No Tricks – Just How to Round on a Number Line

It wasn’t until a few years after the Common Core was adopted in California did I start teaching students how to round on a number line.  Before that, what did I use?   Rounding rhymes, tricks, and gimmicks.  Sometimes it sounded like a cheerleading squad as kids recited the rounding rhyme.  Oh, my. I look back and want to go back and teach my former students how to round again!

I’m here to tell you to ditch the tricks, rhymes, gimmicks, and rules.  Why? Because it doesn’t really work!  Instead, we need to use a math tool that will build a conceptual understanding of rounding.  In this post, I’ll show you why using learning to round on a number line is much more powerful than learning a rhyme or a trick or a gimmick.  Plus, read to the end to sign up for my newsletter and receive some FREE Rounding Task Cards.

What is Rounding?

Very simply, rounding is transforming a given number into a friendlier number, sometimes called a compatible number.  A friendly or compatible number is a number that is easier to work with either in our heads or on paper.  Can you think of any friendly numbers? How about 10, 20 , 30, 40, etc? Those numbers are easily added, subtracted, multiplied or divided using mental math.

For students learning to round, understanding the relationships between numbers is the key.  What I mean by the relationships is number sequence and the quantity between numbers.  That is why learning to round on a number line greatly helps with this understanding of the relationship between numbers.

Why do I Need to Learn to Round?

Your students are always wondering why we have to learn certain skills or concepts.  Rounding is a skill that everyone uses daily.  Have you ever estimated the total for items you are about to purchase? What about estimating how much space to put between seeds you are planting in your garden? Or have you ever estimated how far you might have to travel to reach a destination?

We estimate all the time.  Rounding is the skill you need to form an estimate. An estimate is a reasonable guess.  Do your students sometimes come up with solutions or answers that are not reasonable?  Probably because they are not understanding the relationships between the quantities in a problem.  Even in straight calculations, students sometimes don’t ask if their answer is reasonable.  But with a quick rounding of numbers, students can see that their actual sum, difference, product or quotient is reasonable or not.

Round on a Number Line

Which brings us to the use of a number line.  Why a number line? Let’s remember that with the introduction of the Common Core State Standards for Mathematics (CCSSM) and the Standards for Mathematical Practice (SMP), there has and continues to be a shift in mathematics teaching.  Conceptual understanding needs to come first.  Students need to see math and hold it in their hands to really understand it conceptually as they learn to use procedures and become fluent.

Conceptual understanding does not happen with rhymes, gimmicks, and tricks. So ditch those.  We develop conceptual understanding by making math visual, hands-on and contextualized in a real world or real-life situation.  That’s why using a math tool such as an open number line helps build conceptual understanding.

Take a look at number 46.  To adults, 46 we know represents a certain quantity.  We can determine it is made up of 4 tens and 6 ones.  We know that it is less than 47 but more than 45.  There’s much more we know.  But what about third graders?  I say third graders because that is the first grade level in which the CCSSM has a specific standard for rounding (3.NBT.A.1)  How have first graders and second graders been prepared for learning to round?

In those previous grades, teachers laid the foundation of understanding the relationships between numbers or quantities. Students learned to identify quantities by counting. Students learned to compare numbers to know if one number is less than, greater than or equal to another.  They learned how to decompose numbers.  They learned about counting patterns (2s, 5s, 10s, 10 more/less, 100 more/less), the big idea of unitizing (grouping by a base number, in our case, base 10).

And very importantly, they learned about place value.

Second graders learned to not only read, write and count to 1,000, they also learned about the value of digits, and how a number can be represented in many ways (word form, expanded form, standard form).  They also learned to be flexible with numbers by either decomposing or compensating numbers to add and subtract.  All of these skills are prerequisites to rounding.

Making Math Visual So They Can See It

Do you think all those prerequisites concepts were learned without visuals and math tools? Of course not.  Students used counters, place value charts, a hundred chart, pattern blocks, and many other visuals and math tools to become proficient with those skills.  Rounding is no different. We can not use rhymes (especially difficult for English Language Learners – ELLs), gimmicks (hard to use in novel situations) or tricks (relies on steps which can easily be forgotten or confused).

That’s where learning to round on a number line is so powerful. A number line is visual.  Kids can visually see the space or distance between numbers. Students already know how to count by tens and hundreds from previous grades so they are using something they are already familiar with (schema) to help with the reasoning.  A number line helps students to think through a problem visually and make sense of the terms nearest or closest (difficult vocabulary for ELLs).

Learning How to Round on a Number Line

An open number line template in a clear plastic sheet protector can easily become interactive with the use of a single counter or marker that moves back and forth across the line.  One thing I would have students do before using the number line to round is practice PLACING numbers on a number line.  For example, on a blank open number line template have them place or write zero and ten.  Then find the halfway point and put five. Then have them place the other numbers until zero through ten are placed.

Notice anything? Are the students not spacing correctly?  This is not unusual or unexpected.  It’s all about understanding space, the distance or quantities between numbers.  But as long as students understand which numbers to place at the beginning and ending intervals (starting and ending numbers) and the halfway number, that is really all they need to understand to round on a number line.

You Are Building Conceptual Understanding!

