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Create lifelong mathematicians

Take your learners further with the researched-based teaching approach proven to raise attainment and build maths confidence.

A teaching approach you can count on

You strive for excellence in your practice. But when no one can decide what best practice looks like, and half of your students think they ‘ can’t do maths ’ — it’s not easy.

What if you had access to teaching methods proven to develop learners’ problem-solving and critical-thinking skills? Or strategies to enrich advanced learners and support struggling learners? What if you could see your students’ faces light up as they start to believe in their own mathematical capabilities?

Based on methods developed in Singapore and the pedagogy of influential educational theorists, Maths — No Problem! is a teaching framework proven to help students gain a mastery level understanding of maths.

It has already transformed primary maths teaching in schools around the world.

Will your school be next?

Resources designed for the NZ learner

Keep your students on the right track with resources designed for the New Zealand Curriculum and maths problems based on real-world situations. Lessons are directly linked to NZ National Curriculum objectives, acknowledge Aotearoa NZ’s bicultural foundations, and cover all number and non-number topics.

Consistency from start to finish

Give your learners the right learning experience at the right time. Using a tried-and-tested spiral methodology, topics build on one another to help learners develop mathematical fluency. Content is covered in an age-appropriate order and revisited to close conceptual gaps and enrich every learner’s experience.

Assessment in every lesson

Get a clear view of progress. During lessons, non-negotiable learning objectives give you the information you need to support struggling learners and stretch advanced ones. Varied activities encourage students to challenge their thinking through collaborative discussion while independent exercises help learners build on their existing knowledge.

Flexible teacher support

Teach maths for mastery with confidence. From daily lesson structure to extension activities and common misconceptions, online Teacher Guides support you in every lesson. Not sure when to introduce concrete manipulatives or where to differentiate content? The answers you need are all in one place.

Meet the characters

Illustrated characters act as learning companions, guiding students through content and providing familiarity as problems become more complex. Characters from New Zealand, as well as local flora and fauna help learners understand maths’ place in the world around them.

What to expect when adopting a mastery approach

Here’s an inside look at some of the ways mastery has shifted attitudes towards primary maths in this teacher’s classroom.

How Maths — No Problem! works

Tools to take students further

Close conceptual gaps with evidence-based resources proven to foster a deep understanding of maths in children of all attainment levels.

Strategies for success

Develop your learners’ metacognition with strategies like the CPA approach, bar modelling, number bonds, and effective questioning.

Support when you need it

Take the uncertainty out of teaching maths for mastery with hands-on PLD courses and workshops, online teacher guides, and online training videos.

[Students] are having fun with maths. They can talk about what they’re doing, [show] deeper understanding… and clearly explain their thinking… This is working for all kids. – Marie Nelson, Maths Lead, St Paul's Primary School Auckland, New Zealand

Ready to see what it’s all about?

Maths — No Problem! resources, step-by-step teaching support, and online PLD videos are a click away. Request a free demo to see how it all works, or email [email protected] for more information.

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Year 11 maths

Here is a list of all of the maths skills students learn in year 11! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. To start practising, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

Here is a list of all of the maths skills students learn in year 11! To start practicing, just click on any link.

• A.1 Identify rational and irrational numbers
• A.2 Compare and order rational numbers
• A.3 Square roots
• A.4 Cube roots

Ratios, rates and proportions

• B.1 Identify equivalent ratios
• B.2 Write an equivalent ratio
• B.3 Unit rates
• B.4 Unit prices
• B.5 Solve proportions
• B.6 Solve proportions: word problems
• B.7 Scale drawings: word problems

Consumer maths

• C.1 Simple interest
• C.2 Compound interest
• C.3 Continuously compounded interest
• C.4 Percent of a number: GST, discount and more
• C.5 Find the percent: discount and mark-up
• C.6 Multi-step problems with percents

Coordinate plane

• D.1 Coordinate plane review
• D.2 Midpoints
• D.3 Distance between two points

Solve equations

• E.1 Model and solve equations using algebra tiles
• E.2 Write and solve equations that represent diagrams
• E.3 Solve one-step linear equations
• E.4 Solve two-step linear equations
• E.5 Solve advanced linear equations
• E.6 Solve equations with variables on both sides
• E.7 Solve equations: complete the solution
• E.8 Find the number of solutions
• E.9 Create equations with no solutions or infinitely many solutions
• E.10 Solve linear equations: word problems
• E.11 Solve linear equations: mixed review

