Tuesday, October 15, 2013

Rounding Without Tricks

There are many songs, poems, and tricks to teach rounding. Many of them are super cute, and really creative. But I think sometimes, all those tricks can get in the way of a true understanding of what rounding is. Rounding isn't an isolated skill, it's a strategy we use to estimate. It can be hard to teach - and hard to learn - but when done well, it reinforces SO MANY abstract concepts about numbers.

Two Essential Questions About Rounding:
Which two groups of 10 (or 100 or 1000) is this number in between?
Why do you need to round a number?

CCSS.Math.Content.3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

Each of these questions will obviously have different answers depending on the number and on the context of the problem.

Today, I'm going to share how I introduce rounding and help guide students towards answering those essential questions. I think one of the main reasons why so many teachers use those songs, poems, and tricks to teach rounding is that they are fun, easy to remember and they engage kids. This lesson will fulfill the need to have a fun, memorable, engaging lesson, without sacrificing the conceptual understanding of what rounding is.

DISCLAIMER: This is one of those lessons that has worked wonders for me. However, it may not appeal to everyone - you'll see why in a minute. ;) If you don't want to do EXACTLY what I do, I'll give you an alternative context down below. I also do not have pictures of this activity in action in my room, so I made an illustration to show what I'm talking about. Hopefully it will make sense! :)

First, I construct a "Rounding Roadway" on the classroom rug by making a giant number line out of duct tape. I put mini whiteboards at each mark, and label them with groups of 10 (using 0 - 100 for the first few rounds, then extending later).

I pick a student to be the first driver. I hand them a "steering wheel" made out of paper, and ask them where they want to go today. Popular answers are amusement parks and Papa Gino's. If there's ONE thing I have learned about third graders over the years, it is that THEY LOVE PAPA GINO'S.

You may need to activate a little prior knowledge about highways here - there are exits that are numbered in order. When you get on the highway, you will need to get off at one of these exits in order to get gas, use a restroom, get a snack, etc. Now let's pretend there's a highway called the Rounding Roadway. On the Rounding Roadway, there are exits at each number from 0 - 100, but not all the exits have restrooms. In fact, only the exits that are groups of TEN have restrooms. These are the exits we've marked on the number line. You may also want to give students a few numbers and have them place them on the number line before getting going.

I ask the student to follow my lead as I begin to tell the story, which might go something like this: 
Jose is really excited to go to his FAVORITE restaurant, Papa Gino's, today. He gets in his car and gets on the rounding roadway. The student will move to 0 on the rounding roadway. 

He drives down the road, past exit 1, past exit 2, and he keeps going until he gets to Exit 27. Student will move down the roadway until they have reached Exit 27. Here's where some of that number sense understanding comes in - where is exit 27 if it isn't marked? How do we know? 

Uh oh. Jose has a PROBLEM. See, he drank 2 big glasses of water before he got in the car. He didn't go to the bathroom, because he was just SO excited about getting to Papa Gino's. So now....he's gotta go to the bathroom! He needs to go BADLY. But remember what I told you about the restrooms on the Rounding Roadway? They are ONLY at the exits that are groups of TEN. Jose is at Exit 27, so where are the two closest restrooms? 20 and 30.

He needs to get to the restroom as soon as possible. Should he go to Exit 20 or Exit 30? Let students discuss - they will VERY quickly tell you he should go to Exit 30 because it is closer. Ask students how they can prove this is the closest group of 10 on the number line. 

Here's what I love about this - first of all, it gets kids' attention in a big way. Secondly, EVERYONE can identify with this situation - I mean, when you gotta go, YOU GOTTA GO. It's applicable in the real world. But more importantly, this helps students recognize that rounding is all a matter of deciding what number is closest - not about letting the ones digit "tell" you to round up or down.  And a number line is, in my opinion, the best way to visualize how close one number is to another. This lesson has a hook that doesn't compromise the integrity of the skill.

We repeat the same process with new drivers, new destinations, and new numbers ("exits"). After we've done a few of them, I ask students to start making some observations about rounding. When do you round up to the bigger number? When do you round down the smaller number? We rounded 56 AND 64 to 60...why? And so on.

