A hands-on mathematics laboratory
We are all mathematicians.
Whenever we share, compare and ask why.
Start with numbers and follow their connections through seven journeys. Experiment with an idea, then read its reasons at your own pace.
Explore the seven journeys ↓My starting point
Where would you like to begin?
Choose the mathematics you would like to start with, regardless of age. You can change it at any time.
Start with matching and counting. You do not need fractions or multiplication yet.
Begin with shapes, measurements and data →MathIsland at a glance
A map of mathematics: seven journeys
Explore the mathematics in each journey and open a familiar place first.
Numbers
Start with parts of a whole and explore values that familiar numbers cannot express.
Start by sharing a whole →Parts of one whole
Read the same quantity as a picture, a fraction and a decimal.
Read 3 connected lessons →NumbersBeyond familiar numbers
Extend numbers when familiar ones cannot express a value.
Read 3 connected lessons →All concepts on this journey
Mathematical language
Name unknown quantities and express shared rules with symbols.
Unknown numbers and balance
Find an unknown by preserving equality.
Read 3 connected lessons →Mathematical languageReverse repeated multiplication
Distinguish the questions asked by powers, roots and logarithms.
Read 3 connected lessons →All concepts on this journey
Relationships
Move between comparisons, tables, graphs and functions.
Quantities that change together
Look for patterns and distinguish ratios from proportionality.
Read 3 connected lessons →RelationshipsFrom input to output
Read the same function in a table, a graph and an expression.
Read 3 connected lessons →All concepts on this journey
Change
Follow nearby values towards instantaneous change and accumulation.
Instantaneous change and accumulation
Connect limits with derivatives and integrals.
Read 3 connected lessons →ChangeMake closeness precise
Revisit calculus through definitions and their conditions.
Read 3 connected lessons →All concepts on this journey
Space
Move and reflect shapes, then compare lengths, areas and directions.
Move, reflect and measure
Use shapes to distinguish length, area and volume.
Read 3 connected lessons →SpaceMeasure without reaching
Connect lengths using similarity and right triangles.
Read 3 connected lessons →All concepts on this journey
Uncertainty
Compare possibilities and read what samples and distributions can tell us.
What a collection of numbers tells us
Read the shape of data, not only a representative value.
Read 3 connected lessons →UncertaintyReason under uncertainty
Distinguish chance, new information and sampling.
Read 3 connected lessons →All concepts on this journey
Information
Organize numbers and explore how a model changes as it reduces error.
Work with several numbers at once
Organize numbers by position and role before calculating.
Read 3 connected lessons →InformationLearn by reducing error
Explore how functions and derivatives meet in learning.
Read 3 connected lessons →All concepts on this journey
One whole, different shares
When more people share the same bar, how does one person's share change?
Find a way to explore
Read the mathematics in everyday life
Explore how the assumptions change a calculation.
Looking for a particular idea?
Search and browse the contents →Read, try and think again
A place to connect explanations, experiments and proofs. Begin with one lesson and follow the next question when you are ready.