Single-variable inequalities

• F.1 Graph inequalities
• F.2 Write inequalities from graphs
• F.3 Identify solutions to inequalities
• F.4 Solve one-step linear inequalities: addition and subtraction
• F.5 Solve one-step linear inequalities: multiplication and division
• F.6 Solve one-step linear inequalities
• F.7 Graph solutions to one-step linear inequalities
• F.8 Solve two-step linear inequalities
• F.9 Graph solutions to two-step linear inequalities
• F.10 Solve advanced linear inequalities
• F.11 Graph solutions to advanced linear inequalities

Relations and functions

• G.1 Relations: convert between tables, graphs, mappings and lists of points
• G.2 Domain and range of relations
• G.3 Identify independent and dependent variables
• G.4 Identify functions
• G.5 Find values using function graphs
• G.6 Evaluate a function
• G.7 Complete a function table from a graph
• G.8 Complete a function table from an equation
• G.9 Interpret the graph of a function: word problems

Direct and inverse variation

• H.1 Identify proportional relationships
• H.2 Find the constant of variation
• H.3 Graph a proportional relationship
• H.4 Write direct variation equations
• H.5 Write and solve direct variation equations
• H.6 Write inverse variation equations
• H.7 Write and solve inverse variation equations
• H.8 Identify direct variation and inverse variation

Linear functions

• I.1 Identify linear functions
• I.2 Find the gradient of a graph
• I.3 Find the gradient from two points
• I.4 Find a missing coordinate using gradient
• I.5 Find the gradient and y-intercept of a linear equation
• I.6 Graph an equation in y=mx+c form
• I.7 Write an equation in y=mx+c form from a graph
• I.8 Write an equation in y=mx+c form
• I.9 Write an equation in y=mx+c form from a table
• I.10 Write an equation in y=mx+c form from a word problem
• I.11 Write linear functions to solve word problems
• I.12 Complete a table and graph a linear function
• I.13 Compare linear functions: graphs, tables and equations
• I.14 Write equations in standard form
• I.15 Standard form: find x- and y-intercepts
• I.16 Standard form: graph an equation
• I.17 Equations of horizontal and vertical lines
• I.18 Graph a horizontal or vertical line
• I.19 Point-gradient form: graph an equation
• I.20 Point-gradient form: write an equation
• I.21 Point-gradient form: write an equation from a graph
• I.22 Gradients of parallel and perpendicular lines
• I.23 Write an equation for a parallel or perpendicular line
• I.24 Find the distance between a point and a line
• I.25 Find the distance between two parallel lines
• I.26 Transformations of linear functions

Simultaneous equations

• J.1 Is (x, y) a solution to the simultaneous equations?
• J.2 Solve simultaneous equations by graphing
• J.3 Solve simultaneous equations by graphing: word problems
• J.4 Find the number of solutions to simultaneous equations by graphing
• J.5 Find the number of solutions to simultaneous equations
• J.6 Solve simultaneous equations using substitution
• J.7 Solve simultaneous equations using substitution: word problems
• J.8 Solve simultaneous equations using elimination
• J.9 Solve simultaneous equations using elimination: word problems
• J.10 Solve simultaneous equations using any method
• J.11 Solve simultaneous equations using any method: word problems
• K.1 Powers with integer bases
• K.2 Powers with decimal and fractional bases
• K.3 Negative exponents
• K.4 Multiplication with exponents
• K.5 Division with exponents
• K.6 Multiplication and division with exponents
• K.7 Power rule
• K.8 Evaluate expressions using properties of exponents
• K.9 Identify equivalent expressions involving exponents
• L.1 Convert between exponential and logarithmic form: rational bases
• L.2 Evaluate logarithms
• L.3 Change of base formula
• L.4 Identify properties of logarithms
• L.5 Product property of logarithms
• L.6 Quotient property of logarithms
• L.7 Power property of logarithms
• L.8 Properties of logarithms: mixed review
• L.9 Evaluate logarithms: mixed review

