otago problem solving answers 2015

Otago Problem Solving

Otago university maths  problem-solving challenge.

At Kenakena we have been focusing on delivering a school-wide maths programme where problem-solving is at the heart.

Problem Challenge is a mathematics problem solving competition aimed primarily at Intermediate School children. It is organised by members of the Department of Mathematics at the University of Otago ( https://www.maths.otago.ac.nz/pc/ ).

Children participating in the competition attempt to answer five questions in 30 minutes on each of five problem sheets, which are done about a month apart starting in April.

The Otago University programme is well suited to what we do and our participating students do really well. Children from Years 6 to 8 are nominated by their teachers based on a recognised ability to solve demanding mathematical problems. In 2015, 55% of our students who participated achieved an Excellence award!

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Registration

Dates for 2024.

Set 1 Set 2 Set 3 Set 4 Set 5   Final Challenge 11 April 16 May 20 June 25 July 22 August   Thursday 17 October

Dates for 2025

Rules for problem challenge.

• Eligibility: Children up to Year 8 are eligible to take part, and must be entered in their correct year. The competition is normally restricted to Years 6, 7 and 8, although it is possible to enter very able Year 5 children and classify them as Year 6.
• Security: Each set of questions is provided a few days before the administration day to give you time to make sufficient copies for your pupils. The original and copies must be kept secure.
• No preparation: Prior to each Problem Challenge set you must not prepare the children specifically for any problems on the set. Although you will have seen the questions and answers beforehand, any “problem solving” instruction given to the children must be of a general nature and must not give them any special advantage. We want honest assessments of your pupils’ abilities.
• Duration: Children should be given 30 minutes to complete each set. If children finish early, you must not mark their work until after the 30 minutes.
• No help given: You may not assist pupils during each Problem Challenge set, other than perhaps to explain the meaning of an unfamiliar word or phrase. It is important that all children throughout the country are on an equal footing. You may wish to refer to the glossary of common mathematical words that are used in the competition, and to ensure all your children understand their meanings.
• Dates: Administer the Problem Challenge sets on the days specified where at all possible. If this is not suitable, then please arrange to do it as close as possible to this day, and standardised throughout the school if there are pupils in more than one class involved. We understand that occasionally because of school camps or sports activities the Problem Challenge set may have to be postponed to a different week.
• Calculators: The use of calculators is permitted but should be of little advantage. All the problems we set are capable of being done “by hand”.
• Absentees: Inevitably children will miss tests for various reasons. Teachers may at their discretion allow a child to complete a challenge later, under the usual conditions, provided they are confident the child has not seen the questions or answers. Because of the logistics involved, the awarding of certificates will be based on the total number of problems correct and cannot take absences into account.

Rules for Final Challenge

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Problem Challenge: Otago Maths Competition Book 6 (2015 - 2019) - including Final Challenge

Test/Exam Preparation | Mathematics Study & Revision Guides

Each year Intermediate School children (Years 7 & 8) tackle 25 challenging maths questions of a problem solving nature. Each year Intermediate School children (Years 7 & 8) tackle 25 challenging maths questions of a problem solving nature. The sixth competition book is similar to Books 3, 4 and 5 and features all 125 problems from 2015 to 2019, together with the corresponding questions from the Final Challenge competition (another 100 questions). It features coloured illustrations, full solutions and analysis, and ideas for extension work. Another 116 pages of problem solving!

$39 .99 NZD

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• ISBN : PRCHOTAG6
• Publisher : University of Otago
• Imprint : University of Otago
• Publication date : November 2023
• Product Type : books

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Welcome to the Junior Mathematics Competition!

This year the competition will be held in two parts – the first being a multiple-choice and short answer exam sat entirely online , while the second part will be a paper exam limited to the top 15 percent of participants in the first part.

The first part of the competition will be sat from Monday April 4 to Friday April 8 inclusive , while the second part will be held on Wednesday May 11 .

2022 is the 37th year of this highly successful Competition.

