Mathematics and Statistics · Years 7–8 · SOLVE
Think like a mathematician and statistician
Find the pattern, prove it, and predict what comes next.
8 inquiry worlds · 60 hands-on activities · 24 readings
Choose your world
8 Mathematics and Statistics worlds to explore
Each world is a full inquiry: a real question, week-by-week sessions, hands-on activities, readings and a real audience. The whole class works on the same world, in any term.
4 weeksWhat the Data ShowsSleep, rain, reaction times and backyard birds. Ask a real question, collect the numbers, and find out what they actually say.Explore this world →
5 weeksPatterns, Proof and PredictionTiles, tournaments, sunflowers and a pattern that lies. Find the rule, predict step 100, then prove it or break it.Explore this world →
5 weeksMoney Moves: Budgets, Percentages and InterestIs 30% off really a deal? Which phone plan wins after a year? Run the numbers on real money choices before you spend a cent.Explore this world →
5 weeksMeasure Up: Designing SpacesHow many bags of soil fill a garden bed? How many litres fit in a tank? Measure a real space, draw it to scale and design something better.Explore this world →
5 weeksFind Your Way: Maps, Angles and CoordinatesGrids, bearings, scales and stars: build a real orienteering course that gets people from start to finish without getting lost.Explore this world →
5 weeksGames of Chance: Probability LabRoll, spin, flip and draw hundreds of times to find out which games are really fair, then design a fair game for the school gala.Explore this world →
5 weeksNumber Detectives: Primes, Powers and CodesCrack codes, hunt primes and dive below zero, then build an escape room where every lock opens with number clues.Explore this world →
5 weeksShape Shifters: Transformations and TessellationSlide, flip, turn and grow shapes into a pattern with no gaps, then prove it works and give it a real wall or path.Explore this world →
Your journey: SOLVE
Every Mathematics and Statistics world moves through the same stages.
- See the Pattern
- Organise Information
- Link Ideas
- Verify
- Explain
Background reading
Read to understand
Short readings from every world, written for Kōkiri Learn students.
- Mean, median or mode: which average tells the truth?Three kinds of average, what an outlier does to them, and why the one you choose can change the story.
- Data detectives: how statisticians investigateThe PPDAC cycle (Problem, Plan, Data, Analysis, Conclusion) is how statisticians turn a question into an answer they can trust.
- Graphs that tell the truth, and graphs that trickHow to choose the right graph, read its shape, centre and spread, and catch a graph that has been drawn to mislead.
- From pattern to rule: square and triangular numbersHow mathematicians turn a pattern into a rule with letters, and use a picture to prove it always works.
- When patterns break: why mathematicians want proofA pattern that goes 2, 4, 8, 16 and then 31 shows why checking cases is not enough, and why proof matters.
- Spirals, seeds and the Fibonacci numbersWhy sunflowers, pine cones and broccoli grow in spirals, and how to test the claim that nature 'uses' Fibonacci numbers.
- Percentages in the wild: sales, GST and tricky dealsHow percentages work in shops, why 35% off is the same as paying 65%, and the percentage tricks worth watching for.
- Budgets, plans and the 28-day trapHow a budget works, how to compare weekly, monthly and yearly costs fairly, and what 'buy now, pay later' really means.
- Interest: when money grows, and when it costs youSimple interest, compound interest and why starting to save early makes such a big difference.
- Kilo, centi, milli: the metric system made simpleHow metric units fit together, how to convert between them, and how to use your body as a measuring tool.
- Squared and cubed: area, volume and litresWhy area is measured in square units and volume in cubic units, how litres connect to cubes, and what happens when you scale a design up.
- Reading a site before you designHow designers read the sun, water, wind and slope of a place, and draw it to scale before they build anything.
- Grids, coordinates and grid referencesHow two numbers can pin down any place, from a spot on the school field to a hut in the Tararua Range.
