COMPLETE SEMESTER 3A
Semester 3A · Seven chapters and cumulative practice
Explore seven original instructional chapters, chapter reviews and practice exams, plus a cumulative review and an untimed semester practice examination. Internally reviewed; external learner testing is pending.
Open Semester 3A →COMPLETE SEMESTER 3B
Semester 3B · Eight chapters and cumulative practice
Fractions, measurement, geometry, area, perimeter, time, and money—with complete lessons, chapter practice, 74 cumulative review questions, and an untimed semester practice examination. Internally reviewed; external learner testing is pending.
Open Semester 3B →COMPLETE SEMESTER 4A
Semester 4A · Nine chapters and cumulative practice
Original instruction across place value, operations, factors and multiples, fractions, and graphs—with chapter practice, a 69-question cumulative review, and a 60-question practice examination. Internally reviewed with controls; external educator and learner trials remain outstanding.
Open Semester 4A →COMPLETE SEMESTER 4B
Semester 4B · Eight chapters and cumulative practice
Original instruction in measurement, area and perimeter, decimals, angles, lines and shapes, and cuboids, including chapter assessments, a 64-question cumulative review, and a 60-question practice exam. Internally reviewed with controls; external educator and learner trials are pending.
Open Semester 4B →SEMESTER 5A · INTERNAL REVIEW COMPLETE
Semester 5A · Eight chapters and cumulative practice
50 independently authored lessons, 14 practice units, chapter assessments, a 64-question cumulative review, and a 60-question practice exam. Internal checks completed with controls; external educator, accessibility, and learner trials remain pending.
Open Semester 5A →SEMESTER 5B · INTERNAL REVIEW COMPLETE
Semester 5B · Seven chapters and cumulative practice
45 independently authored lessons, 10 practice units, seven chapter reviews and exams, three cumulative reviews, and a separate 60-question semester examination. Internal checks completed with controls; external educator, accessibility, and learner trials remain pending.
Open Semester 5B →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.