  # Inside Track: Subtracting 0 and 10

### Key Idea:

Subtracting 0 or 10 involves thinking about the processes involved, rather than learning a “rule”.

These two strategies are bundled together as “special cases” of subtraction. Neither is particularly difficult, though students should still be invited to think about what each means.

Subtracting zero, like adding zero, does not change the original term. Students can think about this in the context of everyday stories in which nothing is removed. For example, “My Aunt Jane went shopping. A shop had 25 pumpkins for sale. Aunt Jane decided that the pumpkins were too big for her cooking pot, so she didn’t buy one. How many pumpkins were left on display?”

Subtracting 10 from a number between 11 and 19 is a place value question. Each of these numbers is made up of 1 ten and a number of ones. If ten is subtracted, then just the ones are left. The written symbol for the original number will be made up of a “1” for the ten and another digit for the ones. The answer to the “take away 10” question will be the same as the second digit.

Students will easily see the connection between the original number and the answer if the number is represented using a pair of ten frames.

### Extending These Facts:

For more capable students, put to them questions to take away 20, 30, or another number of tens. This could start with questions such as “35 – 30 = ?”, and move to harder questions such as “48 – 20 = ?”.  