Yes, by using that open number line, students are building their understanding of rounding by visually seeing how numbers relate to each other and important benchmark numbers (beginning, ending and halfway points).  That visual image of the number line will eventually become a mental math number line in their heads.

By the way, why do I use an open number line versus a labeled number line? There’s a good reason not to use a labeled number line.  A labeled number line takes part of that productive struggle out of the equation. If you provide the beginning and ending numbers and halfway numbers, you’ve taken away the opportunity for students to make sense of the problems (SMP 1), and reason quantitatively through a problem (SMP 2).  They already have the prerequisite skills, so they should be able to reason what numbers are needed on the number line.

But in case they really are confused or need an additional scaffold, provide them with a hundred chart that they can use to find the information needed.

Real Life Contexts to Round on a Number Line

So many times we wonder as teachers whether something we teach has real-world application, especially with the shift in math teaching that emphasizes real-world problem-solving.  But as I noted earlier, we use rounding and estimation all the time in our daily lives.

There’s always the temptation to have students learn and practice procedures FIRST before attempting word problems or problem-solving.  We don’t grow up to sit at a desk to round numbers all day long (unless maybe you’re preparing a budget request with estimated costs).

Give the students some a real-world context for needing to round numbers such as shopping and road trip mileage.  Tell students about the ways you used rounding and estimation in your life.  Which leads to the question – when to round?

When do I Need to Round?

Only when an exact answer is not needed.  An exact answer is not needed when estimation is called for.  That can be tricky for students because of the vocabulary associated with estimation:  about, approximately, nearest, closest, round, around, etc.

Teaching these vocabulary words is better in the context of a real-world example:   I’m going to the school book fair.  I brought the money that I’ve been saving and I have \$40.  At the book fair, I pick 5 books that cost \$9.00, \$13.00, \$28.00, \$16.00 and \$15.00.  About how much money will I need to purchase all of them? Will my \$40 be enough to buy all of them? If not, which ones can I buy with the \$40 I have?

Most students can relate to this situation.  They might immediately start performing mental math to find the total. Or they might just get confused and not know what to do.  Someone might suggest they just go to the checkout and let them figure it out.  But you say NO.  There’s a better way.  Rounding the prices of each book to the nearest \$10.

That’s when students will learn to decontextualize the situation (SMP 1 and 2) and use a math tool strategically (SMP 5).  By using an open number line, students will learn how to place friendly or interval numbers, the halfway number and then place the given number.  Then reason and explain (SMP 3) that the given number is closer to one of the friendly numbers than the other.  By introducing a real-life situation, the context helps students understand the need to round before learning the procedure to round.

And Then What?

Using the rounded numbers, we hope students will see that using friendlier numbers makes it easier to add them using mental math. Since there isn’t enough money to purchase all the books, the friendly numbers will help us decide which books to purchase that will total up to or less than \$40.

Now students can practice more rounding on the number line just by changing the objects being bought, the prices or the available money in the situation.

Rounding Resources

At the bottom of this post, I’m offering some basic Rounding Task Cards that you can use with students in a center or as a whole class practice, warm-up or exit ticket.  I’ve included a blank template so you can add your own task cards with numbers you choose to then round to the nearest ten or hundred.  Just sign up below for my newsletter!

If you’re looking for more resources because you don’t have time to prepare PowerPoints and practice problems or you find your existing curriculum needs to be supplemented, then I encourage you to preview my Rounding on a Number Line PowerPoint and Printables resource made especially for the third-grade CCSSM standard 3.NBT.A.1.

Rounding on a Number Line PowerPoint and Printables

I created this Rounding on a Number Line PowerPoint for rounding to the nearest ten and hundred and to the nearest ten in a 3 digit number.  I’ve divided the PowerPoint into three lessons:

• Lesson 1: Rounding to the Nearest 10
• Lesson 2: Rounding to the Nearest 100
• Lesson 3: Rounding a 3 Digit Number to the Nearest 10

Each lesson is delivered in a real-world context.  Shopping for clothes in Lesson 1, road trip mileage for Lesson 2 and 3.  The use of the open number line is the prominent visual used and the animation illustrates the concept of closer to.

Each lesson comes with a follow-along printable that can be used as guided practice or independent practice or even homework.  There are additional supports for all students, but especially ELLs and Students with Disabilities (SWDs).  These include

• vocabulary card with kid-friendly definitions, visuals or examples
• student glossary
• bookmark
• posters
• sentence frames
• Frayer Model template
• open number line template
• rounding challenge (DOK levels 2 and 3)

You can check out the FULL PREVIEW here.

Another Resource for You

I’ve also created a Pinterest Board that you can follow with resources, tips and ideas for rounding (sorry no rhymes, gimmicks or tricks allowed!).  Just click below to follow.

Finally, sign up for my newsletter below and get the FREE set of 12 Rounding Task Cards. They are 4 task cards for rounding to the nearest 10, 4 task cards for rounding to the nearest 100, and 4 template cards for to create your own.  Just print and but apart and you’re ready to go!

Don’t Go Yet!

Are you new to the 1:1 classroom setting? Then you’ll want to read my Valuable Tips for the 1:1 Classroom.

Check out how I use Google Classroom to present at Back to School Night for Parents.