**The Mathematical Association**

**Mathematical Reasoning, Justification and Proof**

**Saturday 28**

Planned Venue UCL, London

^{th}March 2020Rescheduled as a Webinar

Summary: In this workshop Charlie Gilderdale from NRICH selected some of his favourite problems and showed how they can be used to introduce students to mathematical reasoning, justification and proof, so that they can learn to develop convincing arguments.

Due to the lockdown on 24^{th} March we were unable to meet at UCL, London. Thanks to Mark Horley the professional development was rescheduled as a seminar using Zoom for audio and visual and Bitpaper as a whiteboard. Delegates had the option to team up with a family member, another delegate or opt for a blind date. I opted for a blind date, I was stood up, but this did not dampen my enthusiasm.

Charlie began with an introduction to the different strands of a student’s processing of a problem.

We were soon working in our pairs on the first challenge of the morning.

__Challenge 1 Cryptarithms. __

I was happy to get one answer. Although as many as five were possible. We were encouraged to remind students to consider multiple solutions

Challenge 2 The Number Jumbler

This was my favourite challenge of the day. I love emoji’s and they make it a very colourful and engaging challenge. Charlie mentioned that this task is a way to tap into a student’s curiosity. I have used it with all my student’s this week to do just that, year 6 to year 12 and they have all enjoyed it. I have left it with them all to see if they can reason it. Sue Cubbon provided us with an excellent algebraic explanation. We were left wondering about 90 and 99 which was soon clarified.

Challenge 3 Fruity Totals

This was my fruity totals. It is a challenge which helps with students understanding of equations and formulae. I challenged myself to reason it, without going straight to simultaneous equations. It was useful to remind myself to choose the rows & columns with the least number of different fruits. Row 2 and 4 & column 3.

__Challenge 4 Unequal averages__The first task here was to find a set of five numbers with an equal mode, median, mean and range. I thought I’d got one in blue but red beat me to it! Sorry Charlie for messing with your board.

There were many more challenges on averages and other further challenges we didn’t have time to do.

I thoroughly enjoyed having an introduction to what NRich has to offer. It will provide me, if not my students, with plenty of puzzling over this lockdown. Thank you to Charlie and Mark for making it possible in difficult circumstances.

*If there are any errors, omissions or misrepresentations, please let me know at [email protected]*

This was a really good session and I have used some of the resources highlighted to challenge my year 7 class during remote teaching this last week. Thanks again for making this an online session rather than cancelling. Refreshing and thought provoking to take part.

Sue