art of problem solving nz

• Global Issues Problem Solving
• Community Problem Solving
• Scenario Writing
• Scenario Performance
• 2024 Registration
• Expression of Interest
• Resources for Purchase
• Downloadable

Programme Information

Future Problem Solving is a highly regarded and well-researched international educational program that develops creative, critical and caring thinking skills in students from Year 1 – Year 13. Students grapple with global and community issues, identify underlying problems and create positive solutions to those issues. Above all, it aims to give young people the skills to design and promote positive futures as citizens of the 21st Century.

Listen to this

Thank you Hannah, for being such a great ambassador for FPSNZ.

Components of the Future Problem Solving Programme

There are three programme components in Future Problem Solving. In Global Issues Problem Solving and Community Problem Solving, students work in teams or as individuals and in Scenario Creation, they work as individuals.

Click here for the cost of participation.

Goals of the Future Problem Solving Programme

To develop an active interest in the future

To encourage creative thinking

To develop critical and analytical thought

To strengthen oral and written communication skills

To present an effective problem solving model

To develop research techniques

To work co-operatively in teams.

Links to the New Zealand Curriculum

Future Problem Solving has close links to the New Zealand Curriculum (NZC). It reflects the Principles of the NZC and in particular provides a vehicle for exploring the Future Focus Principle. See NZ Curriculum Update 15 for information about this principle. Students have the opportunity to both develop their own key competencies and to explore how other people develop and apply the key competencies whilst problem solving. Topics for Global Issues are deliberately selected across a range of learning areas, whilst Community Problem Solvers will develop skills and knowledge across the learning areas through authentic contexts. Teachers ('Coaches') will have the opportunity to apply the effective pedagogies as they facilitate 21st century collaborative learning.

Read about Kerikeri High School’s exploits in FPS here:

http://www.stuff.co.nz/auckland/local-news/northland/bay-chronicle/5900409/Kerikeri-schools-deal-with-problems-in-style

Read David Huebner, US Ambassador to NZ and Samoa’s blog entry on the NZ teams at the International Finals in 2010:

http://blogs.newzealand.usembassy.gov/ambassador/2010/07/kiwis-solve-problems-in-wisconsin/

“Future Problem Solving is of value to those considering entering the business/management worlds as it teaches them to be innovative in an ever-changing environment and to implement solutions having considered all the implications." 

- Lecturer in Management – Parent of a Future Problem Solving student.

Future Problem Solving NZ

Sample Problems

• Algebra - with solutions
• Combinatorics
• Number Theory

Past NZMO Problems

• 2023 NZMO2 with solutions
• 2023 NZMO1 with solutions
• 2022 NZMO2 with solutions
• 2022 NZMO1 with solutions
• 2021 NZMO2 with solutions
• 2021 NZMO1 with solutions
• 2020 NZMO2 with solutions
• 2020 NZMO1 with solutions
• 2019 NZMO2 with solutions
• 2019 NZMO1 with solutions

International Sites and Competitions

• International Maths Olympiad
• International Maths Olympiad Foundation
• Art of Problem Solving
• Australian Maths Trust
• United Kingdom Maths Trust
• Harvard MIT Maths Tournament
• Canadian Mathematical Olympiad
• Asian Pacific Mathematical Olympiad
• Tournament of Towns
• Dutch Mathematical Olympiad
• Singapore Mathematical Society
• Putnam Competition
• International Mathematics Competition
• Simon Marais Competition

New Zealand sites

• Auckland Mathematical Association
• Canterbury Mathematics Association
• Bay of Plenty Mathematical Association
• Northland Mathematics Association
• Otago Mathematics Association
• Waikato Mathematical Association
• Wellington Mathematics Association
• Maths Craft

Problem and Puzzle Pages

• Northwestern University Math Problem Solving Group
• Crux Mathematicorum
• KöMaL Magazine
• The Mathematical Gazette
• Berkeley Math Circle
• The Riddler
• Project Euler
• Purdue Problem of the Week
• Cut the Knot
• Calculus Problem of the Week
• Torsten Sillke Puzzles
• Macalester College Problem of the Week
• Nick's Mathematical Puzzles
• William Wu Riddles
• Math Puzzle
• Mudd Math Fun Facts

Books, Interesting Sites and Other Resources

Problem solving tactics.

Every aspiring olympiad mathematician should own a copy of PST.

Derek Holton's Mathematical Olympiad Series

This book series could be very useful to some of you - I would recommend getting the one at the right level for you rather than all of them. A few libraries in New Zealand hold these books - just search in the national library catalogue .

