Place Value & Number Sense
Target mastery benchmark
Read, write, compose and decompose any whole number up to 9,999 using base-10 positional structure.
1 · Visual intuition
Every number is a tiny city. Units are people, tens are buses, hundreds are streets and thousands are whole districts. Move a digit one place to the left and it becomes ten times more powerful — the same symbol, a completely different job.
Base-10 blocks (thousand cube, hundred flat, ten rod, unit cube) mapped onto a 4-column place value chart.
- •Units, Tens, Hundreds and Thousands as powers of ten
- •Positional value: the place a digit sits decides what it is worth
- •Expanded notation and standard form
- •Composing and decomposing whole numbers in more than one way
- •Comparing and ordering 4-digit numbers digit by digit
My notes
Use this space to take notes while your teacher explains the theory and worked examples.
2 · Core theory & worked examples
Worked Example 1 — Reading the value of a digit in 4,582
- 1Write the number into the place value chart: 4 | 5 | 8 | 2.
- 2Label the columns from the right: Units, Tens, Hundreds, Thousands.
- 3The digit 5 sits in the Hundreds column, so its value is 5 x 100 = 500.
- 4Check by expanded notation: 4,582 = 4,000 + 500 + 80 + 2. The 500 term confirms the answer.
Worked Example 2 — Composing 3,000 + 400 + 20 + 9
- 1Match each part to its column: 3,000 -> Thousands, 400 -> Hundreds, 20 -> Tens, 9 -> Units.
- 2Place the leading digit of each part into its column: 3 | 4 | 2 | 9.
- 3Any missing column would be written as 0 — here no column is empty.
- 4Standard form: 3,429. Say it aloud: three thousand, four hundred and twenty-nine.
Think Like a Mathematician: a zero is never 'nothing'. It is a place-holder doing the heavy job of keeping every other digit in the right column.
3 · In-class guided practice (10 questions)
- Bronze1
In the number 6,738, what is the value of the digit 7?
Working Space & Method:Final Answer: - Bronze2
Write 5,000 + 200 + 60 + 1 in standard form.
Working Space & Method:Final Answer: - Bronze3
A base-10 diagram shows 2 thousand-cubes, 3 hundred-flats, 0 ten-rods and 6 unit-cubes. What number is modelled?
Working Space & Method:Final Answer:
- Silver4
Write 7,045 in expanded notation, showing the exact value of each non-zero digit by its place value.
Working Space & Method:Final Answer: - Silver5
Order these from smallest to largest: 4,092 4,920 4,029 4,209.
Working Space & Method:Final Answer: - Silver6
Using the digits 8, 0, 4 and 9 exactly once each, write the largest possible 4-digit number and the smallest possible 4-digit number.
Working Space & Method:Final Answer: - Silver7
By how much does 3,478 increase when the 4 and the 7 swap places to give 3,748?
Working Space & Method:Final Answer:
- Gold8
A bank safe uses a 4-digit code. The thousands digit is 8, the hundreds digit is 0, the tens digit is half of the thousands digit, and the units digit is 1 less than the tens digit. What is the code?
Working Space & Method:Final Answer: - Gold9
I am a 4-digit number. My thousands digit is 6, my hundreds digit is half of my thousands digit, my tens digit is 0, and all my digits add to 12. What number am I?
Working Space & Method:Final Answer: - Gold10
Using the digits 5, 1, 7 and 2 exactly once each, build the 4-digit number closest to 5,000. Justify your answer.
Working Space & Method:Final Answer:
4 · Mastery checkpoint & reflection
- I can state the value of any digit in a 4-digit number.
- I can write a number in expanded notation more than one way.
- I can order 4-digit numbers confidently.
My reflection