Rounding and place value
Reading three-digit numbers by place value and rounding to the nearest ten and hundred
About four lessons of 45 to 60 minutes
Nobody counts a crowd one person at a time
When the announcer says a stadium holds about 30,000 fans, nobody counted every single person. When a toy costs $4.95 and you say it is about 5 dollars, you are not being lazy, you are rounding. We swap an exact number for a nearby friendly number that is quicker to say, quicker to add, and easier to picture.
To round well you first have to really know your numbers, which digit is the hundreds, which is the tens, which is the ones. Today you will read three-digit numbers by place value, then use a number line to round to the nearest ten and the nearest hundred by asking one simple question: which friendly number is closer?
- A crowd of 29,613 fansreported as about 30,000, rounded to the nearest ten thousand
- A price tag of $4.95about 5 dollars, rounded to the nearest dollar
- A trip of 187 kilometresabout 200 kilometres, rounded to the nearest hundred
- 47 plus 28about 50 plus 30, which is 80, a quick estimate before you work it out exactly
What students will be able to do
Students will read the value of each digit in a three-digit number, write numbers in expanded form, and round two- and three-digit numbers to the nearest ten and nearest hundred by reasoning about the nearer friendly number on a number line and by using the digit to the right of the rounding place.
- I can say what each digit in a three-digit number is worth.
- I can write a number in expanded form, such as 356 = 300 + 50 + 6.
- I can find the midpoint between two tens or two hundreds.
- I can round a number to the nearest ten and to the nearest hundred.
- I can use rounding to estimate a sum and check if an answer is reasonable.
Standards this unit teaches
- 3.NBT.A.1Common Core (US)Round to the nearest ten or hundred
Use place value understanding to round whole numbers to the nearest 10 or 100.
- 3.NBT.A.2Common Core (US)Add and subtract within 1000 (application)
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction. The place-value partitioning here is the foundation of those strategies, and rounding is how students estimate to judge whether a sum or difference is reasonable.
- 2.NBT.A.1Common Core (US)Three-digit place value (foundation)
Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones. This Grade 2 understanding is the foundation the rounding work in this unit rests on.
- AC9M3N01Australian Curriculum v9 (ACARA)Represent and order numbers
Recognise, represent and order natural numbers using naming and writing conventions, including partitioning numbers by place value into hundreds, tens and ones.
- AC9M3N05Australian Curriculum v9 (ACARA)Estimate to judge reasonableness
Estimate the quantity of objects and use estimation to determine whether the outcome of a calculation is reasonable. ACARA v9 places rounding within this estimation descriptor at Year 3 rather than as a separate content point.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Digit
- one of the symbols 0 to 9 that a number is written with
- Place value
- the value a digit has because of where it sits, so the 5 in 356 means 50
- Expanded form
- a number written as the sum of its place-value parts, such as 300 + 50 + 6
- Round
- to swap a number for the nearest friendly ten or hundred
- Midpoint
- the number exactly halfway between two tens or two hundreds, such as 45 between 40 and 50
- Estimate
- a close-enough answer found quickly, often by rounding first
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Reading a number by place value
ConcreteA three-digit number is really three amounts stuck together: some hundreds, some tens, and some ones. Build 356 with base-ten blocks, 3 hundred-flats, 5 ten-rods and 6 unit-cubes, and the value of each digit becomes something you can hold. The 3 is not just three, it is 3 hundreds, worth 300.
The bar below shows 356 partitioned into 300, 50 and 6. See how the hundreds part is by far the longest, it carries most of the number's size, while the ones part is a thin sliver. Reading a number this way is what makes rounding make sense.
- In 356, what is the 5 worth? What is the 3 worth?
- Build 428 with blocks. How many hundreds, tens and ones?
2. Writing a number in expanded form
PictorialOnce you can read a number by place value, you can write it in expanded form: the number split into the value of each digit added together. 356 = 300 + 50 + 6. This makes it impossible to forget that the 5 means 50 and not 5, because you write the 50 out in full.