This mathematics competition is for students in years 9 to 11 (forms 3 to 5), although younger students may also take part. Every student throughout New Zealand sits the competition on exactly the same days, usually two Wednesdays in April in May (one for each part).

The competition lasts for 50 minutes per part (so one hour, 40 minutes in total). The emphasis is on problem solving, so expect surprises!

Mathematical skills are important, but so is careful reading. Students who read the questions carefully and work out exactly what is being asked generally do better than those who jump in and write down the first thing that springs to mind.

Although many of the same questions are asked for each year level, students only compete against students at the same level as themselves. (However students in years 7 or 8 are regarded as being in year 9 for the purposes of the competition.)

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Past examination papers

Copies of past examination papers are available online through the Library website.

Not all examination papers are available online as departments sometimes embargo the publication of particular examinations.

Past exam papers

Paper co-ordinators may request an embargo on the publication of an exam paper:

Email [email protected] AND [email protected]

Lists of embargoed papers can be found in AskOtago Teams, in the relevant folder for year and semester: Examinations and Exam Support

See also Return of exam scripts for more information.

Related Articles (4)

The AskOtago team can help you find what you’re after.

Otago Problem Solving

The competition started around the early 1990’s in South Island schools, but after about two years, the competition became available to schools all over New Zealand with students in years 7 and 8. Some younger children can sometimes participate too. In most years about 650 schools enter problem challenges, involving over 35,000 children.

Each year students answer 5 questions in 30 minutes, over 5 sets of work, and at the end of each competition everyone receives a certificate. 10% get excellence, 30% get a merit, while the others receive a participation award.

We think that everyone who participated had a great time and enjoyed pushing themselves in that category. A quote from Harry, “I really loved the challenge and even though I didn’t do brilliantly I have thoroughly enjoyed it and improved on my maths.”

Here are some questions from the quiz

The school soccer team has played 15 games with a success rate of 80%. In order to raise their success rate to 90% in the shortest possible time, how many consecutive games must they win?

All of Toby’s marbles are either blue, red, green, or yellow. One third of his marbles are blue, one quarter of them are red, and seven of them are green.

What is the smallest number of yellow marbles that Toby could have?

Written by Aydin Khajehzadeh and Harry Baddington

Examination scripts and results

Key dates and deadlines for 2024

The table below shows the key dates and deadlines (over a 12-week period) for the University's provisions for Recounts and return of examination scripts following the date of the release of confirmed results for the 2024 examination periods.

Final results

Final results for papers can be viewed in the Examinations and Results section of the student eVision portal as soon as they become available each teaching period. Initially "Unconfirmed" will be shown alongside them. Once "Unconfirmed" is no longer showing, results are official.

The University of Otago uses the following scale to convert numerical marks into grades:

Viewing your examination script

You may request to view your script from the start of week 1 to the end of week 12 from the date of the release of confirmed results.

There are no application forms or fees associated with viewing your examination script.

On-campus students

Contact the relevant teaching department to arrange a time to view your script in the Department.

Distance Learning students

Please email us for information regarding viewing your script:

Email [email protected]

Applications for a recount must be made within four weeks from the date of the release of confirmed results (see above for dates). A recount involves a careful re-check of the marks that count toward your final result in a paper. The purpose of a recount is to ensure that no answer, no portion of an answer, or any work undertaken during the teaching period which counts for the final result, has been overlooked. No personal information accompanying the application is passed onto the examiners.

Your work is not re-marked; at the University of Otago there is no provision for any work to be re-marked.

Application and payment information

To apply please complete the Recount of Results form .

The administration fee is $36 per paper, regardless of how many examinations a paper has. This is because a recount is a check of all marks that comprise the final grade in a particular paper. Please see below for information on paying administration fees . Where a recount results in a change of mark, the administration fee will be refunded.

The submitted form and payment must be received by the deadline. Late applications are not accepted.