Exponential and logarithmic functions

• M.1 Domain and range of exponential and logarithmic functions
• M.2 Evaluate an exponential function
• M.3 Match exponential functions and graphs
• M.4 Solve exponential equations by rewriting the base
• M.5 Solve exponential equations using common logarithms
• M.6 Solve logarithmic equations I
• M.7 Solve logarithmic equations II
• M.8 Exponential growth and decay: word problems
• N.1 Identify monomials
• N.2 Multiply monomials
• N.3 Divide monomials
• N.4 Multiply and divide monomials
• N.5 Powers of monomials

Polynomials

• O.1 Polynomial vocabulary
• O.2 Model polynomials with algebra tiles
• O.3 Add and subtract polynomials using algebra tiles
• O.4 Add and subtract polynomials
• O.5 Add polynomials to find perimeter
• O.6 Multiply a polynomial by a monomial
• O.7 Multiply two polynomials using algebra tiles
• O.8 Multiply two binomials
• O.9 Multiply two binomials: special cases
• O.10 Multiply polynomials

Factorising

• P.1 HCF of monomials
• P.2 Factorise out a monomial
• P.3 Factorise quadratics with leading coefficient 1
• P.4 Factorise quadratics with other leading coefficients
• P.5 Factorise quadratics: special cases
• P.6 Factorise quadratics using algebra tiles
• P.7 Factorise by grouping
• P.8 Factorise polynomials

Quadratic equations

• Q.1 Characteristics of quadratic functions
• Q.2 Complete a function table: quadratic functions
• Q.3 Solve a quadratic equation using square roots
• Q.4 Solve a quadratic equation using the zero product property
• Q.5 Solve a quadratic equation by factorising
• Q.6 Complete the square
• Q.7 Solve a quadratic equation by completing the square
• Q.8 Solve a quadratic equation using the quadratic formula
• Q.9 Using the discriminant

Functions: linear, quadratic, exponential

• R.1 Identify linear, quadratic and exponential functions from graphs
• R.2 Identify linear, quadratic and exponential functions from tables
• R.3 Write linear, quadratic and exponential functions
• R.4 Linear functions over unit intervals
• R.5 Exponential functions over unit intervals
• R.6 Describe linear and exponential growth and decay
• S.1 Identify the direction a parabola opens
• S.2 Find the vertex of a parabola
• S.3 Find the focus or directrix of a parabola
• S.4 Find the axis of symmetry of a parabola
• S.5 Write equations of parabolas in vertex form from graphs
• S.6 Write equations of parabolas in vertex form using properties
• S.7 Convert equations of parabolas from general to vertex form
• S.8 Find properties of a parabola from equations in general form
• S.9 Graph parabolas
• T.1 Find the centre, vertices or co-vertices of an ellipse
• T.2 Find the length of the major or minor axis of an ellipse
• T.3 Find the foci of an ellipse
• T.4 Write equations of ellipses in standard form from graphs
• T.5 Write equations of ellipses in standard form using properties
• T.6 Convert equations of ellipses from general to standard form
• T.7 Find properties of ellipses from equations in general form

Radical expressions

• U.1 Simplify radical expressions
• U.2 Simplify radical expressions involving fractions
• U.3 Multiply radical expressions
• U.4 Add and subtract radical expressions
• U.5 Simplify radical expressions using the distributive property
• U.6 Simplify radical expressions: mixed review

Rational exponents

• V.1 Evaluate rational exponents
• V.2 Multiplication with rational exponents
• V.3 Division with rational exponents
• V.4 Power rule with rational exponents
• V.5 Simplify expressions involving rational exponents I
• V.6 Simplify expressions involving rational exponents II

Rational functions and expressions

• W.1 Rational functions: asymptotes and excluded values
• W.2 Simplify complex fractions
• W.3 Simplify rational expressions
• W.4 Multiply and divide rational expressions
• W.5 Divide polynomials
• W.6 Add and subtract rational expressions
• W.7 Solve rational equations

Number sequences

• X.1 Identify arithmetic and geometric sequences
• X.2 Arithmetic sequences
• X.3 Geometric sequences
• X.4 Evaluate variable expressions for number sequences
• X.5 Write variable expressions for arithmetic sequences
• X.6 Write variable expressions for geometric sequences
• X.7 Number sequences: mixed review

Measurement

• Y.1 Convert rates and measurements
• Y.2 Precision
• Y.3 Greatest possible error
• Y.4 Minimum and maximum area and volume
• Y.5 Percent error
• Y.6 Percent error: area and volume

