Anthony Harradine is tireless in trying to save Australian Maths Ed. He is responsible for MathsCraft and Numerical Acumen, and all manner of things. Anthony invariably takes a positive, Nice Guy approach to all this. Nonetheless, we get along very well.

Of late, Anthony has been working hard at reforming things at Adelaide’s Prince Alfred College. Which has caused fights. Well, more accurately, Battles. And fights. But this post is about the Battles.

One of the activities Anthony and his fellow teachers have been arranging is Maths Battles, an idea Anthony imported from England. Here, teams of students battle away, competing with each other to quickly answer problems, all under the intimidating gaze of the stupidly-robed adjudicators.* And, now, under the intimidating gaze of the parents.

PAC’s most recent Maths Battle was fought in public, with parents and UFC talent scouts invited to look on. It was, reportedly, a raging success. From PAC’s summary of the event:

*Sunday saw the first public mathematical battles happening at Prince Alfred College (and as far as we know, in South Australia, maybe even in Australia!). Two groups of Year 7 and Year 8 students have been working on their mathematical knowledge and problem solving skills during their Sunday training sessions as part of the Co-curricular Mathematics program, which has proven to be quite popular in its inaugural year.*

*To celebrate the semester’s work, students showcased their problem solving and reasoning skills in front of peers and parents, in three rounds of mathematical battles. In teams of four they solved ten questions and challenged their opponents, carefully scrutinising and criticising each other’s solutions, which led to beautiful – and sometimes heated – debates about Mathematics. We congratulate all participants on an excellent effort and the winning teams on their hard-earned victory.*

It seems to be a very good thing. A few of the more numerical Battle questions are below. And teachers who would like to find out more can email Anthony.

*) The photos are reproduced with the kind permission of, and gathered by, PAC.

**Q1. **What is the remainder when 1 + 2 + ⋯ + 2021 + 2022 is divided by 2023?

**Q2. **Using the following digits exactly once, make four 2-digit prime numbers: 1,2,3,4,5,6,7,9. What is the sum of these prime numbers?

**Q3. **Lisa is given a set of 4 different digits. By using all the digits exactly once, she makes the smallest 4-digit number possible. Using the same set of digits, she then makes the largest 4-digit number possible. If the sum of the smallest and largest 4-digit numbers that can be made with Lisa’s set is 10 560, what are Lisa’s 4 digits?

**Q4. **An oddie number is a 3-digit number with all three digits odd. How many 3-digit oddie numbers are divisible by 3?

**Q5. **The five-digit number 839𝐴2 is divisible by 12. What digit does 𝐴 represent?

**Q6. **The following set of numbers is written on the board: {3, 7, 12, 14, 22, 35 and 49}. Anthony erases 3 numbers from the set. Then Tayla erases three numbers from the remaining set. The sum of the numbers that Anthony erased is 4 times the sum of the numbers that Tayla erased. Which number remains on the board?

I use problems from mathematics competitions from different countries for extending Year 7 and 8 students. We have one extension lesson/week … but never on Sunday! The style of questions above is similar to those in the competition run by the UK Mathematical Challenge. (I am not suggesting that the questions above are from this competition.)

From the Gardiner books you bought? How do you use them, and for all students, or a selected or self-selected subset?

The books are organised by year level (approximately) and the chapters are organised by topic; I choose questions by topic and year level, and look at the questions; I make up a list of questions that would take a lesson or a bit more for the students to work on; sometimes a question will suggest related or similar questions and I get carried away and use them. My students have been selected by teachers as above average students – which matches Gardiner’s audience. This semester my students are in Years 7 and 8.

Thanks, Terry. I think you may have given the titles in a previous comment, but could you give them again here?

Sounds like fun!

I can’t find the video right now or would vex you. But there’s a cool one where Richard Feynman reminisces about his high school “algebra team” which required great speed in known techniques along with (or instead, it varied) skill in using unusual techniques to bypass the usual techniques. He sounded like he really loved it and missed it, still, in his 60s. Even after having won a Nobel Prize and having run a section of human calculators at Los Alamos!

Thanks (and thanks for not finding the video). These competitions can clearly be very meaningful to kids, beyond the mathematics learned.

Problem books by Tony Gardiner.

Extension Mathematics Alpha (aimed at Years 7-8)

Extension Mathematics Beta (aimed at Years 8-9)

Extension Mathematics Beta (aimed at Years 9-10)

Mathematical Challenges (Problems from UK Schools Mathematical Challenges)

More Mathematical Challenges (Problems from UK Junior Mathematical Olympiad 1989-1995)

Thanks, Terry. I assume the second Beta is meant to be Gamma. And yes, the Mathsteasers books are great. I’ll hunt for the comp books.