line that you recommend to use with this lesson? Or are you just writing the regular number line w/all the numbers on a whiteboard for all kids to see?

    Reply
    • Donna Boucher

      I use an open number line, Julie, which includes only the numbers I need to round the number I’m working on, so I just write it on my white board during the lesson. The post does include some printables you can use for practice.

      Reply
  18. Laura

    I absolutely LOVE this lesson! I am working on my Elem. Math Specialist Degree and this is EXACTLY what we are learning. Students MUST understand the concept to attach real meaning to and to connect further concepts down the road. Tricks may work for some, but can be forgotten. This develops number sense that will help them so much more in the long run! Thank you so much and thanks for the freebies!

    Reply
  19. Diane

    Hi Donna

    I’m an Aussie teacher and a big fan of your work. I came to your blog today to read your Formative 5 post and saw this post first. Perfect timing!!! I was just programming for next weeks maths on rounding and estimation 🙂
    I had a stairs graphic to show the kids…its now in the trash bin and a link to this page has replaced it in!!!!

    Reply
  20. PENNY GREENLER

    great work! exactly what I was looking for to teach Rounding on an open number line and you have it made for us. thank you

    Reply
  21. Marion Morrin

    Im delighted with this resource – just what I need this week. It makes so much sense. Thank you!

    Reply
  22. Kate Blackmore

    Thank you, this is a great explanation. I asked my daughter (who is ten) what she knows about rounding and she said: Let’s pretend you want to round something that is 33c – you have to decide whether to round it up to 35c or down to 30c. It hadn’t occurred to me that she would do that over rounding to the nearest 10 but that’s because here in Australia we have no 1c or 2c coins. I can include her knowledge in my lesson too.

    Reply

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