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Junior or Senior Resources?
Junior Resources (Yr 7 to 10)
Senior (NCEA Exam Resources)
Problem Challenge Competition Collections
| This 95-page book is a compilation of the 125 problems from the first five years of the competition together with their answers and solutions. There is also a brief introduction to problem solving and some statistical data listing the percentage of students who successfully answered each of the questions. | |
| 1999 ($32) This book is a compilation of the 100 problems from the next four years of the competition, together with the 20 questions from the first competition, held in 1999. It features coloured illustrations, full solutions and analysis, and ideas for extension work. The introduction looks in detail at three typical problems and discusses useful techniques for general problem solving. | |
| ) ($36) The third competition book is similar to Book 2 and features all 125 problems from 2000 to 2004, together with the corresponding questions from the competition (another 100 questions). It features coloured illustrations, full solutions and analysis, and ideas for extension work. | |
| ) ($36) The fourth competition book is similar to Book 3 and features all 125 problems from 2005 to 2009, together with the corresponding questions from the competition (another 100 questions). It features coloured illustrations, full solutions and analysis, and ideas for extension work. Another 114 pages of problem solving! | |
| ) ($36) The fifth competition book is similar to Books 3 and 4 and features all 125 problems from 2010 to 2014, together with the corresponding questions from the competition (another 100 questions). It features coloured illustrations, full solutions and analysis, and ideas for extension work. Another 115 pages of problem solving! | |
| ) ($36) 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 competition (another 100 questions). It features coloured illustrations, full solutions and analysis, and ideas for extension work. Another 116 pages of problem solving! |
- You can pay by credit card , or if you are ordering on behalf of a school or group that is in our database and has a University of Otago debtor code then you can pay later after receiving an invoice . If you wish to use the invoice option please sign in to the admin page first and then return to this page.
- Note that you can also order books at the same time as registering for the competition , in which case you should use the registration order form (only available during the registration period).
Year 8 maths
Here is a list of all of the maths skills students learn in year 8! 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 8! To start practicing, just click on any link.
Number theory
- A.1 Prime or composite
- A.2 Prime factorisation
- A.3 Multiplicative inverses
- A.4 Divisibility rules
- A.5 Highest common factor
- A.6 Least common multiple
- A.7 HCF and LCM: word problems
- A.8 Standard form
- A.9 Compare numbers written in standard form
- A.10 Classify numbers
- B.1 Understanding integers
- B.2 Integers on number lines
- B.3 Graph integers on horizontal and vertical number lines
- B.4 Absolute value and opposite integers
- B.5 Compare and order integers
- B.6 Integer inequalities with absolute values
Operations with integers
- C.1 Integer addition and subtraction rules
- C.2 Add and subtract integers using counters
- C.3 Add and subtract integers
- C.4 Complete addition and subtraction sentences with integers
- C.5 Add and subtract integers: word problems
- C.6 Integer multiplication and division rules
- C.7 Multiply and divide integers
- C.8 Complete multiplication and division sentences with integers
- C.9 Evaluate numerical expressions involving integers
- D.1 Decimal numbers review
- D.2 Compare and order decimals
- D.3 Decimal number lines
- D.4 Round decimals
Operations with decimals
- E.1 Add and subtract decimals
- E.2 Add and subtract decimals: word problems
- E.3 Multiply decimals
- E.4 Multiply decimals and whole numbers: word problems
- E.5 Divide decimals
- E.6 Divide decimals by whole numbers: word problems
- E.7 Estimate sums, differences and products of decimals
- E.8 Add, subtract, multiply and divide decimals: word problems
- E.9 Multi-step inequalities with decimals
- E.10 Maps with decimal distances
- E.11 Evaluate numerical expressions involving decimals
Fractions and mixed numbers
- F.1 Understanding fractions: word problems
- F.2 Equivalent fractions
- F.3 Write fractions in lowest terms
- F.4 Fractions: word problems with graphs and tables
- F.5 Least common denominator
- F.6 Compare and order fractions
- F.7 Compare fractions: word problems
- F.8 Convert between mixed numbers and improper fractions
- F.9 Compare mixed numbers and improper fractions
- F.10 Round mixed numbers
Operations with fractions
- G.1 Add and subtract fractions with like denominators
- G.2 Add and subtract fractions with like denominators: word problems
- G.3 Add fractions with unlike denominators
- G.4 Subtract fractions with unlike denominators
- G.5 Add and subtract fractions with unlike denominators: word problems
