We first teach rounding in 3rd grade; we start with rounding to the nearest 10 and 100. Rounding is an often overlooked standard in the curriculum; however, it’s one of the math skills we use most often. We round every day. When we look at the prices in a store, we round. If you’re on a budget, you’re going to round the prices of everything you’re buying to determine if it fits in your budget. When you calculate a tip at a restaurant, you round the numbers. It’s unnecessary to do the long multiplication to determine exactly 15% or 20% of $19.27. We also “reverse round.” When people talk about data in round numbers we must understand what range that rounded number might denote. We’re going backwards. For example, if I say that a hall can accommodate 100 guests, this is a round number. The actual square footage of the space and fire allowance may be 98 or 102 or 95. In any of these cases, the manager would probably round the capacity to 100. So, we know that if we have 101 guests, we’re probably okay, but if we have 120 guests, we might not be able to accommodate everyone.
When I teach my 3rd grade students a new concept, I always start with vocabulary. Vocabulary often isn’t given enough credence in math class, but to understand what we’re trying to calculate, we need to be able to define it. So, what is rounding? What is a round number? Rounding, by definition, means adjusting a number so that it’s less accurate but more convenient. When we round, we find a round number, or a number that we can work with easily and often ends in zero. Zeros are round, so that makes it easy to remember! Rounding, in practice, simply means figuring out what multiple of powers of ten (tens, hundreds, thousands, tenths, hundredths, thousandths, etc) it’s nearest to.
Once we’ve defined what we’re trying to teach, we need to determine whether or not the students are ready to learn this new concept. In this case, we’re asking ourselves, “Do they have the pre-requisite knowledge and skills to learn how to round to the nearest 10 and 100?” In the best case scenario, a student should have learned and mastered all of the 2nd grade math standards before beginning 3rd grade math, but at minimum, we should make sure that students have a strong understanding of place value before they learn 3rd grade rounding. This is probably the biggest challenge that students face when they try to learn rounding. Many parents and teachers skip place value, or they don’t cover it thoroughly enough. Place value is so intrinsic in our number system; it seems so obvious that it’s easy to assume a child knows place value. Being able to identify the digit in the ones, tens, and hundreds place does not mean a child understands place value. Being able to add and subtract with regrouping does not mean a child understands place value. Children should be able to use their knowledge of place value to manipulate numbers. If you have place value cubes, you can experiment to see if your child can build the same number different ways. For example, how many different ways can your child build 236. Can they make 236 without any hundreds? Without any tens? What happens if you only use one hundreds cube? They also need to be able to count by 10s and 100s. Both of these skills should be easy at this point. If the child needs to count up to count by 10s or 100s, they’re not ready to learn rounding.
If your child understands these concepts, they’re ready to learn rounding. By using what a child already knows and understands, rounding is easy. Rounding can become confusing when children are taught to simply memorize that numbers that end in 0 through 4 round down and numbers that end in 5 – 9 round up. That doesn’t work when we round to other powers of 10. For example, 236 rounded to the nearest hundred is 200. The number ends in 6, but we round down. I start with something that will always work. If we’re rounding by 10s, we want to first identify which tens the number in question falls between. We can even take this a step further back and do this without numbers.
Then, we can add a number to the mix, but we can still use these two vocabulary terms – the old (nearest) and the new (rounded) in tandem. Ask your child to identify which tens the number is between, and have your child label the number line independently.
- What ten is 48 nearest to? Start by asking your child to find which tens 40 is between. Then, ask, “Which ten is 48 nearest to? What is 48 rounded to the nearest 10?” When your child answers, 50, repeat their answer with the vocabulary. Yes, 48 rounded to the nearest 10 is 50.
This step can be repeated as many (or as few) times as necessary. As you go, gradually drop the usage of the old vocabulary (nearest) and encourage your child to answer in a complete sentence (48 rounded to the nearest 10 is 50) too.
We also want to look at approximately where a number should go. We don’t need to really label all the ones. Where would 32 go on this number line? We can use the second number line without the trees to practice this. Your child should be able to tell you that 76 would be somewhere on the “hump” of this number line or that 89 is almost at 90.
Once your child is comfortable with this concept, (s)he can gain some extra practice with the first cryptogram in our Rounding to 10s and 100s Cryptogram package. The first cryptogram only includes questions rounding to the nearest 10. The secret message provides a way for students to self-check some of their answers, motivating them to find and correct their mistakes.
And you don’t need to check these because they’re self-checking. The answers to some of the questions are not included in the secret message. This provides an extra level of challenge and a means to evaluate skill mastery. You do need to check these ,but the answer key is provided.
After practicing rounding to the nearest 10, we can teach students to round to the nearest 100. I usually include mixed practice at this point, so we continue rounding to the nearest 10, but now we add questions that require rounding to the nearest 100. This ensures that students understand the implications of place value in rounding; they have decision making to do! I also give students the same number in different questions. For example, what is 237 rounded to the nearest ten? What is 237 rounded to the nearest 100? These answers are not the same, and we can see now that “numbers ending in 5 through 9” don’t always round up. 237 rounded to the nearest 100 is 200. And, we can use the same number line. We can put 200 and 300 on the number line if we’re rounding to the nearest 100 or 230 and 240 on the number line if we’re rounding to the nearest ten.
At this point, they’ll be able to do our Rounding to 10 and 100 Self-Checking Puzzles. This activity reinforces the concept of rounding, and it works great as a class activity, a station or center, or a homeschool activity.
When all of the puzzles are put together, flip them over to check them. If the pictures match up, all of the puzzles were assembled correctly
For extra practice, students are now ready to complete the 2nd cryptogram in the Rounding to 10s and 100s Cryptogram package. This cryptogram includes mixed practice rounding to the nearest 10 and 100.
When students are proficient at rounding to the nearest 10 and 100, the next step is to learn how to “reverse round.” This means asking ourselves questions such as:
What numbers round to 30 if I’m rounding to the nearest 10?
What’s the lowest number that would round to 30 if I’m rounding to the nearest 10?
What’s the highest number that would round to 30 if I’m rounding to the nearest 10?
To answer these questions, we need to look at what numbers round to 30. Through this process, we realize that numbers both smaller and larger than 30 round to 30. It’s through this process that we identify the acceptable range for rounded numbers that we encounter every day.
Once you’ve introduced reverse rounding, the third cryptogram in the package provides practice on this concept.
In subsequent grades, your child will learn how to round to thousands, tenths, hundredths, thousandths, etc.