When you made a new ten in Grade 1 (Adding That Makes a New Ten), you traded 10 ones for 1 ten. Let’s look closely at why that trade is fair, because every carry and every borrow is this same trade.
Why it works
A ten-rod is just 10 ones stuck together. Trading 10 loose ones for 1 rod is like trading 10 pennies for a dime: you have the same amount, packed a different way. Nothing was added and nothing was lost. Breaking a ten into 10 ones is the same trade, done backward.
Worked example: Trade ones for a ten
What number is 3 tens and 14 ones?
- Count the value: $30 + 14 = 44$.
- Trade 10 ones for 1 ten: now 4 tens and 4 ones.
- Count again: $40 + 4 = 44$. The same amount!
Answer: 44
Worked example: Break a ten
Show 52 using only 4 tens.
- 52 is 5 tens and 2 ones.
- Break 1 ten into 10 ones: 4 tens and 12 ones.
- Check: $40 + 12 = 52$.
Answer: 4 tens and 12 ones
Key idea
10 ones = 1 ten, and 10 tens = 1 hundred. Trading or breaking changes how a number is shown, never how much it is.
Common mistake
Thinking a trade changes the number, so you stop trusting your answer. Check by finding the value both ways: 3 tens and 14 ones is $30 + 14 = 44$, and 4 tens and 4 ones is $40 + 4 = 44$.
Grown-up tip: Trade coins at home: 10 pennies for 1 dime. Count both piles to see that they match.