- G.6 Add and subtract mixed numbers
- G.7 Add and subtract mixed numbers: word problems
- G.8 Inequalities with addition and subtraction of fractions and mixed numbers
- G.9 Estimate sums and differences of mixed numbers
- G.10 Multiply fractions and whole numbers
- G.11 Multiply fractions and whole numbers: word problems
- G.12 Multiply two fractions using models
- G.13 Multiply fractions
- G.14 Multiply fractions: word problems
- G.15 Multiply three or more fractions and whole numbers
- G.16 Divide whole numbers by unit fractions using models
- G.17 Reciprocals
- G.18 Divide whole numbers and unit fractions
- G.19 Divide fractions
- G.20 Divide fractions: word problems
- G.21 Estimate products and quotients of fractions and mixed numbers
- G.22 Add, subtract, multiply and divide fractions and mixed numbers: word problems
- G.23 Evaluate numerical expressions involving fractions
Rational numbers
- H.1 Identify rational numbers
- H.2 Convert between decimals and fractions or mixed numbers
- H.3 Absolute value of rational numbers
- H.4 Compare rational numbers
- H.5 Put rational numbers in order
- H.6 Add and subtract rational numbers
- H.7 Apply addition and subtraction rules
- H.8 Multiply and divide rational numbers
- H.9 Apply multiplication and division rules
Exponents and square roots
- I.1 Understanding exponents
- I.2 Evaluate powers
- I.3 Solve equations with variable exponents
- I.4 Powers with negative bases
- I.5 Powers with decimal and fractional bases
- I.6 Evaluate numerical expressions involving exponents
- I.7 Square roots of perfect squares
- I.8 Estimate square roots
Ratios, rates and proportions
- J.1 Understanding ratios
- J.2 Identify equivalent ratios
- J.3 Write an equivalent ratio
- J.4 Equivalent ratios: word problems
- J.5 Unit rates
- J.6 Compare ratios: word problems
- J.7 Scale drawings: word problems
- J.8 Do the ratios form a proportion?
- J.9 Do the ratios form a proportion: word problems
- J.10 Solve proportions
- J.11 Solve proportions: word problems
- J.12 Estimate population size using proportions
- J.13 Rate of change
- J.14 Constant rate of change
Proportional relationships
- K.1 Find the constant of proportionality from a table
- K.2 Write equations for proportional relationships from tables
- K.3 Identify proportional relationships by graphing
- K.4 Find the constant of proportionality from a graph
- K.5 Write equations for proportional relationships from graphs
- K.6 Identify proportional relationships
- K.7 Interpret graphs of proportional relationships
- K.8 Write and solve equations for proportional relationships
- L.1 What percentage is illustrated?
- L.2 Convert between percents, fractions and decimals
- L.3 Compare percents to fractions and decimals
- L.4 Estimate percents of numbers
- L.5 Percents of numbers and money amounts
- L.6 Percents of numbers: word problems
- L.7 Solve percent equations
- L.8 Solve percent equations: word problems
Consumer maths
- M.1 Which is the better coupon?
- M.2 Add, subtract, multiply and divide money amounts: word problems
- M.3 Price lists
- M.4 Unit prices
- M.5 Unit prices: find the total price
- M.6 Percent of a number: GST, discount and more
- M.7 Find the percent: discount and mark-up
- M.8 Sale prices: find the original price
- M.9 Multi-step problems with percents
- M.10 Simple interest
- M.11 Compound interest
Problem solving and estimation
- N.1 Estimate to solve word problems
- N.2 Multi-step word problems
- N.3 Guess-and-check word problems
- N.4 Use Venn diagrams to solve problems
- N.5 Find the number of each type of coin
- N.6 Elapsed time word problems
Units of measurement
- O.1 Estimate metric measurements
- O.2 Compare and convert metric units
- O.3 Metric mixed units
- O.4 Convert between square metres and hectares
- O.5 Convert square and cubic units of length
- O.6 Convert between cubic metres and litres
- O.7 Precision
Coordinate plane
- P.1 Coordinate plane review
- P.2 Quadrants and axes
- P.3 Follow directions on a coordinate plane
- P.4 Distance between two points
Number sequences
- Q.1 Identify arithmetic and geometric sequences
- Q.2 Arithmetic sequences
- Q.3 Geometric sequences
- Q.4 Number sequences: mixed review
- Q.5 Number sequences: word problems
- Q.6 Evaluate variable expressions for number sequences
- Q.7 Write variable expressions for arithmetic sequences
Expressions and properties
- R.1 Write variable expressions
- R.2 Write variable expressions: word problems
- R.3 Evaluate linear expressions
- R.4 Evaluate multi-variable expressions
- R.5 Evaluate absolute value expressions
- R.6 Evaluate nonlinear expressions
- R.7 Identify terms and coefficients
- R.8 Sort factors of expressions
- R.9 Properties of addition and multiplication
- R.10 Multiply using the distributive property
- R.11 Solve equations using properties
- R.12 Write equivalent expressions using properties
- R.13 Add and subtract like terms
- R.14 Add, subtract and multiply linear expressions
- R.15 Factors of linear expressions
- R.16 Identify equivalent linear expressions
One-variable equations
- S.1 Which x satisfies an equation?