Write 407 in expanded form and say what each digit is worth.
- The 4 is in the hundreds place, so it is worth 400.
- The 0 is in the tens place, so it is worth 0 tens.
- The 7 is in the ones place, so it is worth 7.
Answer: 407 = 400 + 0 + 7, or simply 400 + 7. The 4 is worth 400 and the 7 is worth 7.
- Write 285 in expanded form.
- Why does the 0 in 407 still matter even though it is worth nothing?
3. Rounding to the nearest ten on a number line
PictorialTo round 47 to the nearest ten, draw a number line from 40 to 50 and find where 47 sits. The big question is which ten it is closer to, 40 or 50. Mark the midpoint, 45, exactly halfway. Since 47 is past the midpoint, it is nearer to 50. So 47 rounds to 50.
The midpoint is the whole secret of rounding. Anything past the halfway mark is closer to the higher ten, anything before it is closer to the lower ten. Reasoning from distance on the line comes first, the digit rule comes later and rests on this picture.
Round 62 to the nearest ten.
- 62 sits between 60 and 70.
- The midpoint is 65.
- 62 is before the midpoint, so it is closer to 60.
Answer: 62 rounds to 60.
- Round 88 to the nearest ten. Which two tens is it between?
- Where is the midpoint between 30 and 40?
4. Rounding to the nearest hundred
PictorialRounding to the nearest hundred works the same way, just with hundreds as the friendly numbers. To round 356 to the nearest hundred, place it between 300 and 400. The midpoint is 350. Since 356 is past 350, it is closer to 400. So 356 rounds to 400.
To decide which hundred, you look at the tens digit, because the tens tell you how far along you are between the two hundreds. A tens digit of 5 or more means you are at or past the midpoint, so round up. Here the tens digit of 356 is 5, so up to 400 it goes.
Round 235 to the nearest hundred.
- 235 sits between 200 and 300.
- The midpoint is 250.
- 235 is before the midpoint, so it is closer to 200.
Answer: 235 rounds to 200.
- Round 480 to the nearest hundred. Which two hundreds is it between?
- What is the midpoint between 600 and 700?
5. The digit rule and estimating
AbstractOnce the number line makes sense, the quick rule follows from it. To round, look at the digit just to the right of the place you are rounding to. If it is 5 or more, round up, if it is 4 or less, keep the place the same. The awkward middle case, a digit of exactly 5, always rounds up by convention: 45 rounds to 50.
Rounding earns its keep in estimation. To check 47 + 28 quickly, round each number first: about 50 + 30 = 80. The exact answer is 75, close to the estimate, so 75 looks reasonable. Estimating before you calculate is how you catch a silly answer, and it connects place value straight to adding and subtracting within 1000.
Estimate 47 + 28 by rounding each number to the nearest ten.
- Round 47 to the nearest ten: the ones digit is 7, so round up to 50.
- Round 28 to the nearest ten: the ones digit is 8, so round up to 30.
- Add the friendly numbers: 50 + 30 = 80.
Answer: About 80. The exact answer, 75, is close to 80, so it is reasonable.
- Round 617 to the nearest ten using the digit rule.
- Estimate 62 + 19 by rounding first.
Common misconceptions and how to address them
MisconceptionWhen rounding to the nearest hundred, look at the ones digit.
Why it happens: Students learned to look at the ones digit for rounding to tens and apply it everywhere.
How to address it: Look at the digit just to the right of the place you are rounding to. For hundreds that is the tens digit. On the number line, it is the tens that tell you how far between the two hundreds you are.
Misconception45 can round down to 40 because 5 is right in the middle.
Why it happens: The midpoint feels like it could go either way, so students pick the nearer-looking ten.
How to address it: Agree the convention out loud: a 5 always rounds up. So 45 rounds to 50, 250 rounds to 300. It is a rule everyone shares so answers match.
