Another way to develop a student's understanding of quantity is to teach him to round numbers. Rounding numbers to the nearest ten or hundreds place is a foundational skill that will enable a student to estimate solutions to numerical operations (for example, 52 + 46 is close to 50 + 50, so the answer will be close to 100). This page includes intervention strategies that you can use to support your students in this area. As you read, consider which of these interventions best aligns with your student's strengths and needs in the whole-learner domains.
Explicit Instruction
If you are intervening to reinforce your student's ability to round numbers, you should start by explicitly teaching the skill. This sounds like:
Note: The number 35 is halfway between 30 and 40, so the above strategy of seeing which decade number the number is closest to won't work. In this case, you need to teach the exception to the rule. Anytime you see a 5 in the place to the right of the digit you're rounding to, you round up.
Activity A: Rounding with Number Lines or Hundreds Charts
If your student is able to count with a number line or hundreds chart but struggles to round numbers to the nearest 10, teach him Rounding with Number Lines or Hundreds Charts (Petti, 2017). In this strategy, a teacher uses a number line or a hundreds chart to help a student conceptualize if the nearest ten is bigger or smaller than the number being rounded (for example, is 36 closer to 30 or 40?). To do this, the teacher gives the student a number, such as 36, and has him quantify the distance between 30 and 36 (6 spaces on the number line). Then, she has him quantify the distance between 36 and 40 (4 spaces on the number line). Then, the student has to decide which one is closer (40), which will be the decade number that the number should be rounded to.
Note: This intervention can also be used to teach rounding to the nearest hundred, as long as students are able to skip count by 10s.
Rounding with Number Lines or Hundreds Charts in Action
Note: For purposes of clarity, the example below focuses on using a number line to teach this intervention.
Teacher: We are going to practice rounding a number to the nearest ten. I'll give you a number, and then you'll figure out whether it should be rounded to the ten below it or above it by figuring out which is closer. You'll figure it out by counting the spots from your number to the others. Your number is 36. First, how far is 36 from 30?
Student: [Starting at the number 30 and pointing to each tally on the number line up to 36.] 1, 2, 3, 4, 5, 6... It's 6.
Teacher: Now count from 36 up to 40.
Student: 1, 2, 3, 4... It's 4 units away. So 36 is closer to 40 than 30! We'd round 36 up to 40!
Petti, W. (2017). Mathcats: Rounding idea bank. Retrieved from http://mathcats.org/ideabank/rounding.html
Activity B: Rounding with Base Ten Blocks
If your student has learned how to use base ten blocks but struggles to round numbers to the nearest 10 or 100, use these tools to teach rounding (Petti, 2017). In this intervention, a teacher gives a student a number (such as 36) and also a group of base ten blocks that represent that number. Then, she has the student line up the blocks and count how many blocks 36 is from 30 (6) or 40 (4) and decide which one is closer. This intervention can also be used to show that 5 is the cutoff point. In other words, if a student has a number that ends with 35, it is equally close to 30 or 40. However, if the number ends with a number less than 5, it is closer to the lower number (so the student should round down), and if it ends with a number greater than 5, it is closer to the upper number (so he should round up).
Rounding with Base Ten Blocks in Action
Teacher: I'd like you to round 36 to the nearest ten. To do this, line up your base ten blocks, and see if 36 is closer to 30 or 40.
Student (after lining up blocks): Well, I can count the spaces between 36 and 30, and I'd need to take away 6 blocks. But if I count the spaces between 36 and 40, I'd only need to add 4 blocks. So, that must mean that 36 is closer to 40. That means I would round up.
Petti, W. (2017). Mathcats: Rounding idea bank. Retrieved from http://mathcats.org/ideabank/rounding.html
Activity C: Teach and Practice the Rules
Once a student has developed a conceptual understanding of what rounding means and is able to round to the nearest 10, you can teach him to round numbers to the nearest 100 or 1000. When she is rounding to the nearest 100, teach the student to look at the tens place to figure out which hundred the number is closer to (for example, in 126, there is a 2 in the tens place, so 126 is closer to 100 than 200). When she is learning how to round to the nearest 1000, teach the student to look at the hundreds place to round up or down (for example, in 1720. there is a 7 in the hundreds place, so 1720 is closer to 2000 than 1000. The student would round up to 2000). As the student builds fluency with this concept, teach her the rules below.
The rules are as follows:
Teach and Practice the Rules in Action
Teacher: Now that we have learned to round to the nearest 10, we are going to practice rounding to the nearest 100. The rules are the same, but there is one big difference: when we round to the nearest 100, we look at the tens place, not the ones place, to figure out which 100 the number is closest to. What place do we look at?
Student: The tens place.
Teacher: Great! In the number 126, which is the tens place?
Student: The second number, 2, is in the tens place.
Teacher: So, should we round 126 to 100 or 200?
Student: 100.
Teacher: Why?
Student: Because 20 is closer to 0 than to the next 100.
Teacher: I wonder if that's a rule — "If there's a two in the place you're rounding, you'll always round down." Let's test that rule!
