Rounding is one of the worst things in the world to teach, right? It is classic every time. Mention rounding…kids sigh, teachers tense up and everyone’s brains feel muddled. It is HARD to understand rounding when you don’t have strong number sense.

I used to teach every trick under the sun for rounding. I tried the rounding mountain, I tried the rounding coaster. I even would break it down for kids and have them underline the place, circle the number next to it, check to see if it was 5 or higher. There were SO MANY problems. Kids couldn’t figure out the place value, where to start, what to change, what to look for or even what the number was in the end. A few students would understand it, and it would stay that way.

That was when I realized they weren’t understanding the concept behind the tricks. They couldn’t remember the rules of the tricks (not even when it was a rhyme, because they only memorized the rhyme and didn’t get how to use the trick).

** So I threw all of it away**. I took down all of my rounding roller coaster and rounding mountain anchor charts. I decided to start fresh. I told my students this year to FORGET everything they ever learned about rounding.

Then, we counted by tens. Not just 10, 20, 30, 40, 50 60, but also 110, 120, 130, 140, 150. We counted by hundreds in the same way. We talked about what nearest ten and hundred mean. We made number lines that counted by tens and hundreds. THEN, we began rounding numbers.

And this is what we came up with as a class:

It was so simple. If you are asked to round to the nearest ten, begin counting by tens by making a number line. Find the closer ten by checking how many spaces away it is from your number. As we worked with more numbers, they uncovered the mystery of the 5. “What do we do if it is in the middle?!” We round to the higher ten, because that is what the world decided to do so that everyone does it the same.

We could also round to the nearest ten in numbers in the hundreds, because we practiced counting by tens in the hundreds.

We can also round to the nearest hundred in this same simple way!

This whole entire thing was AMAZING. After several days of practice students weren’t drawing out number lines anymore, they were able to picture them in their heads.

On my pre-test I had 5 students who could round to the nearest ten and hundred. By the post-test every student except for ONE student could do it. Only one! I have been able to sit down with that student each day as he comes into school, and he’s getting it now, too.

It made me realize that tricks really aren’t for kids. When students don’t understand the WHY behind the trick, the tricks don’t work. If they don’t understand the number sense behind rounding, no matter what number they underline or look at, it won’t be solid conceptual understanding, and the trick will get mixed up.

Love it! I did the same thing. Number lines work much better than that “5 or higher go higher, lower than 5…” trick. So many kids would think 32 rounds to 20 because “2 is lower than 5, so we go lower.” GAH! It was a hard transition for me, but after 2 years of trying it I’m sold; it really does help the kids more. 🙂

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Amber, I only wish it hadn’t taken me 7 years to figure this out! I am hoping this method helps when they need to round even trickier numbers, too.

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Yes! Yes! Yes! I LOVE your title “Tricks are NOT for Kids”. I agree the number line develops true understanding and supports number concepts.

Brooke

Tales from a Fourth Grade MathNut

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Hey Brooke,

Thanks for taking the time to comment! I think we need a whole blog titled Tricks are NOT for Kids so that we can share strategies for ALL those tricky concepts. 🙂

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I love your thinking. I just found your blog through pinning one of your pins on pinterest. I really focus on pinning things that are meaningful and have a conceptual approach.

Tricks really are so SHORT term that they rarely transition to deeper learning. I push this type of thinking at my school as a math coach. Conceptual understanding is so important to really making learning meaningful. Thank you for your insight.

Greg aka Mr Elementary Math

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Greg,

I would LOVE to be a math coach, but alas our district doesn’t have the funds for that type of position. It is something I aspire to be.

Thanks for taking the time to comment, I am your newest follower on TpT. 😉

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I totally agree! I started teaching rounding this way last year, but I use a road trip concept. I use a toy car and discuss how a number line is like a road. Gas stations are at every ten (or at every hundred, depending on what you’re rounding it to). The number we’re rounding is where you realize “you need to get gas”, so which gas station is closer? This also helps with the 5 being in the middle concept, because we talk about how it would make sense to go forward in the direction of your destination, instead of going backwards 5. The kids have a MUCH better understanding of this when they have a real understanding of the WHY. 🙂

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Wow, what a great idea! That analogy makes it even MORE real world for kids. I love it! Thanks for sharing your idea.

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I am so grateful to see this post! I had just decided to introduce rounding to my second graders when a third grade teacher at my school mentioned that was what her class struggled with the most. I figured I’d give my kids a leg up and introduced the skip counting by tens into the hundreds and used the number lines as well. When I mentioned introducing rounding to my class, my lead teacher said “Oh! I have the perfect thing for that! It’s a rounding mountain!” I tried it and the kids had no idea what I was talking about so I went back to the number line. Thank you for reassuring me that I made the right choice!