Problem solving

• Z.1 Word problems: mixed review
• Z.2 Word problems with money
• Z.3 Consecutive integer problems
• Z.4 Rate of travel: word problems
• Z.5 Weighted averages: word problems

Two-dimensional figures

• AA.1 Classify triangles
• AA.2 Polygon vocabulary
• AA.3 Triangle Angle-Sum Theorem
• AA.4 Midsegments of triangles
• AA.5 Triangles and bisectors
• AA.6 Identify medians, altitudes, angle bisectors and perpendicular bisectors
• AA.7 Perimeter
• AA.8 Area of triangles and quadrilaterals
• AA.9 Area and perimeter in the coordinate plane I
• AA.10 Area and perimeter in the coordinate plane II
• AA.11 Area and circumference of circles
• AA.12 Area of compound figures
• AA.13 Area between two shapes
• AA.14 Area and perimeter of similar figures

Introduction to congruent figures

• BB.1 Congruence statements and corresponding parts
• BB.2 Solve problems involving corresponding parts
• BB.3 Identify congruent figures

Congruent triangles

• CC.1 SSS and SAS Theorems
• CC.2 ASA and AAS Theorems
• CC.3 SSS, SAS, ASA and AAS Theorems
• CC.4 SSS Theorem in the coordinate plane
• CC.5 Congruency in isosceles and equilateral triangles
• CC.6 Hypotenuse-Leg Theorem
• DD.1 Identify similar figures
• DD.2 Ratios in similar figures
• DD.3 Similarity statements
• DD.4 Side lengths and angle measures in similar figures
• DD.5 Similar triangles and indirect measurement
• DD.6 Perimeters of similar figures
• DD.7 Similarity rules for triangles
• DD.8 Similar triangles and similarity transformations
• DD.9 Areas of similar figures

Right triangles

• EE.1 Pythagoras' Theorem
• EE.2 Converse of Pythagoras' theorem
• EE.3 Pythagoras' Inequality Theorems
• EE.4 Special right triangles

Angle measures

• FF.1 Quadrants
• FF.2 Graphs of angles
• FF.3 Coterminal angles
• FF.4 Reference angles

Trigonometry

• GG.1 Trigonometric ratios: sin, cos and tan
• GG.2 Trigonometric ratios: csc, sec and cot
• GG.3 Trigonometric ratios in similar right triangles
• GG.4 Find trigonometric ratios using the unit circle
• GG.5 Trigonometric functions of complementary angles
• GG.6 Sin, cos and tan of special angles
• GG.7 Csc, sec and cot of special angles
• GG.8 Find trigonometric functions using a calculator
• GG.9 Symmetry and periodicity of trigonometric functions
• GG.10 Inverses of sin, cos and tan
• GG.11 Inverses of csc, sec and cot
• GG.12 Solve trigonometric equations I
• GG.13 Solve trigonometric equations II
• GG.14 Trigonometric ratios: find a side length
• GG.15 Trigonometric ratios: find an angle measure
• GG.16 Solve a right triangle
• GG.17 Law of Sines
• GG.18 Law of Cosines
• GG.19 Solve a triangle
• HH.1 Parts of a circle
• HH.2 Central angles
• HH.3 Arc measure and arc length
• HH.4 Area of sectors
• HH.5 Circle measurements: mixed review
• HH.6 Arcs and chords
• HH.7 Tangent lines
• HH.8 Perimeter of polygons with an inscribed circle
• HH.9 Inscribed angles
• HH.10 Angles in inscribed right triangles
• HH.11 Angles in inscribed quadrilaterals

Circles in the coordinate plane

• II.1 Find the centre of a circle
• II.2 Find the radius or diameter of a circle
• II.3 Write equations of circles in standard form from graphs
• II.4 Write equations of circles in standard form using properties
• II.5 Convert equations of circles from general to standard form
• II.6 Find properties of circles from equations in general form
• II.7 Graph circles

Surface area and volume

• JJ.1 Introduction to surface area and volume
• JJ.2 Surface area of prisms and cylinders
• JJ.3 Surface area of pyramids and cones
• JJ.4 Volume of prisms and cylinders
• JJ.5 Volume of pyramids and cones
• JJ.6 Surface area and volume of spheres
• JJ.7 Introduction to similar solids
• JJ.8 Surface area and volume of similar solids
• JJ.9 Surface area and volume review

