# reverses investigation

In order for students to ensure they are fantastic at written methods of addition and subtraction they need loads of practise. Rather than setting hundreds of different questions, I use the following investigation so students get the required practise with a minimal amount of marking on my part. The subtraction sections should always involve borrowing / stealing.

## starter - 99

On whiteboards, ask the students to perform the following set of instructions;

- choose a 2-digit number that is not a multiple of 11

- reverse the digits

- subtract the smaller number from the larger number (using column subtraction)

- reverse this new answer

- add the answers from step 3 and 4 (using column addition).

- students reveal their boards. They should all get 99.

Note: If students get an answer of 9 in step 3. then they need to write it as 09 (using the 0 as a place holder) and then reverse it in step 4. to 90.

## good old 1089

The process described above is commonly used with an initial 3-digit number. The answer should always be 1089, meaning that it is extremely simple to check students’ answers. Here’s an example

- choose a 3-digit number with different first and third digits

- reverse the digits

- subtract the smaller number from the larger number (using column subtraction)

- reverse this new answer

- add the answers from step 3 and 4 (using column addition).

- students reveal their boards. They should all get 1089.

Note: If students get an answer of 99 in step 3. then they need to write it as 099 (using the 0 as a place holder) and then reverse it in step 4. to 990.

## extending the investigation

From here the natural progression is to go to four digits. Unfortunately there is not a single solution to this one, but there are a limited number and challenging students to find them is a nice extension. Once students have found the solutions then they can try describe which starting numbers create each of the totals. A solution up to four digits can be found here: