Making Sense of Rounding

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.

Have you ever thought that maybe people who think they are not good at math really have just never been taught math in a way that makes sense to them? Personally, I think that’s behind a lot of our math problems. Take rounding for example. We teach kids a complicated procedure for rounding. And to make it easy for them to remember, we make up little rhymes:

Four or less
Let it rest
Five or more
Let it soar!

Catchy, huh? How about this one:

Find your place
Look next door

Five or greater
Add one more
All digits in front stay the same
All digits behind, zero’s your name

Well, at least that one mentions place, as in place value, but it really does little to make sense of rounding. It teaches kids to ignore the actual number and just consider the digits.

A while back I wrote about using an open number line to round numbers. I encourage you to check out that post; it even contains a little freebie you can download. Basically, the idea is that 46 rounds to 50 because it’s closer to 50 than 40. It’s really just that simple. Students need to be able to determine which two multiples of ten a number comes between and then just decide which one it’s closer to. The only thing that needs to be explained is that if it’s right in the middle, it rounds up to the next multiple of ten. Why? Because someone decided that it should a long time ago. The same idea, of course, works for rounding to the nearest hundred, or thousand, or tenth, etc.

I created some cards that can be used to practice rounding to either the nearest ten or hundred. There are four types of cards–2-digit numbers and 3-digit numbers, with and without labels on the number lines. These cards would be great for small group instruction. The cards with labels on the number lines offer more support as students are just learning the concept, and the cards without labels can be used to help students decides on which multiples the number is between on their own. In a workstation, the cards could be used for a good, old-fashioned game of War. Players each turn over a card, round their number, and compare the rounded numbers. The larger rounded number wins. What to add some computation into the mix? Have players record their rounded numbers and add up the rounded numbers. The player with the largest sum after five rounds wins. Cards are so versatile, which is one reason I like to create cards and use them for instruction.

Grab your free cards here. I’d love to hear how you use them in your classroom!

11 Comments

  1. Sue

    A great article. I need to share it with my peers!
    Thanks

    Reply
  2. Louise Ferguson

    Thank you for sharing your fantastic ideas!!

    Reply
  3. Maureen Beyrer

    We use a vertical number line in teaching rounding. It is even more powerful than the horizontal line.

    Reply
    • Vanessa smith

      can you explain this please

      Reply
      • Donna Boucher

        A vertical number line goes from floor to ceiling. The thinking is that it’s more intuitive for students to see smaller numbers at the bottom with numbers getting larger as the number line gets taller. Check out this blog post for more information.

        Reply
  4. Carol Green

    Surely we need to remember ‘bankers rounding ‘ where the .5 rounds to the nearest even integer… 1.5 =2 and 2.5 =2?
    Any thoughts?

    Reply
    • Donna Boucher

      Oh! Really? I have never actually heard that before. I just Googled it, and of course it is a thing. I know when I taught rounding of decimals in 5th grade, we followed “regular” rounding rules.

      Reply
  5. Marisa Tindel

    I totally agree with you! Kids need to understand math. What advice or suggestions do you have for rounding really large numbers like 3,425,780 to the hearts ten thousand’s place? This is always where my 4th graders struggle.

    Reply
    • Donna Boucher

      You can still use the same method! Which two ten thousands is the number between? 3,420,000 and 3,430,000. What’s right in the middle? 3,425,000. Which side of 3,425,000 is 3,425,780 on? Again, make sure to show it using the open number line. And I would definitely introduce the strategy with small numbers (hundreds, thousands, etc.) and then extend it to the ten thousands.

      Reply
      • MCraig

        I believe what she was referring to is the fact that students have such a hard time with the larger numbers. My students struggle to tell me (or cannot at all) tell me the two ten thousands the number is between. Smaller numbers do not bother them, but they just do not have a lot of practice with larger numbers. I try to give students as much practice with large numbers as I can before I have to do rounding, but it comes at the beginning of the year about the third or fourth week of school. That is just not enough time for most of my students to get comfortable with the larger numbers. Any suggestions at speeding up the process is appreciated. (The pace of our curriculum is really difficult with students. Especially now with COVID.)

        Reply
  6. Andrea

    just shared this with my 3rd gr team. children need to know what the number represents before they can understand how to round it.

    Reply

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