Evan Chen's Notes

Evan has amassed a nice collection of lecture notes aimed at students training for the IMO.

Advice from Geoff Smith

Geoff is the president of the IMO board, so is intimately familiar with the IMO, and has some excellent advice and resource suggestions.

Bertrand’s Postulate

The fact that, for every positive integer n, there is a prime between n and 2n is known as Bertrand’s postulate. It arises occasionally in Olympiad style problems (usually with the note “You may assume Bertrand’s Postulate …”). Michael Nielsen has a nice post giving an elementary proof at the Polymath wiki.

Number theory

At least a couple of good, comprehensive introductions to elementary number theory are available online. These notes by Jim Hefferon and W. Edwin Clark are nicely written and gently-paced. These ones by Naoki Sato are a bit more Olympiad-focused.

Chrystal’s Algebra

A classic (pre 1900) textbook on algebra by Chrystal has been scanned and made available electronically . Volume 1 is not likely to be of much interest for training purposes but chapters 23 and 24 (on combinatorics), 32 through 34 (continued fractions), and 35 (number theory), of volume 2 are.

Discrete and polyhedral geometry

Problems in discrete geometry (i.e. the border between combinatorics and geometry) have made several appearances on the IMO. A nice book by Igor Pak covers much of the important material in this area — the book is aimed at undergaduate and graduate students in maths, but the first few chapters in particular are suitable for Olympiad level students. As in many cases, the important thing is not the results themselves (though Helly’s theorem is a useful tool in lots of setting) but the “style” of proofs in this area.

The Princeton Companion to Mathematics

The Princeton Companion to Mathematics , an “encyclopedia of modern pure mathematics” is a fantastic book, edited by mathematician Timothy Gowers . It touches on a lot of topics, some of which are quite advanced, however section 1.3 on fundamental definitions and structures is very useful, in particular the parts about limits and continuity, and section 5.13 is a good overview of the Fundamental Theorem of Algebra. You may also find some useful notes on how professional mathematicians go about problem-solving.

Useful list for problem solving

Having the right mental habits is one of the keys to being a successful problem solver. A really good list was posted at a math education blog . The list is supposedly for sixth grade (i.e. year six) students, but is much more universal than that.

Abstract Math

The site Abstract Math by Charles Wells presents some useful insights on writing and doing proofs. The author’s opinions in some areas are arguable (so you should read and think about them, rather than follow the advice verbatum). For instance, I wouldn’t recommend the “Languages of Math” section which is far too detailed at present. However, there are little gems to be found everywhere, and from within that section comes the link to Timothy Gowers article, “The language and grammar of mathematics.” . By the way, the Tricki is alive, although small and incomplete, but it is still a great resource.

How to Write Proofs

Another site that walks through how to write proofs, which could be useful. Again, take things with a pinch of salt.

Recommended Mathematics Literature

This site is now fairly old, but still has some good recommendations for mathematics textbooks, puzzle books and other good reading.

Integer sequences

Neil Sloane, who is the father of the encyclopedia of integer sequences , has produced a paper , which highlights seven of them. There are no problems to solve there (other than some hard open ones!), but lots of interesting stuff. For example, you might like to try and prove the following result before reading it:

Consider the sequence defined as follows a(1) = 1, a(2) = 2, and for n >= 3, a(n) is the smallest positive integer not yet in the sequence such that gcd(a(n), a(n-1)) > 1. Prove that every positive integer eventually appears in the sequence.

The Geometry Junkyard

David Eppstein has put together an interesting collection of random things related to geometry. I guarentee you will find something interesting.

Gusty Games

Our very own Ross Atkins runs monthly programming workshops on this website. There are also some fun and interesting mathematical challenges in the "apps" section, as well as a couple of puzzle apps published to the Android and iOS stores.