What to do at an exit with a 5 in the ones place, like 75? It's equally spaced between 70 and 80. Well, if we really want to get to our destination, does it make more sense to move forwards or backwards? We round up.

Once students get the hang of it, I extend the numbers past 100. So let's change Exit 0 to Exit 200. Before we erase all the rest of the whiteboards, is there a quicker way? Just add a 2 in the hundreds place! Exit 262 is between 260 and 270, and it's closer to 260, so we round down. This can also be used to round to the nearest hundred - just adjust your numbers on the whiteboards.

NOW. Some of you may be totally comfortable talking about peeing in class. Some of you....some of you are thinking I'm a crazy person. And that is totally cool with me. ;) If you are thinking to yourself that this is just insane, here's another option: The car is almost out of gas and you need to find a gas station. Gas stations are only at the exits that are groups of 10 (or 100).

After a while, drop the "story" and just work with the number line. Another extension is to erase all the whiteboards before giving the student a number. Let's say you give them the number 213. How should we label the number line? Let students discuss and decide.

Follow this lesson by giving kids some unmarked or open number lines to work with. Give them a number and have them label and use the number line to find the closest group of 10 or 100.

I decided to create a powerpoint based on this lesson and I love how it turned out! Students will meet the Millers - a fun-loving family who learns the importance of rounding on the open road. ;) It includes a 5-section Powerpoint slideshow with rounding to the nearest 10 and rounding to the nearest 100 mini-lessons, practice problems, "think about it" problems, and real world applications. There are also student response pages to accompany the presentation. Click {HERE} to check it out in my TpT store!

I hope you'll come check out my blog, One Lesson at a Time! If you are looking for more resources to teach rounding, here are some resources available at my Teachers Pay Teachers store. You can also stop by my Facebook page for fun teaching tidbits and fans-only freebies!


  1. I do something very similar but talk about going to a friend's house. You live at house 0 and your friend lives at house 10 (or whatever house numbers you want that end in the 0's). One your way there, it starts to pour and you have to get inside. However, no one is home at the houses in between so you have a choice to go home or go to your friend's house. No running because it's raining that hard. (I always get laughter at that point.) We go through the same process you went through above with changing the numbers and stories. :)

    1. That's a great idea! Thanks for sharing! :)


  2. I love it! I teach rounding on a number line because for years kids would come to 4th and say, "5 or higher round up, below 5 round down," and end up telling me 43 rounds to 30 because the 4 has to go down. GAH!

    However I never thought to relate the concept of "find the closest" to exits on a highway! I love this! It's got a hook, and it really relates the real world to the concept. Thanks for sharing; I'm definitely doing this next year. :D

  3. This is a great idea & I love it! However, do you have some sort of adaption for higher numbers - like in the thousands, ten thoushands, and hundred thousands that 'don't' end in zeros but rather have digits that aren't zero in each place value? (4th grade level)
    Or...is the whole idea to teach at the ten and hundreds level until they get it?

  4. Thank you so much for sharing this! It drives me nuts to see teachers using tricks to teach math. It takes all of the meaning out of it! Then they have no understanding to build on when they get to the upper grades. I am definitely going to use this to work with my 3rd graders on rounding!
    Chris Making Meaning

  5. This is a great idea! I appreciate how you stayed true to the math and gave an engaging story. Rounding can be such an abstract concept and not very engaging for students.

  6. I am a former 5th grade math teacher who is now homeschooling my 8 year old son. I taught all the rounding tricks in the book when I was a teacher. Today I introduced rounding to my son with your Rounding Roadway. Wonderful lesson. He gets the concept! Thanks for posting this. :)

  7. So glad I found this! I am teaching math again this year and can't wait to use this. I shared it on my 5 on the Fifth post. Love it!!

    I Teach. What's Your Super Power?

  8. This is such a great idea!! We're in the middle of rounding right now!! I'm trying it Monday!! Thanks!

  9. Thank you for the clever approach to an important concept. I agree that teaching "tricks" is a disservice to our students. I am a math interventionist and will be using this idea to help one of my kiddos who is struggling with rounding.


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