Primary 3 · Mathematics · Number
Place value to 10 000
Reading, writing, building and ordering four-digit numbers using thousands, hundreds, tens and ones, and regrouping numbers in flexible ways.
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These lessons were written around Australian Curriculum strands and matched to Singapore levels by age (Primary 1 is the first year of primary school). They are not aligned to MOE syllabuses or the PSLE, so check them against the syllabus your child is working towards.
This lesson uses some Australian examples (places, animals or contexts). Swap in local examples from Singapore as you teach.
Learning goals
Learners will
- 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 looks like
- 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.
The big idea
Our 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
Reading a four-digit number
Write 6000 + 400 + 9 as a number and say it in words.
- Put 6 in the thousands column and 4 in the hundreds column.
- There are no tens, so put 0 in the tens column.
- Put 9 in the ones column.
- 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.
- All three have 4 thousands, so compare the hundreds.
- 4099 has 0 hundreds, so it is the smallest.
- 4909 and 4990 both have 9 hundreds. Compare tens: 0 tens is less than 9 tens.
- So 4909 comes before 4990.
Answer: 4099, 4909, 4990
Regrouping across a thousand
What is 100 more than 3950?
- 3950 has 9 hundreds. Adding one more hundred makes 10 hundreds.
- 10 hundreds make 1 thousand, so the thousands go from 3 to 4 and the hundreds become 0.
- The tens (5) and ones (0) do not change.
Answer: 100 more than 3950 is 4050.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
What number is 3 thousands, 4 hundreds, 0 tens and 6 ones?
3406 — 3000 + 400 + 0 + 6 = 3406. The 0 holds the tens place.
What is the value of the 7 in 7215?
7000 — The 7 is in the thousands place, so it is worth 7000.
Which number is the smallest?
4099 — All have 4 thousands. 4099 has 0 hundreds while the others have 9 hundreds, so 4099 is smallest.
What is 1000 more than 5682?
6682 — Adding 1000 increases the thousands digit by one: 5 thousands becomes 6 thousands, so 6682.
Which is another way to make 1520?
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.
Write this number: 6000 + 400 + 9
6409 — 6 thousands, 4 hundreds, 0 tens and 9 ones make 6409.
Which number comes between 2998 and 3000?
2999 — Counting on: 2998, 2999, 3000. The number in between is 2999.
How many hundreds are there altogether in 4000?
40 — Each thousand is 10 hundreds, so 4 thousands is 4 × 10 = 40 hundreds.
Watch out for
- 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.
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.
Go further
- 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'.
About 35 minutes
You'll need
- 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
Key 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.
Still tricky?
For parents
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