Baker, K. (2019, February 16). How to Teach Rounding So Students Actually Understand. Teaching Made Practical. https://teachingmadepractical.com/teaching-rounding-so-students-understand/
Activity D: Estimating when Performing Operations
Once a student has mastered rounding to the nearest ten, hundred, and thousand, he can estimate numbers to get an approximate answer when performing operations (Petti, 2017). This will help a student get a general sense of the answer before he completes the problem using the exact numbers. In order to estimate when adding, subtracting, multiplying, or dividing, the teacher teaches the student to round all the numbers in the problem and then solve it. The place that the student will round to depends on the number of digits the numbers contain. Here are some guidelines:
Estimating when Performing Operations in Action
Teacher: Now that we have learned to round numbers, we are going to practice this strategy to get an estimate of an answer when solving a problem. Right now, we'll practice rounding with addition problems. If my problem was 42 + 64, I would round to the nearest ten to estimate my answer. By rounding before I solve the problem, I have an idea of what my actual answer will be close to. This will help me check that my answer is correct.
Teacher: So, I'll round 42 to 40 and 64 to 60, which makes the new problem: 40 + 60. Because I've rounded, I can quickly solve this problem in my head: 40 + 60 is 100. This means that my actual answer will be close to 100!
Teacher: Let me check. 42 + 64 = 106. Is that close to 100? Yes!
Teacher: Now, you'll try rounding numbers to solve addition problems.
Petti, W. (2017). Mathcats: Rounding idea bank. Retrieved from http://mathcats.org/ideabank/rounding.html
Activity E: Rounding Decimals
Once a student has been introduced to decimals, he can learn similar rules for rounding decimals. In order to carry out this process, he must demonstrate a strong understanding of place value, as well as the ability to round numbers to ten, hundred, and thousand. In this strategy, a student focuses on rounding the numbers after the decimal place. However, instead of rounding to the nearest ten, hundred, or thousand, the student rounds to the nearest tenth, hundredth, or thousandth, which is how place value is described for numbers behind the decimal point. When learning to round to the nearest tenth, the teacher teaches the student to look at the hundredths place to figure out whether to round up or down (for example, in 0.16, there is a 6 in the hundredths place, so the student would round to up to 0.2). When learning how to round to the nearest hundredth, the teacher teaches the student to look at the thousandths place (the number to the right of the hundredths place) to round up or down (for example, in 0.727 there is a 7 in the thousandths place, so the student would round up to 0.73). When rounding decimals, the same rules apply:
Rounding Decimals in Action
Teacher: Now that we have learned about decimals, we are going to practice rounding decimals so that we can estimate the solutions to problems that include decimals. The rules are the same, but there is one big difference: when we round numbers located behind the decimal points, we look at the tenths, hundredths, or thousandths place, not the tens, hundreds, or thousands place. What place do we look at?
Student: The tenths, hundredths, or thousandths place.
Teacher: We know that the tenths place is the first number after the decimal, the hundreds is the second number behind the decimal, and the thousandths number is the third place behind the decimal. If I asked you to round 0.25 to the nearest tenth, you would look at the number in the 100s place and decide whether to round up to the bigger tenth or down to the smaller tenth. What digit is in the hundredth place?
Student: 5. So I should round up to .3.
Teacher: Why?
Student: Because .25 is exactly between .2 and .3— if it's exactly in the middle, you always round up.
Petti, W. (2017). Mathcats: Rounding idea bank. Retrieved from http://mathcats.org/ideabank/rounding.html
Think about the following scenario, which takes place after a teacher has explicitly taught a student strategies for rounding numbers.
Teacher: "Can you round 36 to the nearest ten?"
Student: "36. Let's see. It's closer to 30 because it has a 3 in the front."
In such a case, what might you do?
When you are planning your lessons, you should anticipate that your student will make errors throughout. Here are a series of prompts that you can use to respond to errors. Keep in mind that all students are different, and that some students might respond better to some types of feedback than to others.
| Level of Support | Description of Scaffold | Script |
|---|---|---|
| Smallest Scaffold | Try Again. Ask the student to try again, looking back at a number line or other visual support that might help him. | "Try to round the number again, using your number line to help you." |
| Medium Scaffold | Back it Up. If a student is struggling, back up your process. Remind him to count each tally on the number line to see which tens place the number is closer to. | "I can see that you are stuck. Let's look back at the number line. How far is 36 from 30?" (6) "How far is 36 from 40?" (4) "Which number is closer?" (40) "So, do we round 36 up or down?" (Up to 40) |
| Highest Scaffold | Model. If the student continues to struggle, model how you would use a number line to round the number. | "I can see that you are stuck. I'll show you how I use the number line to round this number." |
If your student struggles to meet your objective, there are various techniques that you might try in order to adjust the activity so as best to meet your student's needs.
| Activity | Description of Strategy | Script |
|---|---|---|
| All Activities | Which Place is This? A student who is struggling to round numbers may need additional practice with place value. To help solidify a student's understanding of place, use manipulatives (such as base ten blocks) to help a student understand that the position a number is in is related to its value. | "Let's use base ten blocks to help us understand how 36 is made of tens and ones. That way, we can see how we use the ones place, not the tens place, to round this number." |