# Number Lines and Rounding

I get requests from many teachers to help with instructional strategies regarding rounding, so I am happy to share my thoughts (and freebies) with you. Difficulty with rounding usually means students lack number sense. The essential goal of rounding is: Can you name a benchmark number (whole, tens, hundreds, thousands, tenths, hundredths, etc.) that a given number is closer to? I have found the more experience a student has with number lines, the better they will be with number sense, and the better they are with rounding to the nearest ___.  Then this rounding practice must be applied to real world problems to estimate sums, differences, products, or quotients.

When doing a google search for tips on rounding (ie Pinterest), you very often find an assortment of rhymes (such as “5 or more let it soar, 4 or less let it rest”) and graphics showing underlining of digits and arrows pointing to other digits. These steps are supposed to help children think about how to change (or round) a number to one with a zero. Many students can recite the rhyme, but then misunderstand the intent, often applying the steps to the wrong digit, showing they really don’t have number sense but are just trying to follow steps.

My answer (and that of other math specialists) is teaching students how to place any number on a number line, and then determining which benchmark number it is closest to. Continue reading to see examples and get some free activities.

You may find that just because a student can count sequentially from 0-100 or higher (either orally or in writing) doesn’t mean that they have number sense. This also includes concepts such as greater or less than. Placing a number on a number line is more effective and efficient towards gaining number sense than using an alligator to decide which one he is eating. When using a number line, the “arrows” at the end automatically show the less than and greater than signs.

1. In KG and 2nd grades, you can build this number sense by having students place numbers on number lines during your “calendar” daily math time. Show a number line section and how it relates to the other numbers around it. I can see that 17 comes between 10 and 20, and is greater than 15 or 16, but less than 20.
2. In 1st and 2nd grade, use a 100 chart (which is essentially a squished up number line) to locate numbers. If locating 23, you can see it is 3 away from 20 and 7 away from the next ten (which is 30). This also works toward helping students learn their number bonds of 10 – in the above case 3 and 7 are number bonds of 10.
3. In 1st and 2nd grade, use a number line and 100 chart to locate numbers and prove a number is less than or greater than another number. After students are adept at locating and placing numbers on the number line, they should be noting that the mid-point on number lines involve the use of the digit 5. For example: 15 is half way between 10 and 20; 45 is half way between 40 and 50; 150 is half way between 100 and 200; .15 is half way between .10 and .20.

After these 2 concepts are mastered, then the matter of rounding should be readily apparent. If I am trying to round 37 to the nearest 10,

I can locate 37 on a number line and note that it comes between the benchmark tens of 30 and 40. I know that 35 is half-way between 30 and 40, I know that 37 is more than 35 but less than 40, I know that 37 is 7 away from 30 and 3 away from 40. Therefore, I know that 37 is closer to 40 — so 37 is rounded to 40.

The number line provides a pictorial representation of the number, whereas the underlining and arrow method are abstract processes. You know I preach the CPA progression for understanding (conceptual/concrete, pictorial, abstract). When students have used these concrete and pictorial/visual methods to mastery, then they may begin to mentally  process this information. What is 334 rounded to the nearest 100? “This number is between 300 and 400. Because it is less than 350, it is rounded to 300.” or What is 286 rounded to the nearest 10? “This number is between 280 and 290.  Because it is 6 away from 280 and only 4 away from 290, then it is closer to 290.”

Here are some examples of how to concretely and pictorially practice this important skill.

The above activity is free here. You will get the large blank number lines plus benchmark numbers to fit any needs (less than 100, 100-1000, and decimals). You will need to create your own target numbers (white cards).

The Rounding Charts (pictured at the beginning of this post) are available free. I have included one for each set of 100. (0-100, 100-200, 200-300, on up to 900-1000).

Two rounding games for rounding decimals are included, free. They are appropriate for 4th – 6th grades: Rounding Round Up Game and Rounding Match.

A blank one-page template of open number lines for rounding  is also included free here.

Enjoy!!

## 2 thoughts on “Number Lines and Rounding”

1. Barbara Keck

Cindy, do you have something specific for rounding to the nearest 25 cents on a number line? I still have one student who not only recognizes her struggle, but is asking for additional practice.

• cindyelkins

I have emailed you a photo of something to try. Basically, use an open #line, show the end benchmarks (whole dollar) and the mid point (showing 50 cents). Next step, show the points to represent 25 cents and 75 cents. Determine between which two amounts the target number belongs – and which of those points is it closest to.