# Arranging Digits

Extensive lesson notes on some of these tasks are available on a subscription basis from the Maths 300 resource bank.

Problems can be enlarged on a photocopier to A3 posters.

What I find useful is to model some of these tasks with the whole class with big numbers (Digits 1 to 9, and 0 to 9 when required), so that kids see that the problem is not a trivial problem.

## * How could I convince someone I've found them all?

These tasks are a wonderful contrast to setting kids 'busy work' of 'gazinta worksheets.' Kids are doing so many more mental computations in the quest for the solution.

Gazinta worksheet...the sort of stuff spewed out by an endless range of websites.

### Ordering Numbers - Teaching Notes

Challenging students to find all the ways of arranging 4 digits (or 3 digits as an introductory task) provides an excellent opportunity to integrate the development of number sense and place value with combination theory. Many adults would find this a challenging task, and yet it is accessible to young students with appropriate scaffolding.

Students respond well to the physical aspect of holding a large digit on a laminated card, with instructions coming from the audience (the rest of the class). Having the students repeat the task back at their desk with a smaller format helps to reinforce the mathematical concepts embedded in the task.

This task offers a good window for a teacher to observe students’ strategies in ‘working as a mathematician’ and how they record and publish their data.

There are several formats and ways these resources might be used:

Students out the front of the class holding cards, responding to questions posed by the teacher or the class. Eg. Can you make the biggest number? Smallest number? An odd number? And another? And another? A number between 2000 and 3000? And another? And another?

Large format cards (18 in all, showing all arrangements of 4 numbers, with a zero) can be used for students standing out the front, arranging them in ascending or descending order. The ledge on a whiteboard might be useful for this. If you have carpet on your walls, 1-2 velcro tabs on the back of each card would work well.

Small format cards (same as above) can be used as a table-top version for students, once they are familiar with the structure of the task. The task can be further extended by using a count-down timer or stopwatch (eg. http://www.online-stopwatch.com/full-screen-stopwatch or http://www.teachit.co.uk/custom_content/timer/TeachitTimer.zip. If students collect their data, a good opportunity for graphing arises. Using the Teachit Timer, students can nominate their own time, and try to beat it.