Understand the model.
See the mathematics.
Everything a tutor needs to make the transition into Singapore-style mathematics: the method, original bar-model diagrams, grade-level lessons, formulas, exercises, and a mastery tracker.
Navigate the reference
Teaching methods
Concrete–pictorial–abstract, number bonds, mental flexibility, and how to bridge visual work to algebra.
Explore concepts →Bar-model atlas
Part-whole, comparisons, fractions, ratio, before-and-after problems, and original diagrams.
See models →Formula sheet
Print-ready arithmetic and fraction rules, geometric formulas, metric conversions, and percentages.
Open quick reference →Practice library
Fresh Grade 3–5 questions with explanations, separated from the publisher's placement materials.
Work problems →Progress through the grades
Grade 3
Whole numbers, fractions, measurement, area/perimeter, time, money, and first models.
3A + 3B →Grade 4
Factors, larger arithmetic, mixed numbers, decimal operations, geometry and multistep models.
4A + 4B →Grade 5
Fraction operations, expressions, decimal reasoning, volume, ratio, rate and percentages.
5A + 5B →A better way to accelerate
For a strong student entering a new curriculum, separate mathematical understanding from familiarity with the school's representations. A child who solves a problem using algebra but cannot interpret a bar model might need a brief method bridge, not months of arithmetic review.
- Diagnose with fresh problems and listen to reasoning.
- Explain how the Singapore Math representation corresponds to existing knowledge.
- Fill specific conceptual gaps before skipping chapters.
- Reassess independently, including after a delay.
- Advance to the next A/B level when the evidence supports it.
Scope: This independent guide follows the broad published Dimensions Math textbook topics for Grades 3–5. It is not an official Singapore Math Inc. product, placement test, or substitute for the books. All teaching diagrams and practice questions are newly authored.