The Math Ladder

"You Have Reached Level 5" Should Mean Something

Most learning apps invent their own levels. Undugu levels are benchmarked to real, named international competitions and national syllabi โ€” so when your child climbs a level, you know exactly what it means in the outside world.

Abacus champions exploring the Undugu smart abacus at AIAMA 2026 in Taipei
The Principle

Honest, External, Verifiable

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Benchmarked, Not Invented

Each Undugu level maps to a published external standard โ€” a Math Kangaroo grade, a MOEMS division, a Singapore Primary year. We say "benchmarked to," never "certified by."

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Earned Under Real Conditions

A student reaches a level by performing at that standard under realistic timed conditions โ€” not by tapping through content.

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A Path to Real Contests

The ladder's top is participation in actual external competitions โ€” the same contests sat by millions of students worldwide.

The Levels

Climb Through the History of Mathematics

Levels are named for great mathematicians, ordered so difficulty follows the history of the science โ€” from ancient Egypt to the modern era.

  1. 1
    Ahmes โ€” number setting, direct addition & subtraction
    Benchmarked to Math Kangaroo Grade 1
  2. 2
    Pythagoras โ€” full addition & subtraction with Small and Big Friends
    Benchmarked to Math Kangaroo Grade 2
  3. 3
    Archimedes โ€” multiplication
    Benchmarked to Math Kangaroo Grade 3
  4. 4
    Al-Khwarizmi โ€” division (the word "algorithm" comes from his name)
    Benchmarked to Math Kangaroo Grades 3โ€“4
  5. 5
    Fibonacci โ€” decimals, mixed operations, number patterns
    Benchmarked to Singapore Primary 4 ยท MOEMS Division E entry
  6. 6
    Newton โ€” measurement, unit conversion, rates, science-context problems
    Benchmarked to Singapore Primary 5 ยท Math Kangaroo Grade 5
  7. 7
    Gauss โ€” mental abacus mastery, number theory, working with unknowns
    Benchmarked to MOEMS Division E ยท SASMO
  8. 8
    Relativity I โ€” fractions, percentages, ratio, geometry arithmetic
    Benchmarked to Singapore Primary 6 ยท Math Kangaroo Grade 6
  9. 9
    Relativity II โ€” logic, combinatorics, competition test craft
    Benchmarked to AMC 8 ยท MOEMS Division M
  10. 10
    Beyond โ€” participation in real external contests
    Actual Math Kangaroo / MOEMS / SASMO entry
Younger & Wider

Before the Ladder, and Beside It

Little Ahmes (ages 3โ€“6): a pre-level track of colors, shapes, counting, patterns, and first bead play โ€” preparing little hands and minds for Level 1.

World Knowledge track: memory and recall training through flags, maps, and capitals โ€” exercising the same visualization and memory skills the abacus builds, in a different domain.

Benchmark References

The standards behind the ladder:

  • Math Kangaroo โ€” the world's largest school math competition, held in over 100 countries
  • MOEMS โ€” Math Olympiads for Elementary & Middle Schools (US, since 1979)
  • SASMO โ€” Singapore & Asian Schools Math Olympiad
  • Singapore Primary syllabus โ€” the national curriculum behind Singapore's top world-ranking math results
  • AMC 8 โ€” the Mathematical Association of America's middle-school competition

Undugu is independent of these organizations; levels are benchmarked to their published standards, not endorsed by them.

Give Your Child a Measured Path

Follow the ladder from first bead to competition-ready.