Reading, writing and comparing numbers to 1000
Hundreds, tens and ones: numerals, number names and expanded form, then comparing three-digit numbers with the greater than, less than and equal to symbols
About three to four lessons of 40 to 55 minutes
Every seat has a value, and so does every digit
Picture the seats in a big theatre. The front seats near the stage are the cheap ones, the seats further back cost a bit more, and one special block costs the most of all. A seat is worth what it is worth because of where it sits, not because of its shape. Digits are exactly like this. The digit 3 is worth 3 ones in the number 3, worth 30 in the number 35, and worth 300 in the number 356. Same digit, different value, all decided by its place.
A three-digit number has three places: hundreds, tens and ones. Read them in order and you can say any number up to 1000, write it in words, split it into its place-value parts, and compare it with another number by checking the biggest place first. Today you will read, write and compare numbers all the way to 1000 by giving every digit the value its seat deserves.
- 356 = 3 hundreds, 5 tens, 6 onesthe 3 is worth 300, the 5 is worth 50, the 6 is worth 6
- Write 245 in wordstwo hundred forty-five
- Expanded form of 245200 + 40 + 5
- Compare 245 and 254same hundreds, more tens in 254, so 254 > 245
What students will be able to do
Students will read and write three-digit numbers to 1000 as numerals, as number names in words, and in expanded form as hundreds plus tens plus ones, and will compare two three-digit numbers by reasoning from the largest place value first, recording the result with the >, = and < symbols.
- I can name the value of each digit in a three-digit number as hundreds, tens or ones.
- I can write a three-digit number in words.
- I can write a number in expanded form as hundreds plus tens plus ones.
- I can compare two three-digit numbers by looking at the biggest place first.
- I can record a comparison with the >, = or < symbol pointing the right way.
Standards this unit teaches
- 2.NBT.A.3Common Core (US)Read and write numbers to 1000
Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- 2.NBT.A.4Common Core (US)Compare three-digit numbers
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
- AC9M2N01Australian Curriculum v9 (ACARA)Partition three-digit numbers by place value (Year 2)
Partition, rearrange and regroup two- and three-digit numbers using their place value into hundreds, tens and ones. Naming, writing and comparing a number all rest on this partitioning.
- AC9M2N03Australian Curriculum v9 (ACARA)Count collections to at least 120 (Year 2)
Count collections of up to at least 120 by making equal groups and skip counting. Counting on in hundreds and tens is how students read where a three-digit number sits.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
- Grade 1 place value: tens and ones teaching unitseeing a two-digit number as tens and ones, now extended to hundreds
- Grade 1 comparing and ordering numbers teaching unitthe greater than and less than symbols, now for three digits
- How to teach place valuethe value of each digit by its position
- How to teach expanded formwriting a number as its place-value parts added together
- How to teach comparing numbersdeciding which number is greater, less or equal
Words to teach and display
- Place value
- the value a digit has because of its position
- Hundreds
- the place that counts groups of one hundred, the left digit of a three-digit number
- Digit
- one of the number symbols 0 to 9 that a number is written with
- Expanded form
- a number written as its place-value parts added, like 200 + 40 + 5
- Number name
- the number written out in words, like two hundred forty-five
- Greater than / less than
- the symbols > and < that show which number is bigger, with the wide end at the bigger number
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. Hundreds, tens and ones
ConcreteBuild 245 with base-ten blocks: 2 hundred-flats, 4 ten-rods and 5 unit cubes. The picture says it all. The 2 is not just 2, it is 2 hundreds, worth 200. The 4 is 4 tens, worth 40. The 5 is 5 ones, worth 5. Read the number from the biggest place to the smallest: two hundred forty-five. A three-digit number is always hundreds, then tens, then ones.
Each place is worth ten of the place to its right: ten ones make a ten, ten tens make a hundred. That is why moving one place to the left makes a digit worth ten times as much.
Give every digit its full value out loud before writing anything: 'two hundred, and forty, and five'. Saying the value stops the 2 from being read as a bare 2.
- In 245, what is the 4 worth? What is the 2 worth?
- Which place is worth the most, and which the least?