• Store Locator
• Sign In/Register Email Address Password Sign in Forgotten your password? Register
• Your Cart 0 Items 0 Subtotal $ 0 Order Total (NZD) $ 0 Cart Checkout
• Favourites Favourites
• View All Books
• best sellers
• new releases
• coming soon
• BARGAIN BOOKS
• locally loved favourites
• ockham nz book awards - shortlist
• nz book awards for children and young adults - finalists
• action & adventure
• comics, graphic novels & manga
• contemporary
• crime & thrillers
• general fiction
• poetry & plays
• science fiction & fantasy
• short stories
• non fiction
• art & photography
• biography & memoir
• business, finance & law
• computers & information technology
• crafts & hobbies
• education & reference
• health & wellbeing
• home & garden
• mathematics & science
• mind, body, spirit
• religion & spirituality
• sport & recreation
• new zealand art & culture
• new zealand biography & memoir
• new zealand cook books
• new zealand fiction
• new zealand history
• new zealand kids' fiction
• new zealand natural history
• new zealand non fiction
• new zealand pictorial
• new zealand travel & maps
• art & culture
• general maoritanga
• te reo maori
• baby & preschool
• picture books
• View All Stationery
• analysis books
• business books
• invoice books
• manifold books
• multipurpose
• order & delivery books
• receipt & deposit book
• commercial diaries
• designer diaries
• mid year diaries
• new zealand diaries
• standard diaries
• student diaries
• wallplanners
• bags & accessories
• gift & novelty
• journals & notebooks
• keepsakes & record books
• notecards & greeting cards
• archive & storage boxes
• concertina files
• copysafe pockets
• display books
• document wallets
• filing accessories
• index cards & boxes
• letter trays
• lever arch files
• magazine files
• manila folders
• presentation folders
• ringbinders
• suspension files
• desks & tables
• filing cabinets
• miscellaneous
• hygiene/safety
• adhesive, binding & fastenings
• calculators
• conference products
• desk accessories
• dispenser labels
• label makers & tape
• laminators, binders & shredders
• notebooks & pads
• office accessories
• scissors & cutters
• signs & tickets
• staplers & hole punches
• sticky notes
• tape dispensers
• coloured paper
• machine rolls
• photo paper
• photocopy paper
• book covering & book labels
• drawing pads & wallets
• exercise books
• learning & revision
• maths equipment
• pencil cases
• project boards
• refill pads
• school bags & accessories
• ballpoint pens
• erasable pens
• erasers & sharpeners
• fibre tip pens
• fountain pens
• highlighters
• mechanical pencils
• pen refills
• rollerball pens
• whiteboard markers
• View All Art & Craft
• activity & colouring books
• diamond art kits
• drawing & painting kits
• fabric & needle craft kits
• kids art & craft kits
• other craft kits
• coloured pencils
• glitter & embellishments
• modelling materials
• paint brushes
• paper craft
• sketch books & pads
• sewing & cross stitch
• tools & accessories
• View All Toys & Games
• board games
• educational toys
• indoor games
• general toys
• jigsaws & puzzles
• outdoor games
• squishmallows
• trading cards
• View All Technology
• headphones and earbuds
• cables & chargers
• keyboards & mice
• laptop bags & sleeves
• workspace set-up
• brother inkjet cartridges
• brother toners
• canon inkjet cartridges
• canon toners
• epson inkjet cartridges
• hp inkjet cartridges
• cd & dvd
• external hard drive
• memory cards
• usb flash drives
• accessories
• mobile sim cards
• adaptors & chargers
• power banks
• other technology

Digital Gift Card

Physical Gift Card

Check Card Balance

• Back to School
• Customer Service
• Big Deal Club

The Art of Problem Solving Paperback

A resource for the mathematics teacher.

Or 4 payments of $30.55 with

Toggle filter item Description

Product code: 9780803963627

Toggle filter item Synopsis

Toggle filter item delivery.

• The delivery service does not include assembly or setup of kitset or electronic products.
• We do not ship to addresses outside of New Zealand.
• We reserve the right to refuse or negotiate delivery fees for non-standard orders. i.e. large volume orders.
• Physical Gift Cards will require a signature on delivery.
• Overweight threshold is set at 5kgs or greater.

Toggle filter item Shipping & Returns

Products can be returned in store, or by post, for exchange or credit as long as they are returned in saleable condition within 28 days.

Paper Plus Team Reviews

Prices and offers may vary between Paper Plus Website and Paper Plus Stores

All Payment Cards accepted

The home of mathematics education in New Zealand.

• Forgot password ?
• Teaching material
• Problem solving activities

Ideas for using problem solving activities

The Ministry is migrating nzmaths content to Tāhurangi.             Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz).  When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024.  e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

• Consider changing the context, the names of characters, or the numbers in the problem to make it more suitable for your class. Click to download a collection of templates to support you to create your own versions of problems.  
• Captivate your students (hook them into the problem) with a creative introduction.  
• Having shared the problem, have your students retell in their own words what the problem is asking them to find out. To experience success a student must first fully understand the problem.  
• Make suitable materials available. Many students solve a problem and demonstrate their solution using materials.  
• Be clear yourself about exactly what you want your students to learn from their problem solving experience.  Make this explicit to your students. (Finding a solution is only part of the learning).  
• Conclude a problem solving session with your students by identifying important learning and together generalize this to other situations.  
• The problems are set within full lessons which outline a suggested teaching sequence. These are guidelines only.