The teaching method that made Singapore #1 in math worldwide. Visual bar models turn abstract problems into pictures kids can see and solve.
Start with real objects kids can touch and count. Blocks, counters, everyday items. Build understanding through physical experience.
Move to visual representations — bar models, number bonds, diagrams. Kids SEE the math relationship before writing equations.
Only then introduce numbers and symbols. By this point, kids understand WHY 3 + 4 = 7, not just that it does.
This is the CPA (Concrete-Pictorial-Abstract) approach — the foundation of Singapore Math.
Pick a real word problem from our Class 3–5 curriculum. The bar shows you what your child sees inside iMasterly.
“Sam has 24 marbles. He has 3 times as many as Tom. How many does Tom have?”
Whole = 24
Sam's bar = 3 equal parts of Tom's bar.
Want to practise these bar-model problems yourself?
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Bar Models
Part-Whole
Comparison Models
Before-After Models
Fractions with Models
Ratio Models
Percentage Models
Multi-Step Word Problems
Model Drawing
Place Value Discs
Mental Math Strategies
Singapore Math is a teaching method for elementary mathematics built around three core ideas: the Concrete-Pictorial-Abstract (CPA) approach, the use of bar models to visualize word problems, and a deliberate focus on mastery over coverage. Instead of racing through dozens of topics each year, Singapore Math teaches fewer topics more deeply — making sure children fully understand the structure of a concept before moving on. It is widely regarded as one of the most effective elementary math curricula in the world and is the reason Singapore has consistently ranked first or second in international math assessments for over 25 years.
The bar model is the signature tool of Singapore Math. When a child encounters a word problem like “Sam has 24 marbles. He has 3 times as many as Tom. How many marbles does Tom have?”, they don't guess at the operation — they draw the problem as proportional bars. Sam's bar is divided into 3 equal parts; Tom's bar is one of those parts. The relationship becomes visual: 24 ÷ 3 = 8. This same visual technique scales from grade 2 addition to grade 6 fractions, ratios, and percentages — and even into algebra. Once a child has internalized bar modeling, word problems stop feeling like guessing games and start feeling like drawing exercises.
Singapore Math was developed in the early 1980s by the Curriculum Development Institute of Singapore (CDIS), a division of Singapore's Ministry of Education. After Singapore gained independence in 1965, the country's leaders recognized that with no natural resources, their only path to prosperity was a highly educated workforce — and that strong mathematics education would be foundational to everything else. By the late 1970s, Singapore students were performing poorly on international math benchmarks, and the government commissioned a complete rewrite of the national elementary math curriculum.
The 1982 curriculum, titled Primary Mathematics, was led by a team of Singaporean educators including Dr. Kho Tek Hong, who is widely credited as the architect of the bar model method (also called the “Model Method” or “Singapore Bar Model”). The team drew heavily on the work of American educational psychologist Jerome Bruner, whose Concrete-Pictorial-Abstract (CPA) theory proposed that children learn best when new concepts are introduced first with physical objects, then with pictures and diagrams, and only finally with abstract symbols. Bruner's CPA framework became the structural backbone of every Singapore Math lesson — and remains the defining feature of the program today.
The results were dramatic. By 1995, Singapore had risen to first place in the world on the Trends in International Mathematics and Science Study (TIMSS) — the most rigorous international math assessment. Singapore has remained at or near the top of TIMSS rankings every cycle since (1995, 1999, 2003, 2007, 2011, 2015, 2019, and 2023). Singapore students also lead or co-lead the Programme for International Student Assessment (PISA), the OECD's assessment of 15-year-olds in math, reading, and science. By the late 1990s, educators around the world began traveling to Singapore to study what they were doing differently — and Singapore Math began its global spread.
Singapore Math was first introduced to the United States in 1998 by Jeffery and Dawn Thomas, who founded SingaporeMath.com after their own son struggled with American math curricula. They licensed the Singapore Primary Mathematics textbooks for US distribution, and the program quickly took hold in the American homeschool community — which valued the curriculum's depth and clarity over the wider but shallower American standards. By the mid-2000s, Singapore Math had been adopted by hundreds of private schools and homeschool families across the US, UK, Canada, and Australia. Houghton Mifflin Harcourt later released Math in Focus, the official Common-Core-aligned American adaptation of Singapore's Primary Mathematics series, which is now used in thousands of US public schools.
