Compact Method
Since Maruta makes the trades before she writes things down, each column never has more than one digit. That way she does not need the Base-Ten Recording Sheet to tell her the value of the digits—she just uses place value.

She explains it like this:

“8 ones plus 7 ones is 15 ones.

“I trade 15 ones for 1 ten and 5 ones.

“I write 5 in the answer space of the ones column.

“I write a little 1 in the tens column.”

“1 ten plus 7 tens plus 6 tens is 14 tens.

“I trade 14 tens for 1 hundred and 4 tens.

“I write 4 in the answer space of the tens column.

“I write a little 1 in the hundreds column.”

“Finally, I add the hundreds, 100 + 600 + 200. I get 9 hundreds.

“I put 9 in the answer space of the hundreds column.”