MisconceptionRounding changes the digits to the left as well, so 473 to the nearest ten becomes 500.
Why it happens: Students round more than they should and disturb places they should leave alone.
How to address it: Only the rounding place and the digits to its right change. For 473 to the nearest ten, the hundreds stay 4 and the answer is 470, not 500. Underline the digits that are allowed to move.
MisconceptionThe digit's value is just its face value, so the 5 in 356 is worth 5.
Why it happens: Students read digits left to right without attaching place value.
How to address it: Say the value in full: the 5 in 356 is in the tens place, so it is worth 50. Build it with 5 ten-rods to see the fifty.
MisconceptionRound after you calculate, so estimation happens at the end.
Why it happens: Students treat rounding as a finishing touch rather than a way to predict the answer.
How to address it: The point of estimating is to round first, get a quick ballpark, then calculate and check the exact answer lands near it. Round before, not after.
Guided practice (with answers)
1. What is the 8 worth in 480?
Answer: 80. It is in the tens place, so 8 tens.
2. Write 285 in expanded form.
Answer: 285 = 200 + 80 + 5.
3. Round 62 to the nearest ten.
Answer: 60. The midpoint is 65 and 62 is before it.
4. Round 88 to the nearest ten.
Answer: 90. The midpoint is 85 and 88 is past it.
5. Round 235 to the nearest hundred.
Answer: 200. The midpoint is 250 and 235 is before it.
6. Estimate 350 rounded to the nearest hundred.
Answer: 400. A tens digit of 5 rounds up by convention.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start with place value and expanded form to secure the reading, then move to rounding.
Differentiation
- Stay concrete: build each number with base-ten blocks before reading or rounding it.
- Give a pre-drawn number line with the two tens or hundreds and the midpoint already marked.
- Round to the nearest ten until it is secure before introducing the nearest hundred.
- Use a place-value chart so the student can see which column each digit sits in.
- Round to the nearest ten and to the nearest hundred and notice when the two answers differ.
- Round four-digit numbers to the nearest hundred and thousand as a bridge to Grade 4.
- Find all the numbers that round to 400 when rounded to the nearest hundred (350 to 449).
- Estimate a two-step shopping total by rounding each price, then compare with the exact cost.
Assessment: exit ticket
A three-question exit ticket for the last five minutes. It samples place value, rounding to the nearest ten, and rounding to the nearest hundred.
1. What is the 3 worth in 539?
Answer: 30 (it is in the tens place).
2. Round 74 to the nearest ten.
Answer: 70 (the midpoint is 75, and 74 is before it).
3. Round 268 to the nearest hundred.
Answer: 300 (the midpoint is 250, and 268 is past it).
Teacher notes and timings
- Rough timing across four lessons: Lesson 1 place value (section 1), Lesson 2 expanded form (section 2), Lesson 3 rounding to the nearest ten (section 3), Lesson 4 rounding to the nearest hundred, the digit rule and estimating, plus the exit ticket (sections 4 to 5 and assessment).
- Language to keep saying: which friendly number is closer, find the midpoint, look at the digit to the right. Reason from the number line before giving the digit rule.
- The two rounding figures draw real number lines with the midpoint marked. On the hundreds line the point for 356 sits correctly between the 350 and 360 ticks, so students can see it is past halfway.
- A curriculum note for Australian classes: ACARA v9 does not list rounding to the nearest ten or hundred as a separate Year 3 content point. It sits inside representing and ordering numbers by place value (AC9M3N01) and estimating to judge reasonableness (AC9M3N05), which is where this unit is anchored. Explicit rounding of decimals appears later, at Year 7 (AC9M7N05).
- Keep tying rounding back to estimation. The reason to round is almost always to get a quick, reasonable check on a calculation, which is why the unit ends on estimating a sum.
- Present mode and print both work: use the Print button for a clean teacher copy or a student handout, and project the page to teach straight from the number lines.