Today, Singapore Math is used in over 40 countries worldwide. The original Singapore Primary Mathematics curriculum has been continuously refined by the Ministry of Education through multiple editions (1982, 1994, 2001, 2007, 2013, and the latest 2021 syllabus), but the core principles — CPA approach, bar modeling, mastery progression, and number bonds — have remained unchanged. The same techniques that pushed Singapore to #1 in 1995 are the techniques being taught to first graders in Houston, London, Sydney, and Toronto today.
The reason Singapore Math is so effective for elementary students comes down to cognitive load. Most traditional math curricula introduce a topic abstractly — “a fraction is a number written as a/b” — and then ask children to manipulate symbols they don't yet understand. Singapore Math reverses the order. Children handle physical objects (concrete), then look at and draw pictures of those objects (pictorial), then finally connect the pictures to numbers and symbols (abstract). By the time a child writes “3/4”, they have already seen three out of four equal parts in dozens of contexts — pizzas, bars, marbles, distance lines. The symbol is no longer abstract; it is just the shorthand for something they already understand.
The bar model in particular gives children a single visual language that scales across grade levels. The same bar diagram a 2nd grader uses to show “3 + 5 = 8” will, by grade 6, become a tool for solving multi-step ratio and percentage problems that would otherwise require algebra. This is why Singapore students consistently outperform peers on word problems: they have one consistent representation they can reach for, instead of trying to translate every problem into a new equation from scratch.
Singapore Math also emphasizes number sense — particularly through “number bonds,” which decompose numbers into their parts (10 = 6 + 4 = 7 + 3 = 8 + 2). Singaporean first graders spend weeks on number bonds before being introduced to formal addition. The payoff is mental math fluency that lasts a lifetime: a Singapore-trained 4th grader doing 47 + 38 in their head will decompose it as (47 + 3) + 35 = 50 + 35 = 85 — automatically, without thinking. This kind of flexible number manipulation is the foundation of algebra readiness.
If your child is also learning to compute quickly, pairing Singapore Math with Vedic Math is a powerful combination: Singapore Math teaches deep understanding and problem-solving structure; Vedic Math teaches mental computation speed. Many families use both for grades 3-8, and pair them with state test prep for the strongest possible math foundation.
Three big differences. First, Singapore Math covers fewer topics each year but in much greater depth — mastery over coverage. Second, it uses the Concrete-Pictorial-Abstract (CPA) approach: children handle objects before pictures, and pictures before symbols. Third, it teaches the bar model as a universal visual tool for word problems — something American curricula generally do not.
Singapore Math is designed for grades 1 through 6 (with some publishers extending through grade 8). Most families start at the grade level their child is currently in. If transitioning from a traditional curriculum, expect a brief adjustment period as the child learns bar modeling — but most kids catch on within 4-6 weeks.
No. Singapore Math was designed as a national curriculum for all Singaporean students, not as gifted enrichment. The visual approach makes it especially effective for kids who struggle with abstract symbols — the bar model gives them a concrete way to think about problems they would otherwise find overwhelming.
Common Core borrows several ideas from Singapore Math (number bonds, multiple representations, emphasis on problem solving), but US implementations vary widely in depth. Singapore Math is more focused, more sequenced, and more consistent across grade levels. Many US homeschoolers and private schools use Singapore Math precisely because they want a more disciplined version of what Common Core attempts.
Traditional Singapore Math textbooks cost $20-30 per book per grade, plus workbooks. Tutoring-based Singapore Math programs run $30-150 per month. iMasterly includes Singapore Math free as part of K-8 multi-subject learning — alongside Vedic Math, abacus, the standard K-8 curriculum, and state test prep.
Yes, especially with online programs that include video instruction and interactive bar model tools. iMasterly's Singapore Math is designed for independent home use — the AI walks kids through each bar model step-by-step and provides feedback. Many homeschoolers successfully teach Singapore Math at home using textbooks alone, though it requires the parent to learn the method first.
Visual bar models, CPA approach, and problem-solving strategies for K-8.
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