Ones, tens and hundreds, and what each digit is worth. Adding and subtracting in columns, ones first. When a column gets too full or too empty, a trade: 10 ones for 1 ten, 1 hundred for 10 tens. Adding 10 or 100 in your head, counting up to subtract, and estimating first so you can tell whether an answer makes sense. Study cards, hints, a practice quiz at three levels, and four workshop activities that check themselves.
52 take away 27. But two ones cannot give away seven ones.
When a column cannot pay, trade from the one next door — and that column is one smaller afterward. Forgetting to make it smaller is where most wrong answers come from.
Two things people get wrong
⚠️People often think…
In 52 − 27, you do 7 − 2 because 2 − 7 “doesn't work.”
It really doesn't work — which is the signal to TRADE, not to flip the digits around. Flipping gives 35. Trading gives 25, and 25 is the right answer.
Can't take it? Go next door and borrow.
⚠️People often think…
After you trade, the column you took from stays the same.
It is one smaller — you spent it. In 435 − 162, the 4 becomes a 3, so the hundreds are 3 − 1 = 2, not 4 − 1 = 3. Cross it out and write the new digit, every time.
Cross it out. If you didn't write it, you'll forget it.
Trade, subtract, check
1Watch one
52 − 27.
2 ones cannot give away 7.
Trade a ten: 4 tens and 12 ones.
12 − 7 = 5. Then 4 − 2 = 2.
25. Not 35 — the tens shrank.
2Do one with me
63 − 28.
3 ones cannot give 8, so trade. The 3 becomes
And the 6 tens become
So the answer is
💬One sentence, then you move on
Why does the tens digit get smaller after a trade?
3Try one
456 + 10 = ?
I want a hint first
A ten is one bundle. Adding one bundle changes the bundle count and nothing else.
Where this goes
Where this lives
Making change at a register, keeping score, checking whether you have enough saved up.
What this feeds
Next unit is length, time and money — the same counting, with units attached.
Estimate 347 + 285 before you add it. About how much?
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
➕ Adding in columns — the four steps
Line up ones under ones, tens under tens, hundreds under hundreds → add the ONES first; if you get 10 or more, write the ones digit and carry 1 ten → add the TENS, counting the carried ten; if you get 10 or more, write the tens digit and carry 1 hundred → add the HUNDREDS → read the answer and check it against an estimate. 347 + 285: 7 + 5 = 12 (write 2, carry 1), 1 + 4 + 8 = 13 (write 3, carry 1), 1 + 3 + 2 = 6. Answer: 632.
Line up, ones first, ten or more means trade.
🔟 The whole topic in one idea
Every place holds ONE digit, 0 to 9. When a place gets too full (10 or more), you trade 10 of them for 1 of the next place up: 10 ones = 1 ten, 10 tens = 1 hundred. When a place is too empty to subtract from, you trade the other way: 1 ten = 10 ones, 1 hundred = 10 tens. The amount never changes — only how it is written.
Ten of these is one of those.
⚠️ Traps the test loves
Flipping the digits when subtracting: doing 7 − 2 in 52 − 27 because 2 − 7 “doesn’t work.” It doesn’t — so trade a ten. The answer is 25, not 35.
Forgetting the carried 1. The little 1 on top of the tens column is a real ten. Add it.
Writing 12 or 13 inside one column. A place holds one digit — trade the rest to the next place.
Forgetting to make the top digit one less after a trade. In 435 − 162 the 4 becomes 3, so the hundreds are 3 − 1 = 2, not 4 − 1.
Adding 10 as if it were 100 or 1. 456 + 10 = 466 — only the tens digit moves.
Skipping the estimate. 347 + 285 is about 650; if you got 532, something is missing.
🧱 Trades — the chart
When
The trade
Example
Adding, ones reach 10 or more
10 ones → 1 ten
7 + 5 = 12 → write 2, carry 1 ten
Adding, tens reach 10 or more
10 tens → 1 hundred
1 + 4 + 8 = 13 tens → write 3, carry 1 hundred
Subtracting, not enough ones
1 ten → 10 ones
52 − 27: 5 tens become 4, 2 ones become 12
Subtracting, not enough tens
1 hundred → 10 tens
435 − 162: 4 hundreds become 3, 3 tens become 13
Subtracting across a zero
hundred → tens, then ten → ones
400 − 136: 3 hundreds, 9 tens, 10 ones → 264
🎯 How the test will ask
A column sum or difference — “find the answer.” Ones first. Watch for a column that reaches 10.
“Does this problem need a trade?” Look at each column before you work.
“Fill in the missing digit” after a trade — what the 5 became, what the 2 became.
“Add 10” or “add 100” in your head — which digit moves?
“Is this answer reasonable?” Round, add, compare.
A story problem — decide first: put together, or take away?
“Explain why” — say what a trade is: 10 of one place equals 1 of the next.
✅ Before the test, can you…
Say what each digit in a three-digit number is worth?
Add two three-digit numbers with one trade, and with two?
Subtract with a trade without flipping the digits?
Tell before you start whether a problem needs a trade?
Add or subtract 10 or 100 in your head?
Estimate a sum and say whether an answer is reasonable?
Check a subtraction by adding?
Pick your level
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
Workshop
Work like a mathematician: put the steps of a column sum in order, sort problems by whether they need a trade, finish a column subtraction with a trade, then decide whether a friend’s answer makes sense. Every activity checks itself, and hints are free.
Your practice never leaves this device. There is no account and no sign-in. Your work is saved in this browser only, and you can erase it whenever you want.
Your practice record — saved on this device
This is your record of the module on screen — it stays here and goes nowhere. Independent means you got it right on the first tap; supported means you got it after the explain-and-retry, or marked ‘I had it’ on a revealed answer. Both count, and neither is a grade. If your teacher asks, copy the row or show them this screen.
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The answer key is for a teacher: it prints only from here, for the unit on screen. Print the study packet prints the study pages and a blank quiz — never the answers.