1.2 Algebra MCAT - Just Updated for 2021 and 2022 exams!
Quick Maths
Click here for Mr Bowman's YouTube Channel
Junior or Senior Resources?
Junior Resources (Yr 7 to 10)
Senior (NCEA Exam Resources)
What is Problem Challenge?
Most schools with year 7 and 8 children, and some with year 6 children, are on our mailing list and will automatically receive an invitation, in mid-February, to take part in the competition.
The competition has been organised by John Curran and John Shanks, retired members of the Department of Mathematics and Statistics at the University of Otago, with huge administrative help from Leanne Kirk. However John Curran and Leanne retired from the competition at the end of 2023; John Shanks will attempt to run it from 2024, with help from Sarah Stewart handling the book orders.
The value of such problem solving competitions is well recognized overseas. For example, similar schemes are run in Australia, Britain and the United States. Here the New Zealand Curriculum, Mathematics Standards (years 1-8), considers various ways in which effective mathematics teaching can provide quality programmes. Amongst other components, problem-centred activities are highlighted. The document states Cross-national comparisons show that students in high-performing countries spend a large proportion of their class time solving problems. The students do so individually as well as co-operatively. The problems we pose allow children to practise and learn such simple strategies as guessing and checking, drawing a diagram, making lists, looking for patterns, classifying, etc. Although children answer the questions individually on our sets there is ample opportunity for co-operative practise using our resources.
How does it work?
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. They do the problems individually but they can share their answers and strategies in small groups afterwards.
Note that all three levels (years 6, 7 and 8) attempt the same problem set although there are separate awards for each of those levels.
The problems are generally aimed at more able children. However, we hope to keep the first question or two reasonably straightforward, so that all children entered can have some success. Many schools that have taken part before will have a good idea of the standard involved. Here are two recent example sets as a guide.
As a general rule, teachers may wish to enter children for whom they feel a score of say 3 out of 5 is an attainable goal. We felt the problems set last year were about the right level of difficulty, so we will be aiming for much the same standard this year. For schools that want more information, there are five books available that give questions and solutions from the first 24 years of the competition. These books can be obtained by completing the order form .
What must the teacher do?
For each of the 5 problem sets that you receive, you will have to photocopy (or otherwise make available) sufficient copies of the problem sheet for the participants from your school, and administer the challenge on the day specified (or as near as possible).
You must mark the pupil responses (using the solutions provided) and return collated results to us, as well as keeping a record of your results (using your own spreadsheet or on a form provided).
- Results are returned to us on-line . Further details of this together with a log-in code for your school will be supplied with the first set of problems.
- All competition material, including sets, solutions and letters, will be emailed to schools or made available on the website .
- Certificates will be provided in electronic form for schools to print.
How does your school benefit?
The problem sets may be used later as a resource for other children in any way the teacher wishes. For example, small groups could solve the problems co-operatively together, talking through the various strategies that could be applied to each question.
For each set you will receive a summary of the overall results, so that you can evaluate your pupils’ progress. In the past we have received very favourable feedback on the benefit of this. (Individual school results will not be collated or publicised so will remain strictly confidential to you.) Overall results from previous years can be seen here .
All children taking part will receive a certificate of participation. Those in about the top 10% in each year will receive certificates of excellence and those in the next 25% or so will receive certificates of merit. Where schools have provided on-line results, the childrens’ names will already be on the certificates.
Each year $25 book tokens are awarded to children in the top 1% or so of the competition. Note that book tokens are normally given to a maximum of 20% of the entries from each school.
When is Problem Challenge held?
As in previous years there will be a Problem Challenge each month from April to August, spaced at about five week intervals. This year’s administration days can be found here. However, as in the past, there is some flexibility in these dates and no school is precluded from entry on account of the timing. This is explained more fully if you enter.
How much does it cost and how do you enter?
The entry fee consists of $20 per school plus $0.40 per child entered (including GST). We will be mailing all Intermediate schools each February asking for entries: at that stage, if you wish to take part, you will need to register on-line and arrange to pay the registration fee (by credit card or University invoice).
Online registration is available between 19 February and 11 April.
The final challenge.
Children who do particularly well in Problem Challenge during the year are invited to enter a final multi-choice competition in late October. Note that, because of limited resources and in fairness to all, we regret that only those who reach a specified total number of problems correct (regardless of absence, sickness, etc) will be eligible to enter.
Final Challenge provides a great challenge for the very able, and there are more substantial prizes for the best performers at both Years. The competition consists of 10 multiple-choice questions, with five options per question, together with 10 questions that require explicit answers. The problems are similar in style to the usual Problem Challenge questions but generally of a standard comparable to question 5 on the Problem Sets or harder.
- Children have one hour in which to attempt the questions.
- The use of calculators is not permitted.
Problem Challenge Department of Mathematics University of Otago PO Box 56, Dunedin. | Enquiries about the : • Email: • Text: 027 2646598 • Phone: (03) 473 8396 | Equiries about : • Email: • Phone: (03) 479 7759 |
Mailing list
The home of mathematics education in New Zealand.
- Forgot password ?
Thanks for visiting NZMaths. We are preparing to close this site by the end of August 2024. Maths content is still being migrated onto Tāhūrangi, and we will be progressively making enhancements to Tāhūrangi to improve the findability and presentation of content.
For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths
Supporting professional practice
E-ako pld 360.
Interactive PLD modules to support your teaching and inquiry. More information .
Curriculum elaborations
More information about achievement objectives from the NZC.