Transformations

• KK.1 Translations: graph the image
• KK.2 Translations: find the coordinates
• KK.3 Translations: write the rule
• KK.4 Reflections: graph the image
• KK.5 Reflections: find the coordinates
• KK.6 Rotate polygons about a point
• KK.7 Rotations: graph the image
• KK.8 Rotations: find the coordinates
• KK.9 Classify congruence transformations
• KK.10 Compositions of congruence transformations: graph the image
• KK.11 Transformations that carry a polygon onto itself
• KK.12 Congruence transformations: mixed review
• KK.13 Dilations: graph the image
• KK.14 Dilations: find the coordinates
• KK.15 Dilations: scale factor and classification
• KK.16 Dilations and parallel lines
• LL.1 Line symmetry
• LL.2 Rotational symmetry
• LL.3 Count lines of symmetry
• LL.4 Draw lines of symmetry

Probability

• MM.1 Theoretical probability
• MM.2 Experimental probability
• MM.3 Compound events: find the number of outcomes
• MM.4 Identify independent and dependent events
• MM.5 Probability of independent and dependent events
• MM.6 Geometric probability
• NN.1 Mean, median, mode and range
• NN.2 Quartiles
• NN.3 Identify biased samples
• NN.4 Mean absolute deviation
• NN.5 Variance and standard deviation

Data and graphs

• OO.1 Interpret histograms
• OO.2 Create histograms
• OO.3 Interpret stem-and-leaf plots
• OO.4 Interpret box-and-whisker plots
• OO.5 Interpret a scatter plot
• OO.6 Scatter plots: line of best fit

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.

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DU Professor Helps Solve Famous 70-Year-Old Math Problem

Jordyn reiland.

[email protected]

Assistant Professor Mandi Schaeffer Fry is the first faculty member to be published in the Annals of Mathematics since the 1880s.

University of Kaiserslautern Professor Gunter Malle, University of Denver Assistant Professor Mandi Schaeffer Fry and University of Valencia Professor Gabriel Navarro pose for a photo after announcing their theorem in Oberwolfach, Germany.

Whether it be flying trapeze, participating in competitive weightlifting or solving math problems that have confounded academics for decades, Mandi Schaeffer Fry enjoys chasing the next adventure.

Schaeffer Fry, who joined the University of Denver’s Department of Mathematics in the fall of 2023, will be the first faculty member since the 1880s to be published in the Annals of Mathematics , widely seen as the industry’s most prestigious journal.

In 2022, Schaeffer Fry helped complete a problem that dates to 1955—mathematician Richard Brauer’s Height Zero Conjecture.

“Maybe one of the most challenging parts, other than the math itself, was the knowledge of the weight that this would have on the field,” Schaeffer Fry says. “If you’re going to make an announcement like this, you have to be darn sure that it’s absolutely correct.”

Over the years, number crunchers have worked on the problem at universities across the globe, and some found partial solutions; however, the problem was not completed until now.

“Mandi’s accomplishment is exciting. Solving Brauer's Height Zero Conjecture is remarkable,” Mathematics Department Chair Alvaro Arias says. 

The work is also a testament to DU’s achievement as a Research 1 (R1) institution.

Fry and her collaborators—University of Kaiserslautern Professor Gunter Malle, University of Valencia Professor Gabriel Navarro and Rutgers University Professor Pham Huu Tiep—worked around the clock over the course of three months in eight-hour shifts during the summer of 2022 to find a solution.

In April, that work was accepted for publication in the Annals of Mathematics.

'Brauer's Height Zero Conjecture (BHZ) was the first conjecture leading to the part of my field studying 'local-global' problems in the representation theory of finite groups, which seek to relate properties of groups with properties of certain nice smaller subgroups, letting us 'zoom in' on the group using just a specific prime number and simplify things," Schaeffer Fry says. 

"The BHZ gives us a way to tell from the character table of a group (a table of data that encodes lots, but not all, information about the group) whether or not certain of these subgroups, called defect groups, have the commutativity property," she adds.

This paper was especially meaningful to Schaeffer Fry as she had always wanted to work with Malle, Tiep and Navarro as they have been her primary mentors. Tiep was her PhD advisor and this was the first time they had worked together since then.

Fry believes she has solidified her place in the field and knows she’ll likely never top this accomplishment, but she’s always looking for the next adventure—whether that’s in or out of the classroom.

