# 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;

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

2. reverse the digits

3. subtract the smaller number from the larger number (using column subtraction)

4. reverse this new answer

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

6. 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

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

2. reverse the digits

3. subtract the smaller number from the larger number (using column subtraction)

4. reverse this new answer

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

6. 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: