30-minute lesson
Year 3 Mathematics: Place value to 1000
Lesson objective
- Represent three-digit numbers as hundreds, tens and ones.
- Explain the value of each digit in a three-digit number.
- Compare and order numbers to 1000.
- Find 10 or 100 more and less than a given number.
Success criteria:
- I can build a number like 427 with hundreds, tens and ones.
- I can say what each digit is worth.
- I can put three-digit numbers in order from smallest to largest.
- I can find 10 more or 100 more than a number.
Materials
- Pop sticks or straws with rubber bands (bundles of ten and bundles of one hundred)
- Coins and play notes, or paper squares labelled $1, $10 and $100
- Three cups or a sheet of paper divided into 'hundreds', 'tens' and 'ones' columns
- Number cards 0 to 9 (cut from paper)
Introduction
3 minIntroduce today's words:
- hundreds: Groups of one hundred; ten tens make one hundred.
- place value: The value a digit has because of where it sits in a number.
- expanded form: Writing a number as the sum of its parts, such as 500 + 30 + 8.
- zero as a placeholder: A 0 used to show there are none of that place, as in 703.
- order: Arrange numbers from smallest to largest or largest to smallest.
Ask your child what they already know about place value to 1000.
Explanation
6 minIn Year 1, children learnt that ten ones make one ten. Now we take the next step: ten tens make one hundred. Bundle ten bundles of ten sticks together with a big rubber band to show a hundred.
In a three-digit number, each digit has a job depending on its place. In 427, the 4 means 4 hundreds (400), the 2 means 2 tens (20) and the 7 means 7 ones (7). We can write this in expanded form: 400 + 20 + 7.
Zero is important. In 703 there are 7 hundreds, no tens and 3 ones. Without the zero, it would look like 73, a very different number.
To compare numbers, start with the biggest place. 839 and 893 both have 8 hundreds, so look at the tens: 3 tens is less than 9 tens, so 839 is smaller.
To find 10 more, only the tens digit goes up by one: 245 becomes 255. To find 100 more, only the hundreds digit goes up: 672 becomes 772. Watch out when a digit is 9 — 395 + 10 is 405, because 10 tens become a new hundred.
Numbers can also be split in non-standard ways. 250 is 2 hundreds and 5 tens, but it is also 25 tens. This flexible thinking makes mental addition and subtraction much easier later.
Worked examples
5 minBuilding a number
Build 362 using bundles of sticks.
Step 1: The 3 is in the hundreds place, so take 3 bundles of one hundred.
Step 2: The 6 is in the tens place, so take 6 bundles of ten.
Step 3: The 2 is in the ones place, so take 2 single sticks.
Step 4: Check: 300 + 60 + 2 = 362.
Answer: 362 is 3 hundreds, 6 tens and 2 ones.
Ordering numbers
Put 389, 398 and 839 in order from smallest to largest.
Step 1: Look at the hundreds: 389 and 398 have 3 hundreds; 839 has 8 hundreds, so 839 is the largest.
Step 2: Compare 389 and 398 using the tens: 8 tens is less than 9 tens.
Step 3: So 389 is smaller than 398.
Answer: 389, 398, 839
Ten more across a hundred
What is 10 more than 395?
Step 1: 395 has 9 tens. Adding one more ten makes 10 tens.
Step 2: 10 tens make a new hundred, so the hundreds go from 3 to 4 and the tens become 0.
Step 3: The ones stay as 5.
Answer: 10 more than 395 is 405.
Guided practice (do together)
6 min1. What number is 4 hundreds, 2 tens and 7 ones?
(a) 472 (b) 427 (c) 247 (d) 4027
2. What is the value of the 6 in 361?
3. Which number is the largest?
(a) 389 (b) 398 (c) 839 (d) 893
4. Write this number: 500 + 30 + 8
Independent practice
7 min5. What is 10 more than 245?
(a) 246 (b) 345 (c) 255 (d) 235
6. What is 100 more than 672?
7. Which description matches the number 703?
(a) 7 hundreds, 0 tens and 3 ones (b) 7 hundreds, 3 tens and 0 ones (c) 7 tens and 3 ones (d) 73 hundreds
8. How many tens are there altogether in 250?
Questions to check understanding
- Can you build a number like 427 with hundreds, tens and ones?
- Can you say what each digit is worth?
- Can you put three-digit numbers in order from smallest to largest?
- Can you find 10 more or 100 more than a number?
- What was the trickiest part today?
Answer guide
1. 427 — 400 + 20 + 7 = 427.
2. 60 — The 6 is in the tens place, so it is worth 6 tens, which is 60.
3. 893 — 839 and 893 both have 8 hundreds. 893 has 9 tens, which is more than 3 tens, so 893 is largest.
4. 538 — 5 hundreds, 3 tens and 8 ones make 538.
5. 255 — Adding 10 makes the tens digit go up by one: 4 tens becomes 5 tens, so 255.
6. 772 — Adding 100 makes the hundreds digit go up by one: 6 hundreds becomes 7 hundreds, so 772.
7. 7 hundreds, 0 tens and 3 ones — In 703 the 7 is in the hundreds place, 0 is in the tens place and 3 is in the ones place.
8. 25 — Each hundred is 10 tens, so 2 hundreds is 20 tens. Add the 5 tens to get 25 tens.
Review
3 minRecap the success criteria together. Watch for these common misconceptions:
- Writing three hundred and four as 3004. Build it and show that 300 + 4 is written 304, with 0 holding the tens place.
- Thinking the number with the biggest ones digit is the largest (for example, choosing 189 over 312). Always compare from the left.
- Forgetting to regroup when 10 more crosses a hundred (saying 10 more than 395 is 3105). Use bundles to show 10 tens becoming a hundred.
Extension activities
- Draw three number cards and make the largest and smallest three-digit numbers possible.
- Play 'Race to 1000': roll a dice and add that many tens each turn, recording the running total.
- Find three-digit numbers in a catalogue or junk mail and order them from smallest to largest.
Suggested follow-up
- Revisit place value to 1000 tomorrow with two or three quick questions from memory.
- Try the online practice check for this topic and look at any questions that need another go.
Tips for parents
- Money is a great place-value tool: $100, $10 and $1 notes or coins show hundreds, tens and ones.
- Ask 'What is this digit worth?' often, not just 'What digit is in the tens place?'
- Read house numbers, prices and page numbers aloud together and talk about the digits.