Flying high and pumping iron

When Schaeffer Fry isn’t on DU’s campus working with students or conducting research, you can find her flying trapeze and competitive weightlifting.

Schaeffer Fry became involved in competitive weightlifting during graduate school, and, in the last year of her PhD at the University of Arizona, she defended her dissertation one day and got on a plane and competed at the national level for “university-aged” athletes—which included Olympians.

While she now lifts weights more casually, Schaeffer Fry competed last September in an over-35 competition and qualified for the USA Weightlifting Masters National Championships.

It was a “field trip” during a conference in Berkeley, California, in 2018 that led Fry to become enamored with flying trapeze.

In fact, she enjoyed it so much she signed up to be a member of Imperial Flyers, an amateur flying trapeze cooperative located in Westminster. Once she found out about the sport, her previous experience as a gymnast made it a natural fit.

Not only is she working on her own intermediate tricks, she’s also a “teaching assistant” at Fly Mile High, the state’s only flying trapeze and aerial fitness school.

“It’s exhilarating; it’s gotten me a bit over my fear of heights,” she says.

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Welcome to Numicon

Numicon is a mastery, structured Maths approach covering all contexts/strands, 

Providing explicit teaching, explorations, and investigations based on the , science of learning maths., click above to view a presentation, numicon covers all the strands/contexts working together presented in a spiral sequence,  to maintain children's learning throughout the year,  numicon is aligned with the nz curriculum and is flexible to provide opportunities , for your local curriculum and cultural response to be included numicon is inclusive - meeting the needs of all children, numicon welcomes the release of the new draft maths curriculum recently released by the ministry of education along with the expectation of teaching structured maths in 2025.  for the last 15 years we have seen school after school being incredibly successful lifting the achievement level of their students across the full spectrum of gifted through to those who learn differently.  , when you apply the principles of structured maths using a concrete, pictorial, abstract approach with manipulatives, you raise the achievement of every child.  the numicon programme is consistent with the new curriculum and the intentions of the ministry to require schools to implement structured maths in 2025.  the foundations for maths is laid out so well in the first three books of the series. these foundations are not hurried but strong and well-paced., numicon is such an amazing tool making it easy to implement structured maths in your school.  lesson plans are all done for you, the sequence of teaching is laid out, and you are provided with everything you need to deliver explicit teaching.  , you will enjoy teaching maths again and even more importantly, your students will love maths. , numicon is based on years of thorough research from international experts in learning and maths education - vygotsky, gattegno, piaget, skemp, sfard, bruner, davydov, wing, mason and others.  it is continually being updated to meet the needs of all learners. , using numicon results in the enjoyment of maths and exciting results in every school.  once implemented well..., year 3 students are typically working at level 2/end of phase 1. , year 6 students are typically working at nzc level 3/end of phase 2 , year 8 students are typically working at nzc levels 4/5/end of phase 3.

Purchase Numicon and other educational resources on www.edushop.nz  

Award-winning whole-school maths resource

Creating confident mathematicians , research-based , robust and reliable assessment , conversation, mathematical reasoning and problem-solving, download an introduction to numicon  numicon_intro_nz.pdf.

JOIN our facebook groups Numicon NZ and Numicon NZ Users

Numicon is sold in New Zealand by Procon Limited under the licence of  Oxford University Press

Margi Leech and the Edushop Team have been accredited by Oxford University Press to deliver Numicon Professional Development in New Zealand. 

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Opportunities for Students

On this page is information about competitions and activities for your students

Click the blue headings for more information

Mathex is a challenging and fast-paced mathematics contest where teams of four students compete against each other to answer questions as quickly as possible. AMA run the Mathex competition for years 7 to 10 over two nights in August.

Mathsweek is New Zealand’s premier online maths event attracting an audience of over 250 000 students teachers and parents. Mathsweek takes place in August each year.

This is a team competition for students of year 13 calculus. Calcex is held at venues across New Zealand in the last week of term 3. It is the brainchild of Jamie Sneddon.

Junior Mathematics Competition

This competition is for students in years 9 to 11 and was initiated in 1985 by Professor Derek Holton of the University of Otago Mathematics and Statistics Department. The competition attracts around 10 000 entries from 250 schools each year. It takes place on the same day across New Zealand.

Question 3 - The chocolate bar task

Question 4 - The fractions task

Question 5 - Coloured counters

There are some coloured counters in a bowl.

1/4 are black.

