Breaking a Ten Apart

For 62 − 27 there are only 2 ones, and 7 need to go. There are not enough.

Open a ten

Break one rod into ten cubes. Now there are 5 tens and 12 ones.

It is still 62

5 tens and 12 ones is 62, the same as 6 tens and 2 ones. Nothing was added or lost.

You did this in Grade 1, when 34 was shown as 2 tens and 14 ones.

Why you sometimes need to open a ten

In 52 - 27, the ones column asks you to take 7 from 2, and there are not enough ones. Nothing is broken — you just need to fetch more ones from somewhere. The tens column has them, bundled up. Open one ten and you have ten more ones to work with.

What the number becomes

52 is 5 tens and 2 ones. Open one ten and it becomes 4 tens and 12 ones. The value has not changed at all — 40 + 12 is still 52. Only the way it is packaged has changed, which is why this move is always allowed.

Different names, one idea

You may hear this called regrouping, borrowing, exchanging, or trading. They all describe the same move: unbundling a larger unit into ten smaller ones. "Borrowing" is the least accurate name, since nothing is given back.