- Scale and contours: shrinking the land onto paperHow map scales let you measure real distances, and how contour lines turn a flat sheet of paper into hills and valleys.
- Directions, angles and the star compassFrom the eight points of a compass rose to the 32 houses of the kāpehu whetū, direction is all about dividing a circle.
- Why 30 tries is not enoughExperimental probability, why results jump around, and how the Law of Large Numbers brings them back into line.
- Counting the chances: sample spaces, tables and treesHow to list every possible outcome, calculate theoretical probability, and use complements to save time.
- Fair games, the stall and the LottoWhat makes a game fair, why the stall usually wins, and what the real chance of winning Lotto looks like.
- Prime numbers: the atoms of mathsWhat primes are, how to find them, and how factors, HCF and LCM help solve real problems.
- Powers, roots and the rules of the roadSquares, cubes and roots, negative numbers from Ranfurly to the deep sea, and why everyone follows the same order of operations.
- Secret codes: from Caesar to your phoneHow ciphers work, how patterns give them away, and how prime numbers protect messages on the internet today.
- Angles, triangles and the 180° ruleTypes of triangles, why their angles always add to 180°, and how that rule unlocks the angle sum of any polygon.
- Moving shapes: transformations and symmetryThe four ways to move or change a shape on a grid, what they do to coordinates, and how to describe the symmetry of a pattern.
- Tessellations in nature and cultureWhy only some shapes tessellate, where nature uses them, and how weavers and artists in Aotearoa, the Pacific and beyond use geometry with meaning.
New Zealand Curriculum, Phase 3
What Mathematics and Statistics asks for in Years 7–8
A summary of the refreshed teaching sequence. A combined class meets the Year 7 sequence in one year of the cycle and the Year 8 sequence in the other.
In effect from 2026 Official statement ↗
Number
Year 7 sequence
- Exponents, square roots, order of operations
- Primes, factors and multiples
- Negative numbers on a number line
- Fractions, decimals and percentages; money and discounts
Year 8 sequence
- Prime factors, square and cube numbers
- Adding and subtracting negative numbers
- Ratio
- Financial plans: savings, phone plans, budgets
Algebra
Year 7 sequence
- One- and two-step equations
- Substituting into formulae
- Coordinates in four quadrants
- Spotting rules in tables and sequences
Year 8 sequence
- Writing rules with letters to predict
- Simplifying and factorising expressions
- Non-linear patterns: triangular, square and cube numbers
- Plotting patterns
Measurement
Year 7 sequence
- Metric conversions
- Perimeter, area and volume formulae
- Timetables and travel times
Year 8 sequence
- Converting time and volume units
- Missing lengths in practical situations
- Reading schedules and charts
Geometry
Year 7 sequence
- Classifying triangles
- Transformations on a grid
- Nets of 3D shapes
- Angles with parallel and perpendicular lines
Year 8 sequence
- Parts of a circle
- Transformations including enlargement
- Angle sums of polygons
- Map scales
Statistics
Year 7 sequence
- Planning data collection for a statistical question
- Mean, median, mode and range
- Choosing suitable graphs
- Checking data and outliers
Year 8 sequence
- Statistical investigations end to end
- Dot plots, bar graphs and time-series graphs
- Comparing groups with averages and spread
Probability
Year 7 sequence
- Chance experiments with at least 30 trials
- Experimental vs theoretical probability
Year 8 sequence
- Experiments with 100+ trials
- Probabilities as fractions, decimals and percentages
- Complementary events
Trusted NZ sites
Explore more
- CensusAtSchool ↗
CensusAtSchool NZ
Real survey data from NZ students to investigate.
- NZ Maths ↗
NZ Maths
Maths problems and activities for NZ classrooms.
- Stats NZ ↗
Tatauranga Aotearoa
Official New Zealand data on people, places and the economy.
Ready to run it with your class?
Free trial for NZ schools. One combined Years 7–8 class, any term.