1/5 are green.

1. a) Are there more black or more green counters in the bowl?

More Black / More Green (Tick response)

b) Show how you got your answer. You can use words and pictures.

Question 6 - Closest to 3/5

a) Which of these is closest to 3/5

b) Explain why you think this. You can use words and pictures.

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• Properties of numbers

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For younger learners

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Matching Fractions, Decimals and Percentages

To download a printable version of this game, use the links below. There are three sets - set A is the easiest and set C is the most difficult. If you print double sided, then the cards will have an NRICH logo on the back. Otherwise, you can just print the first page. Set A , Set B , Set C

The aim of this game is to match pairs of cards. 

Click on a card in the interactivity below to turn it over. Then click on another one. If the two cards match, they will stay face-up. If the two cards do not match, they will return to being face-down. 

The game ends when all the cards have been matched in pairs. 

Click on the links below if you would like to try some alternative versions of the Level 1 game:

• Play with face-up cards  - the cards are all face-up at the start so you can focus on the maths rather than the memory aspect of the game. How quickly can you match them all?
• Play with a scoring system  - you start with 100 points, lose 10 points whenever you turn over cards that don't match, and add 50 points whenever they do match.

Once you've mastered Level 1, there are four more levels to try, getting progressively more difficult:

• Level 2     Face-up      Face-down
• Level 3     Face-up      Face-down
• Level 4     Face-up      Face-down
• Level 5     Face-up      Face-down

What strategies did you use to work out that two cards matched? Which pairs did you find easy to match?  Which pairs did you find more difficult to match?

We would love to hear about the strategies you used as you played the game.

A pupil from Gamlingay Village Primary sent in the following:

At first my card choices were random, but when I had remembered some cards I tried to match them and remember what was on each card. I also tried to convert the numbers on the cards into the same thing (e.g: decimals, fraction or percentage), which made it easier to tell if they matched one I had remembered.

Madeleine from the British School of Manila in the Philippines had a similar strategy:

My strategy was to look at random ones and guess at the beginning, then at the end I would remember where pairs were and do them quickly.

Callum from Wembrook Primary School wrote:

All you have to do is memorise the cards you have already flipped over and when you find one either in a decimal, a percentage or a fraction you have already found just match it to the equivalent card.

Erik from International School of the Hague (ISH) in the Netherlands wrote:

I did the matching fractions, decimals and percentages problem. The fastest way to get all the cards matched (if you are on cards up) is focusing on the easiest ones first. After you have matched all the easy ones, you have narrowed down the hard ones' possible answers. If you start on the harder ones, you will be looking through the flash cards to find an answer, and that will take you longer and you will get a higher time. Don't work hard, work smart.

Christopher from England wrote:

I recorded what each square was on a piece of paper as a fraction in its simplest form. Then, I matched them up, ticking them off as I went.

Mark from the International School of the Hague wrote:

First, I converted all the irregular values to decimals, to make them equal. For fractions, I converted the denominator to a hundred and then the numerator accordingly, so that the denominator was equal to hundred. The numerator was then the tenths and hundredths place of the decimal.

For the shapes, I counted how many there were in total and then how many were shaded to a fraction. The number of how many were shaded was the numerator and the total number was the denominator, I then did the same process as the fractions. And completed it.

Mahdi from Mahatma Ghani International School in India focused on finding the pairs as quickly as possible with the cards face-down, once you are already fluent with converting between the fractions, decimals and percentages. This is Mahdi's strategy:

For the face-down cards, I started to open the cards two at a time, labeled 1 and 2. If the two match, I open the 3rd and the 4th and continue. If 1 and 2 don't match (which is very likely), I proceed to open the 3rd one. I then recall whether the 3rd matches with any of the previous ones (1 and 2) in any simplified form. If not, I open the forth and continue. This was the general strategy I followed. 

Also, I found out that [by] the 9th card I will definitely have a match. This is due to the pigeon-hole principle (if the first 9 cards were all different to each other, then they would each still have a pair somewhere else - so there would be 9 partner cards - but there are only 16 cards altogether) . So, in the worst-case scenario every card from 1 to 8 has a corresponding match from 9 to 16 in some order. Thus when I open the 9th card it will definitely have a match for one of the 1-8 cards. This makes the strategy easier because I only have to memorize cards till 8 if there is no match. Otherwise, the game will get a lot easier if I luckily get a match before that.

