Lesson Guide
Explanation
A place value chart gives every digit its own column: Thousands, Hundreds, Tens, Ones. Put 3472 in the chart: 3 in thousands, 4 in hundreds, 7 in tens, 2 in ones. The big idea: where a digit sits decides what it is worth — and each column is worth ten times the column on its right.
Your Turn
Draw a quick chart and put 8156 into it. Check: 8 thousands, 1 hundred, 5 tens, 6 ones.
Watch Out
Always start from the RIGHT when filling the chart: ones first, then tens, then hundreds, then thousands.
Explanation
Every digit has a value that depends on its column. In 3472, the 7 sits in the tens column, so it isn't worth 7 — it's worth 7 tens, which is 70. The 4 sits in the hundreds column, so it's worth 400. The digit tells you HOW MANY; the column tells you OF WHAT.
Your Turn
In 5863, what is the 8 worth? What is the 5 worth? Check: 800 and 5000.
Watch Out
When someone asks 'what is the digit worth?', they want the full value (70), not just the digit (7). Read the column name every time.
Explanation
Expanded form stretches a number out so you can see what every digit is worth: 3472 = 3000 + 400 + 70 + 2. It works backwards too — if you see 6000 + 50 + 3, squash it together: 6053. Careful: there were no hundreds, so a zero holds that place.
Your Turn
Stretch out 2815. Then squash 9000 + 300 + 6 back together. Check: 2000 + 800 + 10 + 5, and 9306.
Watch Out
When squashing back, any missing value means a 0 in that place. 6000 + 50 + 3 is 6053, not 653!
Explanation
Sometimes a number is described in a scrambled way: '23 hundreds'. You can't have 23 in the hundreds column — it only fits one digit! So bundle up: every 10 hundreds make a thousand. 23 hundreds = 2 thousands and 3 hundreds = 2300. Same trick for tens: 45 tens = 4 hundreds and 5 tens = 450.
Your Turn
What number is 37 hundreds? What number is 60 tens? Check: 3700 and 600.
Watch Out
Don't just glue digits together — 23 hundreds is NOT 23100. Multiply: 23 × 100 = 2300.
Explanation
With digit cards 7, 2, 9, 4 you can build lots of different numbers — and the columns decide everything. For the BIGGEST number, put the biggest digit in the biggest column: 9742. For the SMALLEST, put the smallest digit first: 2479. The same four cards, wildly different numbers — that's the power of place value.
Your Turn
With cards 5, 8, 1, 3 — build the biggest and the smallest number. Check: 8531 and 1358.
Watch Out
If one card is a 0, the smallest number cannot START with it (0852 is not a real 4-digit number). Put the next smallest digit first: 2058-style.
Explanation
One last look at the hero of place value: zero. In 4023 the zero sits in the hundreds column, keeping it open so the 4 stays worth 4 thousands. Zero never adds anything — but it stops the other digits from sliding into the wrong columns. Whenever you build or write a number, check that every column has its digit.
Your Turn
Which is bigger: 5007 or 570? Check: 5007 — it has thousands! Now try the quiz and the exercises.
Watch Out
A longer number (more digits) is always bigger than a shorter one — the zeros still count as digits.
Step 1: Introduction
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