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Thank you Rochelle! Sometimes I know I am quick to say “Oh, it’s just a hard concept for them” rather than look at my own teaching practices. This is a large reason why I started this blog, was to really look at what I am doing and hopefully have others share with me, too! I truly believe we can reach many more students if we look closely at new ways. Sometimes it is easier to just teach it how we’ve always done it, so I am constantly fighting that urge.

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I have taught rounding the exact same way. I am big on conceptual learning and I’m against the majority of tricks in Mathematics. I believe this is the reason why we don’t have as many students who are sound mathematicians. Too many tricks and no ‘why’ to go along with the trick.

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[…] Tricks are NOT for Kids | Beyond Traditional Math. […]

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This is great stuff! Thanks for sharing how to teach rounding conceptually. I just have one little suggestion you might think about. I videoed a teacher doing a rounding lesson last April. She reviewed with her students that we really start counting with 0 in the whole number system, not with 1. So, if you count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 you have 10 digits. Those ten digits are the basis of the base ten numeration system. They are divided evenly in half. 0, 1, 2, 3, and 4 are five digits and 5, 6, 7, 8, and 9 are five digits. 5 is in the upper group, so 5 rounds up. I thought that was brilliant, a true mathematical concept, and much better than saying the world decided to round up on 5. What do you think?

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I is amazing, Thank you for sharing your insite into teaching how to round numbers! I will be trying this with my 3rd grader who has been in tears trying to understand this concept!

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Thanks for this!! I’ve tried songs, poems, tricks… LOL! THIS makes sense, and we know that what we do for kids MUST make sense. 🙂

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You are so so right. I am teaching it the same way too. The only way to understand the tricks is if you already have the concept mastered, so why use them!!!!

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I am planning on teaching this method you’ve described tomorrow as a reteach lesson. Only 3 of my students understood rounding last week based on the straight teaching from Go Math that I followed. I found your site from Pinterest. wondering, when do you show them place value, or when do you plug in a 3-digit number into a place value chart and teach them to look at the number on the right to determine whether to round up or stay the same? I’m a first year teacher aster several years of subbing. Thanks!

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Once they can picture a number line in their mind, they can usually do pretty well with a place value chart. I would practice with an open number line a ton first, then see if they can do it without!

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For a private tutor / soon to be teacher, rounding is one of those things that I have had trouble working with kids on. And now this has made it so much easier! Many thanks for this 😀

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Reblogged this on Our Global Classroom and commented:

Something to think about 3/4J as we learn about rounding.

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I absolutely agree! If you teach them a trick they will forget it when you move on to a new unit. If you teach them the concept they will remember it and have a deeper understanding.

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Thank you! Tried the roller coaster, tried the rap, and everything in between. The numberline makes sense. I give the analogy of being at the mall with mom. The benchmark numbers are the restrooms- always go to the closest. If you’re in the middle (midpoint) go to the restroom near the cookie shop, which is the bigger number…. And they can relate!

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So helpful it is!

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can you please send me the story for rounding ?

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I TOTALLY AGREE! There are too many rhymes to memorize, songs to learn, and steps to follow. Having a strong understanding of place value is the key. Understanding where a midpoint lies and why it is the midpoint is essential. Thanks for keeping it real- mathematical. As an intervention provider I find that if a child can’t apply a strategy it is almost always because they lack (or have forgotten) key basic skills, such as in this lesson where a child must know how to count by 10s or 100s, that lead to deeper understanding. If we just teach them to apply tricks then they can’t extend that knowledge and apply it to tougher concepts down the road.

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Thank you so much…I have one student, who after much practice, small groups, and some hair pulling (by me!) she still said, I don’t get it…so I am starting from scratch with your number lines…absolutely not all students can handle the tricks…they need to relive the concept that they perhaps missed in the younger grades…

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I was crying and she was crying. Rounding seems so simple to us adults–how can they not get it??? Right? Except, she didn’t. And she tried, tried and tried. Then of course we cried. She, for the frustration and I, for the homeschool insecurities creeping in. I stumbled here in search of a pinterest fix and BAM!!! LIGHTBULB!!! She got it!!! Aahhh, we both are smiling now! The songs and rhymes made it all worse, THIS made sense. Thank you!

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[…] sense. Not really sure where I’m coming from? Check out Beyond Traditional Math’s blog post on the topic. What better way to teach rounding than to take it outside and make it truly […]

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Hi I’m have been stumped by math since first grade although I know the basics I would like to “reteach” myself doing math without the tricks. Do you know where to start? I recently discovered that the way I learned math didn’t make any sense

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Hi! I think the best thing is to read lots of teacher blogs, but also to go to Youcubed.org. There are some cool things to check out there that help you think conceptually!

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