Why do this problem?

This game can be played to improve students' recognition of equivalent fractions, decimals and percentages.

Possible approach  

Level 1 on the interactivity uses cards from Set A. Level 2 on the interactivity uses cards from Sets A & B. Level 3 on the interactivity uses cards from Set B. Level 4 on the interactivity uses cards from Sets B & C. Level 5 on the interactivity uses cards from Set C.

Bring the class together and ask for any tips or strategies that help with the game. You could invite students to create their own sets of cards that they can share and use to play different versions of the game.

Key questions

What could match with 0.3? What could match with 25%? What could match with $\frac35$? Which cards did you find easier to match? Which cards did you find more difficult to match?

Possible support

Encourage students to play in face-up mode a few times before moving on to face-down mode.

Matching Fractions can be used to help children develop their understanding of fractions before moving on to this activity.

Possible extension

The home of mathematics education in New Zealand.

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Problems and solutions for students

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

Education Counts

Site search, search the education counts website, find pages with, narrow results by:, developing mathematical inquiry communities:, 05 problem and launch.

Key Content

In this video Associate Professor Bobbie Hunter explains the importance of coming up with problems that have genuine mathematical value, that connect to big, worthwhile mathematical ideas, that will lead to understandings that will set them up for success at high school.

Leaders from Otumoetai Intermediate discuss how they go about collaboratively devising such problems and then planning the 'launch'. The 'launch' is where the problem of the day is introduced to the children. It is crucial on two counts: the children must understand the problem and believe that it is worth applying themselves to.

This video does not discuss the 'connect', the concluding part of the lesson where the children share how they went about solving the problem and the teacher ties their learning into the big idea.

Evidence in Action

This video provides a window into these critical success factors …

• the children will understand what it is they are trying to solve
• they connect to big, worthwhile maths ideas
• they connect in some way to the lives/communities of the children
• pedagogical leaders 'talk the walk'
• meetings optimise coherence, value and impact of pedagogical design
• choice of problems is linked to the curriculum
• exploration of possible misconceptions
• the problem makes sense to the students
• the problem matters to the students
• Pedagogical leadership.

Key Evidence Informing Action - References

Specialist providers and New Zealand Ministry of Education and central government education agency staff, can contact the Ministry of Education Library for access to the key evidence. For anyone else requiring this material, you can contact your institution or local public library.

DMIC Videos

Developing Mathematical Inquiry Communities (DMIC) Videos:

• Alton-Lee, A. (2003). Quality teaching for diverse students in schooling: Best Evidence Synthesis Iteration (BES) . Wellington: Ministry of Education.
• Alton-Lee, A., Hunter, R., Sinnema, C., & Pulegatoa-Diggins, C. (2012, April). BES Exemplar 1 Ngā Kete Raukura – He Tauira: Developing communities of mathematical inquiry . Wellington: Ministry of Education.
• Anthony, G., & Hunter, R. (2010). Communities of mathematical inquiry to support engagement in rich tasks In B. Kaur (Ed.), Mathematics applications and modeling: Yearbook 2010 Association of Mathematics Educators (pp. 21-39). London: World Scientific.
• Anthony, G., & Walshaw, M. (2010). Te ako pāngarau whaihua: Educational practices series – 19 . International Academy of Education, International Bureau of Education & UNESCO.
• Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics: Educational practices series –19 . International Academy of Education, International Bureau of Education & UNESCO.
• Anthony, G., & Walshaw, M. (2007). Effective pedagogy in mathematics/pāngarau: Best evidence synthesis iteration . Wellington, New Zealand: Ministry of Education.Chapter 5: Mathematical Tasks, Activities and Tools.
• Hattie, J (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London, UK: Routledge. Effect size for teacher clarity = 0.75
• Leach, G., Hunter, R., & Hunter, J. (2014). Teachers repositioning culturally diverse students as doers and thinkers of mathematics. In J. Anderson, M. Cavanagh, A. Prescott (Eds.) Proceedings of the 37th Mathematics Education Research Group of Australasia (pp. 381–388). Sydney, NSW: MERGA.
• Robinson, V., Hohepa, M., & Lloyd C. (2009). School leadership and student outcomes: Identifying what works and why: Best evidence synthesis iteration . Wellington, New Zealand: Ministry of Education. Chapters 5, 6 and 7.

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