- S.2 Write an equation from words
- S.3 Model and solve equations using algebra tiles
- S.4 Write and solve equations that represent diagrams
- S.5 Solve one-step equations
- S.6 Solve two-step equations
- S.7 Solve equations: complete the solution
- S.8 Solve equations: word problems
Two-variable equations
- T.1 Does (x, y) satisfy the equation?
- T.2 Identify independent and dependent variables
- T.3 Solve word problems involving two-variable equations
- T.4 Complete a table for a two-variable relationship
- T.5 Write a two-variable equation
- T.6 Identify the graph of an equation
- T.7 Graph a two-variable equation
- T.8 Interpret a graph: word problems
- T.9 Write an equation from a graph using a table
Two-dimensional figures
- U.1 Identify and classify polygons
- U.2 Name, measure and classify angles
- U.3 Classify triangles
- U.4 Identify trapeziums
- U.5 Classify quadrilaterals
- U.6 Graph triangles and quadrilaterals
- U.7 Find missing angles in triangles and quadrilaterals
- U.8 Interior angles of polygons
- U.9 Lines, intervals and rays
- U.10 Parallel, perpendicular and intersecting lines
- U.11 Identify complementary, supplementary, vertical, adjacent and congruent angles
- U.12 Find measures of complementary, supplementary, vertical and adjacent angles
- U.13 Transversal of parallel lines
- U.14 Find lengths and measures of bisected line segments and angles
- U.15 Parts of a circle
Transformations and congruence
- V.1 Symmetry
- V.2 Identify reflections, rotations and translations
- V.3 Translations: graph the image
- V.4 Translations: find the coordinates
- V.5 Reflections: graph the image
- V.6 Reflections: find the coordinates
- V.7 Rotations: graph the image
- V.8 Rotations: find the coordinates
- V.9 Similar and congruent figures
- V.10 Side lengths and angle measures of congruent figures
- V.11 Congruence statements and corresponding parts
- V.12 Side lengths and angle measures of similar figures
- V.13 Similar figures and indirect measurement
Three-dimensional figures
- W.1 Bases of three-dimensional figures
- W.2 Nets of three-dimensional figures
- W.3 Front, side and top view
- W.4 Base plans
Geometric measurement
- X.1 Perimeter
- X.2 Area of rectangles and parallelograms
- X.3 Area of triangles
- X.4 Area between two shapes
- X.5 Area and perimeter: word problems
Data and graphs
- Y.1 Interpret tables
- Y.2 Interpret line plots
- Y.3 Create line plots
- Y.4 Interpret stem-and-leaf plots
- Y.5 Create stem-and-leaf plots
- Y.6 Interpret bar graphs
- Y.7 Create bar graphs
- Y.8 Interpret histograms
- Y.9 Create histograms
- Y.10 Create frequency charts
- Y.11 Interpret circle graphs
- Y.12 Circle graphs and central angles
- Y.13 Interpret line graphs
- Y.14 Create line graphs
- Y.15 Interpret box-and-whisker plots
- Y.16 Scatter plots
- Y.17 Choose the best type of graph
- Z.1 Calculate mean, median, mode and range
- Z.2 Interpret charts to find mean, median, mode and range
- Z.3 Mean, median, mode and range: find the missing number
- Z.4 Changes in mean, median, mode and range
- Z.5 Identify representative, random and biased samples
Probability
- AA.1 Probability of simple events
- AA.2 Probability of opposite, mutually exclusive and overlapping events
- AA.3 Experimental probability
- AA.4 Make predictions
- AA.5 Compound events: find the number of outcomes
- AA.6 Counting principle
- New Zealand School Math
Year 10 Math
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Year 10 (All topics)
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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.
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IMAGES
COMMENTS
This provides you with practical information about how to implement problem solving in your maths programme as well as some of the philosophical ideas behind problem solving. We also have a collection of problems and solutions for students to use independently.
L.O. 1: Introducing Algebraic Equations. L.O. 2: One-Step Equations. L.O. 3: Two-Step Equations. L.O. 4: Variables on Both Sides.
Each year Intermediate School children tackle 25 challenging maths questions of a problem solving nature. These questions have been collected together in six books, along with fully worked solutions, suggestions for extension activities and an introduction to problem solving.
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 8! To start practicing, just click on any link.
Year 10 math practice, questions, tests, teacher assignments, teacher worksheets, printable worksheets, and other activities for New Zealand School Math, Olympiad, SAT Subject Test: Math Level 1, Kangaroo, and SASMO.
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.