The recount process

Once your application has been received and your payment processed, the relevant department(s) will be asked to re-check all components of your final mark, to ensure that nothing has been omitted or recorded incorrectly. Once this is done, the department advises Student Administration of the outcome, and we advise you via your student email address. The process can take several weeks, so if you haven't been notified of the outcome and would like to check the status of your application, please contact:

Student Administration Email [email protected]

Return of examination scripts

You may apply for the return of your examination script from the start of week 7 until the end of week 12 from the date of the release of confirmed results.

After twelve weeks from the date of the release of confirmed results, unclaimed scripts are disposed of by Departments.

Restrictions

Not all examination scripts can be returned. If your answers involved problem solving, were answered on multi-choice answer sheets for computer marking or a Department requires a particular examination paper to be embargoed from publication and not released into the public domain then you will not be able to have your script returned to you. However, you can still view it.

To find out if an examination script can be returned to you or not, go to the Library's past exam papers webpage and check the examination (embargoed examination papers are noted as such).

Past exam papers – University of Otago Library

Application information

Submit your application to AskOtago:

Return of examination scripts – AskOtago Service Portal

There is no administration fee associated with the return of examination scripts.

Final Examination Only

Students who have failed a paper but who have completed course work satisfactorily may apply for Final Examination Only enrolment. If approved, internal marks are carried over and the examination may be sat at the end of the next teaching period that the paper is offered.

• Approval for Final Examination Only enrolment is at the discretion of the relevant Head of Department.
• Some papers do not have the option of Final Examination Only; if this is the case, you will be advised.
• Final Examination Only enrolment may be granted only once for a particular paper.
• Final Examination Only enrolment is only available for the next teaching period in which the paper is offered after the paper is initially failed.
• Applications will not be approved if the content or assessment of the paper is going to be significantly altered when it is next offered, or if the paper is no longer offered.

Students approved for Final Examination Only enrolment are not entitled to:

• attend any lectures, laboratories, or tutorials
• receive assistance from academic staff
• have access to electronic holdings of course material
• receive printed course material.

Applications for Final Examination Only must be received by:

• Summer School papers – 10 January
• Semester 1 and full year papers – 1 March
• Semester 2 papers – 31 July

Further information about Final Examination Only is available here:

Paying administration fees

Recounts and Health Sciences Professional Programme Special Examinations incur an administration fee. If you have applied for one of these options and are due to pay a fee, you can do so in the following ways:

In person – recounts

• AskOtago Central Hub, Information Services Building by Eftpos

In person – Health Sciences Professional Programmes Special Examinations

Internet banking and telegraphic transfer.

The University of Otago also accepts payment by internet Banking or Telegraphic Transfer with the account details listed below:

Account number:   01-1839-0944124-00 Account name: University of Otago Swift Code: ANZBNZ22 (for payments outside New Zealand)* *Please note that for payments paid by telegraphic transfer, there is a bank fee of NZD $20 charged for each transaction so you will need to add this amount onto the amount payable.

References for online banking

If your payment does not have the appropriate references, we will not be able to identify your payment and this will delay your application. Please see the table below for more information.

Credit card payment to University of Otago

For students outside Dunedin who would like to pay administration fees by credit card, please contact us for further details:

Otago Problem Solving

Kia ora Otago Problem Solvers,

Yes, it is time for the final session! We return to school tomorrow and I'm sure you will all be too busy to do any more Otago questions. Traditionally we have finished well before November.

Thank you to all the students who regularly completed the questions - you know who you are...as do I, as I kept a list! :-)

[email protected]

Term 4 - Week 5 - Session 10 - *If you would like a set of questions, please email me :- ) [email protected]

Term 4 - Week 5 - Session 9 - FINAL SESSION!

