35-minute lesson
Year 3 Mathematics: Place value to 10 000
Lesson objective
- Represent four-digit numbers using thousands, hundreds, tens and ones.
- State the value of each digit in a four-digit number.
- Compare and order four-digit numbers.
- Rename numbers in more than one way, such as 1520 as 15 hundreds and 2 tens.
Success criteria:
- I can read and write numbers up to 10 000.
- I can say what each digit in a number like 7215 is worth.
- I can order four-digit numbers from smallest to largest.
- I can find 10, 100 or 1000 more or less than a number.
Materials
- Play money or paper slips labelled $1, $10, $100 and $1000
- A place-value chart drawn on paper with four columns: thousands, hundreds, tens, ones
- Number cards 0 to 9 (two sets)
- A metre ruler or tape measure (1000 millimetres) to show the size of a thousand
Introduction
4 minIntroduce today's words:
- thousands: Groups of one thousand; ten hundreds make one thousand.
- place value: The value of a digit depends on its position in the number.
- expanded form: A number written as the sum of its place values, such as 6000 + 400 + 9.
- regroup: Rename a number using different place-value parts, such as 1 thousand as 10 hundreds.
- ascending order: Arranged from smallest to largest.
Ask your child what they already know about place value to 10 000.
Explanation
7 minOur number system follows one simple rule: ten of one place make one of the next place. Ten ones make a ten, ten tens make a hundred and ten hundreds make a thousand.
In 7215, the 7 is worth 7000, the 2 is worth 200, the 1 is worth 10 and the 5 is worth 5. Writing 7000 + 200 + 10 + 5 is called expanded form, and it shows the job of each digit.
Zeros hold places. In 3406 there are 3 thousands, 4 hundreds, no tens and 6 ones. Writing it in a place-value chart helps children see why the zero is needed.
To compare numbers, line them up by place and start from the left. 4099 and 4909 both have 4 thousands, but 4099 has 0 hundreds and 4909 has 9 hundreds, so 4099 is smaller.
Adding 10, 100 or 1000 changes just one digit — unless a 9 needs to regroup. 1000 more than 5682 is 6682. But 100 more than 3950 is 4050, because 10 hundreds become a new thousand.
Numbers can be renamed. 1520 is 1 thousand, 5 hundreds and 2 tens, but it is also 15 hundreds and 2 tens, or 152 tens. Renaming like this is what makes mental addition and subtraction of larger numbers possible.
Place value is the key to adding and subtracting larger numbers. For 3400 + 2300, add the thousands (3000 + 2000 = 5000) and hundreds (400 + 300 = 700) to get 5700.
Worked examples
5 minReading a four-digit number
Write 6000 + 400 + 9 as a number and say it in words.
Step 1: Put 6 in the thousands column and 4 in the hundreds column.
Step 2: There are no tens, so put 0 in the tens column.
Step 3: Put 9 in the ones column.
Step 4: Read it: six thousand, four hundred and nine.
Answer: 6409 (six thousand, four hundred and nine).
Ordering numbers
Put 4909, 4099 and 4990 in ascending order.
Step 1: All three have 4 thousands, so compare the hundreds.
Step 2: 4099 has 0 hundreds, so it is the smallest.
Step 3: 4909 and 4990 both have 9 hundreds. Compare tens: 0 tens is less than 9 tens.
Step 4: So 4909 comes before 4990.
Answer: 4099, 4909, 4990
Regrouping across a thousand
What is 100 more than 3950?
Step 1: 3950 has 9 hundreds. Adding one more hundred makes 10 hundreds.
Step 2: 10 hundreds make 1 thousand, so the thousands go from 3 to 4 and the hundreds become 0.
Step 3: The tens (5) and ones (0) do not change.
Answer: 100 more than 3950 is 4050.
Guided practice (do together)
7 min1. What number is 3 thousands, 4 hundreds, 0 tens and 6 ones?
(a) 3460 (b) 3406 (c) 346 (d) 30406
2. What is the value of the 7 in 7215?
3. Which number is the smallest?
(a) 4099 (b) 4909 (c) 4990 (d) 4900
4. What is 1000 more than 5682?
Independent practice
9 min5. Which is another way to make 1520?
(a) 152 ones (b) 1 thousand and 25 tens (c) 15 hundreds and 2 tens (d) 1 thousand, 5 tens and 2 ones
6. Write this number: 6000 + 400 + 9
7. Which number comes between 2998 and 3000?
(a) 2990 (b) 3001 (c) 3999 (d) 2999
8. How many hundreds are there altogether in 4000?
Questions to check understanding
- Can you read and write numbers up to 10 000?
- Can you say what each digit in a number like 7215 is worth?
- Can you order four-digit numbers from smallest to largest?
- Can you find 10, 100 or 1000 more or less than a number?
- What was the trickiest part today?
Answer guide
1. 3406 — 3000 + 400 + 0 + 6 = 3406. The 0 holds the tens place.
2. 7000 — The 7 is in the thousands place, so it is worth 7000.
3. 4099 — All have 4 thousands. 4099 has 0 hundreds while the others have 9 hundreds, so 4099 is smallest.
4. 6682 — Adding 1000 increases the thousands digit by one: 5 thousands becomes 6 thousands, so 6682.
5. 15 hundreds and 2 tens — 15 hundreds is 1500 and 2 tens is 20, so together they make 1520. The others make 152, 1250 and 1052.
6. 6409 — 6 thousands, 4 hundreds, 0 tens and 9 ones make 6409.
7. 2999 — Counting on: 2998, 2999, 3000. The number in between is 2999.
8. 40 — Each thousand is 10 hundreds, so 4 thousands is 4 × 10 = 40 hundreds.
Review
3 minRecap the success criteria together. Watch for these common misconceptions:
- Writing 'four thousand and twenty' as 400020 or 40020. Use a place-value chart to show it is 4020.
- Comparing numbers by the first digit that looks big, rather than lining up places. Always compare thousands, then hundreds, then tens.
- Believing a number can only be split one way. Practise renaming, such as 2300 as 23 hundreds.
Extension activities
- Draw four number cards and make the largest and smallest numbers possible, then find the difference between them using a calculator.
- Look up the distances between Australian capital cities in an atlas and order them from shortest to longest.
- Play 'Guess my number' using place-value clues, such as 'I have 5 thousands and my hundreds digit is double my ones digit'.
Suggested follow-up
- Revisit place value to 10 000 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
- Prices of larger items (a bike, a fridge, a car) make interesting four-digit numbers to read and compare.
- A tape measure marked in millimetres shows 1000 as a real length — one metre.
- Ask your child to read numbers aloud correctly, as saying numbers well supports writing them.