Here’s a big number:

Try different single-digit divisors. No remainders.

This is an example of purposeful practice – exposing the wonder of mathematics whilst providing a reason to practise lots of of bus stop division.

You might want to start by asking pupils to come up with their own dividend “in the tens of millions” and try different divisors. (Here for a quick primer on the mathematical language.) Inevitably they will end up with remainders, which they may or may not carry into decimal places. Then let show them this “magic” number.

Questions to ask:

- What divisors does this work for and why? (Purposeful practice)
- What other dividends could I make like this? (Purposeful practice + reasoning)
- What smaller dividends could I make like this? (reasoning)
- What is the smallest dividend I could make that all numbers 1-9 will divide into without remainders? (reasoning)

Whilst I would want everyone in the class to understand the reasoning through a whole-class discussion, you may have some learners who need the practice on bus stop long division and spend most of their time doing this. Those that are confident with this technique can spend their time exploring deeper into the structure of the number.

Whilst we are on the subject of “Bus Stop”, maybe this technique actually has nothing to do with standing in line waiting for a bus:

“It’s not bus stop, it’s actually the inverse of a model of area for multiplication” @petegriffin7 pic.twitter.com/E1Fc7ogUwT

— Mark Horley Maths (@mhorley) January 30, 2017