Term 4 - Week 4 - Session 8

Term 4 - Week 4 - Session 7

Term 4 - Week 3 - Session 6

Term 4 Week 3 - Session 5

Term 4 - Week 2 - Session 4

Term 4 - Week 2 - Session 3

Term 4 - Week 1 - Session 2

Term 4 - Week1 - Session 1

Session 11 - Thursday 30th September *Last Session of Term 3

Session 10 - Tuesday 28th September

Session 9 - Thursday 23rd September

Session 8 - Tuesday 21st September

Session 7 - Thursday 16th September

Session 6 - Tuesday 14th September

Session 5 - Thursday 9th September

Session 4 - Tuesday 7th September

Kia ora All - for Session 4 I would like you to send me an email [email protected] requesting a copy of today's questions/video. The reason for this is to check how many of you are actually completing the questions - I'm currently only getting the same 6 - 8 students sending me their answers and there are 36 students in the Otago problem solving group.

Thanks Bevan

*If you are not part of the Otago Group and would like to try some of the questions please also send me an email.

Remember to email me your answers - [email protected]

Programming and Problem Solving for Schools

A workbook for year 12 programming.

Many teachers without a formal background in programming are being asked to teach program design and the coding of a solution in a programming language. This is a significant step up and we are doing what we can to help.

In 2011, we developed a workbook which is compatible with the new Digital Technology Achievement Standards 2.45 and 2.46 for NCEA level 2. The student version of the workbook has now been revised and is ready to be used in the classroom. Any teacher who wishes to look at it with a view to using it should request a copy from [email protected] .

The workbook covers the material required for assessment standards 2.45 and 2.46 and a little bit more, but is not "teaching to the standard". The workbook tries to stay focused on the process of problem solving rather than the syntax of any particular language. The problems should be able to be coded in any language from a common algorithm.

After some debate and many trials, we decided to provide a choice of two real-world programming languages in our examples. We use Python and Java. This will make the flow on to year 13 easy, as both of these languages allow Object Oriented design, although we will do not use this aspect of them in the year 12 workbook. There is plenty of on-line assistance for these languages, there are well-tested and reliable (and free) platforms and development environments for both Windows and Mac.

If you have a favourite language, you could take the concepts and ideas and adapt them to the syntax it uses. Any language that can easily produce textual output to the display/screen and has indexed data structures could be used.

What, no graphics? We have unashamedly chosen not to use graphical output because the amount of material to be learned covering the core programming concepts as well as graphics and animation would not fit in the 60 hour target. We believe that problem solving is an enjoyable exercise in its own right.

The material is written with as little jargon as possible and uses plenty of examples. The problems range from easy to challenging. It is impossible to write a "one size fits all" lesson, so each student will be able to choose whether they wish to have a go at the more challenging exercises, or be satisfied with completing the elementary problems.

Each school which uses this material will be charged $100, a share of the cost of its development.

Workbook Contents

• Chapter 0 - Java and Python, setting up (teacher's version only)
• Chapter 1 - The process of programming
• Chapter 2 - Variables and Expressions
• Chapter 3 - Modular programming
• Chapter 4 - Getting input, formatting output
• Chapter 5 - Boolean and Selection
• Chapter 6 - Repetition
• Chapter 7 - Arrays (Java) / Lists (Python)
• Chapter 8 - Strings
• Appendix - contains model answers and notes for the teacher (teacher's version only)
• A Bridge to the Standards - an adaptation of the paper presented to the December 2011 CS4HS workshop in Christchurch (teacher's version only)

We have also produced Python and Java workbooks for Year 13 / Digital Technology Achievement Standard 3.46 / NCEA level 3. The books follow on from the Year 12 versions in the same language, and cover Object Oriented Programming and Graphical User Interfaces. We ask for $200 from each school using these books as a share in the cost of their development.

Professional Practice Fellow Sandy Garner and Professor Anthony Robins

We are the people who design and teach the first year of the computer science degree program at the University of Otago. We have many years of experience teaching programming at this level. We know where high school students should be aiming if they are intending to study programming at a higher level. We are also parents with children at various stages of the NZ secondary school system, and have taught programming at primary, intermediate and secondary schools through our involvement with robotics and RobocupJuniorNZ.

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