# Blog

## Addition and subtraction by a number (example-problem pair)

## Equivalent ratios with algebra (supercharged with fading)

## The Decide, Break, Repair and Simplify process for linear equations (DBRS)

The Decide, Break, Repair and Simplify process was first introduced by Kris Boulton at the Birmingham maths conference in October 2018. The process is used to solve linear equations. I have adjusted it to rearranging the subject of a formula, but will not be posting this until I have presented it again at Sheffield. I presented this for the first time at the Bristol maths conference in March 2019 which was a very scary moment for me!

To say that I was impressed with this method was an understatement. This process breaks the solving of linear equations down into small steps (atomisation).

The first step is known as “Decide” which is the most important step in the process (in my opinion). The decide steps are built up more and more as the linear equations become more advanced. I like to think of this as a bucket that is being filled more and more as students go through this mathematical journey.

We start this journey with expressions such as x+5 and ask the students “how do we get to x through addition or subtraction?”. Once they establish that they subtract 5 we can begin to make them more confident with expressions like x+2801 etc.

We then move on to solving equations of the form x+a=b. For example, solving the equation x+5=20. To do this, we ask students how we get to x from x+5. We subtract 5 so we BREAK the equation by doing x+5-5=20 and then REPAIR by doing x+5-5=20-5. We then SIMPLIFY to get x=15. We can continually build on this. To see how we can do this progressively, check out my powerpoint below!