2. Writing the number in words
PictorialTo write a three-digit number in words, say it place by place. For 356: three hundred, then fifty, then six, which is 'three hundred fifty-six'. The hundreds digit gives the number of hundreds, then you read the last two digits as an ordinary two-digit number. Reading aloud from the biggest place to the smallest is exactly the order you write the words.
Watch the teen and tens words: 356 ends in fifty-six, and a number like 314 ends in fourteen, not forty-teen. The last two digits are read just as they would be on their own.
A zero holds a place but is not spoken as a word. 305 is 'three hundred five', with no tens said, because the tens place is empty.
Write 245 in words and in expanded form.
- Hundreds digit 2: two hundred.
- Last two digits 45: forty-five.
- Put them together: two hundred forty-five.
- Expanded form is the place-value parts added: 200 + 40 + 5.
Answer: In words: two hundred forty-five. Expanded form: 200 + 40 + 5.
- Write 372 in words.
- How do you write 408 in words when the tens place is a zero?
3. Expanded form: the parts added up
AbstractExpanded form writes a number as its place-value parts joined by plus signs. 356 is 300 + 50 + 6. It is the same partition you built with blocks, now written as an addition. Expanded form is useful because it makes each digit's value impossible to ignore: the 5 in 356 is plainly 50, because that is what you write.
Going the other way is just as important: given 300 + 50 + 6, collapse it back to 356 by filling each place. Expanded form and the standard numeral are two ways of writing the same number.
A zero in a place contributes nothing to the sum, so 305 is 300 + 5, with no tens term. The zero still holds the tens place in the numeral so the 3 stays in the hundreds.
Write 306 in expanded form, then say what number 400 + 20 + 9 is.
- 306 has 3 hundreds, 0 tens, 6 ones.
- The tens place is empty, so expanded form is 300 + 6.
- For 400 + 20 + 9, fill the places: 4 hundreds, 2 tens, 9 ones.
- That numeral is 429.
Answer: 306 = 300 + 6. And 400 + 20 + 9 = 429.
- Write 517 in expanded form.
- What number is 700 + 80 + 3?
4. Comparing three-digit numbers
AbstractTo compare two three-digit numbers, start at the biggest place and work right only if you have to. Compare 245 and 254. The hundreds are equal (both 2 hundreds), so move to the tens: 254 has 5 tens against 245's 4 tens. Five tens beat four, so 254 is the greater number. Write it with the symbol pointing its open, wide end at the bigger number: 254 > 245, and the same fact the other way is 245 < 254.
Comparing bars makes this visible: draw 245 and 254 as two bars on the same scale and 254 reaches a little further, so its bar is longer. The symbol's wide end opens toward the longer bar.
Only drop to the next place when the current place ties. If the hundreds differ, the number with more hundreds wins immediately, no matter what the tens and ones are: 512 is greater than 498 because 5 hundreds beat 4 hundreds.
Compare 512 and 498 using >, = or <.
- Start at the hundreds: 512 has 5 hundreds, 498 has 4 hundreds.
- The hundreds already differ, so there is no need to check the tens or ones.
- 5 hundreds beat 4 hundreds, so 512 is greater.
- Point the wide end at the bigger number: 512 > 498.
Answer: 512 > 498 (equivalently 498 < 512).
- Compare 372 and 361. Which place decides it?
- Why does 512 beat 498 without checking the tens and ones?
Common misconceptions and how to address them
MisconceptionRead a digit as its bare value, so the 2 in 245 is just 2.
Why it happens: Students name the digit they see and ignore the place it sits in.
How to address it: Rebuild the number with blocks so the 2 is plainly 2 hundred-flats, worth 200. Always say the full value, 'two hundred', before writing or comparing.
MisconceptionThe number with more digits or a bigger-looking digit is always greater, so 98 beats 100 because 9 is big.
Why it happens: Students compare the loudest digit instead of comparing place by place from the left.
How to address it: Line the numbers up by place. 100 has a hundreds digit and 98 does not, so 100 is greater even though it has a small 1 at the front. Count the hundreds first.
MisconceptionCompare from the ones place, the right-hand digit, first.
Why it happens: Students add and subtract starting from the ones, so they start comparing there too.
How to address it: Comparing goes the other way: start at the largest place, the hundreds. The ones only matter if the hundreds and the tens are both tied.
MisconceptionThe > and < symbols point the same way every time, or the open end faces the smaller number.
Why it happens: The symbols look alike and students forget which way they open.
How to address it: The wide, open end always faces the bigger number and the point faces the smaller. Draw the comparison bars and open the symbol toward the longer bar.
MisconceptionSkip a zero in expanded form or in words so 305 becomes 35 or 'thirty-five'.
Why it happens: Students treat the zero as nothing and drop it, losing the hundreds place.
How to address it: The zero holds the tens place so the 3 stays in the hundreds. 305 is three hundred five, or 300 + 5, and the empty tens place still keeps the digits in their columns.
Guided practice (with answers)
1. What is the value of each digit in 463?
463 = 400 + 60 + 3. Answer: 4 hundreds (400), 6 tens (60), 3 ones (3).
2. Write 372 in words.
Answer: Three hundred seventy-two.
3. Write 508 in expanded form.
Answer: 500 + 8. The tens place is a zero, so there is no tens term.
4. What number is 600 + 30 + 4?
Answer: 634.
5. Compare 245 and 254 using >, = or <.
254 has more tens, so 254 > 245. Answer: 245 < 254. The hundreds tie, and 254 has more tens.
6. Compare 519 and 531 using >, = or <.
Answer: 519 < 531. Hundreds tie at 5, then 531 has 3 tens against 1 ten.
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 to firm up hundreds, tens and ones, then move to comparing three-digit numbers.
Differentiation
- Keep base-ten blocks (hundred-flats, ten-rods, unit cubes) on desks so students build each number before writing or comparing it.
- Give a place-value chart with hundreds, tens and ones columns so every digit has a home column and nothing shifts place.
- Start comparisons where the hundreds already differ (so the biggest place decides) before moving to numbers that tie on the hundreds.
- Provide the words for the hundreds and the joining so students only fill in the last two digits.
- Order a set of four three-digit numbers from smallest to largest and explain the place-by-place reasoning.
- Write a number that is greater than 462 but less than 470, and say how you know it fits.
- Show the same number three ways: as a numeral, in words, and in expanded form, for numbers with a zero in a place.
- Explain why 348 is less than 350 even though its ones digit 8 is bigger than 0.
Assessment: exit ticket
A three-question exit ticket for the last five minutes. It samples place value, expanded form, and comparing, the core of the unit.
1. What is the value of the 7 in 375?
Answer: 70, because the 7 is in the tens place.
2. Write 604 in words and in expanded form.
Answer: Six hundred four. Expanded form 600 + 4 (the tens place is zero).
3. Compare 428 and 482 using >, = or <.
Answer: 428 < 482. The hundreds tie at 4, then 482 has more tens.
Teacher notes and timings
- Rough timing across three to four lessons: Lesson 1 hundreds, tens and ones with blocks (section 1), Lesson 2 writing numbers in words (section 2), Lesson 3 expanded form (section 3), Lesson 4 comparing three-digit numbers and the exit ticket (section 4 and assessment).
- The place-value bar diagrams partition a number into hundreds, tens and ones. The hundreds part is naturally the widest and the ones part the thinnest, which is honest: it shows that a hundred is worth far more than a one. The ones value stays labelled so students still see it is a real 5, not nothing.
- The comparison-bar diagrams draw two whole three-digit numbers on one scale, so their bars sit close in length. The teaching point is to read the symbol from the bars: the wide, open end faces the longer bar, the bigger number.
- Keep hammering the comparison routine: start at the hundreds, and only drop to the next place when the current place ties. This is the habit that scales to comparing much larger numbers later.
- Do not skip zeros. A zero in a place holds the column so the other digits keep their value (305 is not 35). Practise numbers with an internal zero on purpose.
- US and AU alignment: the US names reading and writing to 1000 (2.NBT.A.3) and comparing three-digit numbers (2.NBT.A.4) at Grade 2. ACARA reaches the same ground at Year 2 through partitioning two- and three-digit numbers by place value (AC9M2N01) and counting collections (AC9M2N03). The place-value method here serves both.
- Present mode and print both work: use the Print button for a clean teacher copy or a student handout, and project the bars to partition and compare numbers with the class straight from the diagrams.