Effective teaching of mathematics
Guidance for teachers on implementing principles of effective teaching.
Tracking progress and achievement
Information about tracking students in relation to the NZC.
Accelerating learning
Strategies from the ALiM project for students not on track to meet the expected level.
Gifted and talented
Supporting gifted and talented students to reach their potential.
Other PLD material
Numeracy project PLD , Just-In-Time Maths , Planning examples , NZ maths education reports .
Teaching material
Resource finder.
Filter by strand, AO, LPF aspect, or resource type. Collect resources in your planning space .
Learning at home: information for teachers
Advice and structured weekly plans to support students online and offline learning at home.
Units of work by strand
Number and Algebra , Geometry and Measurement , Statistics .
Rich learning activities
Differentiated activities at Levels 1 to 5 of the NZC.
Problem solving activities
An extensive collection of problem solving sessions.
Acceleration resources
Resources developed to support students not on track to meet the expected level.
e-ako maths adventures
Interactive online resource to help students learn maths. Information about e-ako maths .
Numeracy project resources
NDP information and resources including: planning sheets , material masters , NDP books .
Other resources
Picture books , Figure it Out , Connected , Take This , Learning Objects , Number facts games .
Early childhood education
Supporting rich mathematical interactions in ECE.
Secondary Mathematics and Statistics
Numeracy resources, links to teaching and learning guides, NCEA resources, PLCs, and other useful sites.
Planning space
Manage and create teaching plans. Long-term plans.
Families and whānau
Learning at home.
Weekly plans to support your child's maths learning when they are unable to attend school.
Supporting school maths
Understanding and supporting classroom maths at home.
Maths at our house
Using everyday experiences to explore maths.
Free or low-cost items your child can use for exploring maths ideas.
FAQs and other resources
Frequently asked questions and links to other resources
IMAGES
VIDEO
COMMENTS
This section of the nzmaths website has problem-solving lessons that you can use in your maths programme. The lessons provide coverage of Levels 1 to 6 of The New Zealand Curriculum. The lessons are organised by level and curriculum strand. Accompanying each lesson is a copymaster of the problem in English and in Māori. Choose a problem that involves your students in applying current learning ...
The problems have been grouped below by strand. Hover over each title to read the problem. Choose a problem that involves your students in applying current learning. Remember that the context of most problems can be adapted to suit your students and your current class inquiry. Read more about using these problem solving activities.
The problems have been grouped below by strand. Hover over each title to read the problem. Choose a problem that involves your students in applying current learning. Remember that the context of most problems can be adapted to suit your students and your current class inquiry. Read more about using these problem solving activities.
The problems have been grouped below by strand. Hover over each title to read the problem. Choose a problem that involves your students in applying current learning. Remember that the context of most problems can be adapted to suit your students and your current class inquiry. Read more about using these problem solving activities.
Common Problem Solving Strategies. Guess (includes guess and check, guess and improve) Act It Out (act it out and use equipment) Draw (this includes drawing pictures and diagrams) Make a List (includes making a table) Think (includes using skills you know already)
Quick Maths offers online resources for algebra, trigonometry, and NCEA exam preparation.
Use these maths investigations and challenge cards to help children develop problem-solving skills. Perfect for NZ primary children in years 5 to 6.
Mathematical processes include problem solving, logic and reasoning, and communicating ideas. These are the parts of mathematics that enable us to use the skills in a wide variety of situations. It is worth starting by distinguishing between the three words "method", "answer" and "solution". By "method" we mean the means used to get an answer.
Use these maths investigations and challenge cards to help children develop problem-solving skills. Perfect for NZ Intermediate students in years 7-8.
Problem solving was part of the Mathematical Processes Strand of the New Zealand Mathematics Curriculum (1992). While problem solving is not a category within the New Zealand Curriculum (2007), the key competency of Thinking includes problem solving.
Problem Challenge is a mathematics problem solving competition aimed primarily at children in years 7 and 8 but may be of interest to mathematically gifted children in year 6. It has been offered to schools throughout New Zealand for the past 33 years. The response to the competition has been overwhelmingly positive.
NZ Maths Teaching material Problem solving activities Problems and solutions for students
Space crossing. No strand. Problem solving activities. This problem solving activity has a logic and reasoning focus.
The problems have been grouped below by strand. Hover over each title to read the problem. Listed under 'Units' are extended problem solving investigations which aim to introduce students to an underlying idea of mathematics through a problem. Choose a problem that involves your students in applying current learning. Remember that the context of most problems can be adapted to suit your ...
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). Have key supporting questions ready to ask your students as they work on the problem: Getting started. While working on the problem.
Differentiated activities at Levels 1 to 5 of the NZC. Problem solving activities An extensive collection of problem solving sessions.
This Professional Learning Community (PLC) has been created to provide a forum for discussing problem solving activities. Each month we will post two new problems, a level 1 problem, a level 2 problem and a level 3 problem. Please use the threads to tell us how your students solved the problems. We will include some of the solutions at the ...
Units of Work ? Rich learning activities ? Problem solving activities ? Numeracy activities ? Picture book activities ? Figure It Out activities ?
In this section we discuss "Why teach problem solving?" under two headings: benefits of problem solving, and difficulties of teaching problem solving.
Fraction and Decimals unit with Problem Solving Thanks for visiting NZMaths.
An extensive collection of problem solving sessions. Each session includes a problem, a suggested teaching sequence, and possible extensions.
This problem solving activity has a number (addition and subtraction) focus. More pizzas and things Level Two Number and Algebra Problem solving activities