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Singapore math

Also called Primary Mathematics, Dimensions Math, Math in Focus, concrete–pictorial–abstract, CPA, bar model method.

Ages Ages 4 to 14, with most programs covering 1st to 6th gradeGrades Pre-K–8Planning Laid out for youScreens Some screen timeShelf MathUpdated November 2026

Singapore math is the way of teaching elementary math that grew out of the textbooks Singapore's Ministry of Education wrote in the 1980s. Each new idea is met three ways: first with real objects, then with a drawing, then with numbers and symbols. Word problems are solved by drawing a bar model, a row of rectangles that shows what is known and what is missing. It covers fewer topics each year and stays with each one longer. It suits children who like to see why something works, and adults willing to slow down and use blocks and drawings.

1 Where it came from

Singapore's Ministry of Education developed the Primary Mathematics series in the early 1980s, and a Singapore academic paper traces the concrete–pictorial–abstract sequence to ministry materials first published in 1981. Singapore Math Inc. brought Primary Mathematics to American schools and homeschoolers in the late 1990s, and later wrote Dimensions Math, a newer series from Pre-K to 8th grade. Math in Focus, another Singapore program, is produced by Marshall Cavendish and sold in the US by Houghton Mifflin Harcourt.

2 The big ideas

  • Concrete, then pictorial, then abstract. A child handles blocks or counters, then draws or reads a picture of them, and only then writes the numbers. Many writers credit the idea to the psychologist Jerome Bruner, though Singapore's own researchers treat that link with care.
  • Fewer topics, more depth. A year covers a short list of big ideas, each for long enough that children understand it before moving on.
  • The bar model. One drawing, rows of rectangles standing for amounts, is used again and again for word problems, fractions, ratio and percent.
  • Number sense before speed. Children take numbers apart and put them together (number bonds, making ten) so that mental math rests on understanding.
  • Problem solving is the point. Practice of procedures serves the harder goal of solving problems a child has not seen before.

3 What a lesson looks like

A 3rd-grade lesson might open with one problem on the board: Ana has 18 marbles. Ben has 6 more than Ana. How many do they have altogether? Children first build it with cubes, a tower of 18 for Ana and a tower of 18 and 6 more for Ben. Next they draw it: two bars, the second one longer, with the extra 6 marked off and a bracket around both bars with a question mark. Only then do they write 18 + 18 + 6 = 42. The teacher asks several children to explain their drawings, points out how the picture shows the more than, and the class practices a few similar problems in the textbook before a short workbook page. Over several lessons the problems change one thing at a time, until children are drawing bars for problems with two steps or with fractions.

4 Reading and math

Singapore math is a math approach only. Its word problems ask children to read carefully, and the bar model is partly a reading tool: it turns a sentence into a picture before any arithmetic happens.

5 The adult's job

The adult teaches, and does not just hand out pages. They prepare the objects, ask children to draw and explain, choose examples with care and decide when a class or a child is ready to drop the blocks. Home editions come with teacher's guides that walk a parent through each lesson; the teaching lives in the guide, not only in the student book.

6 How progress is checked

Progress is checked with workbook practice, chapter reviews and tests in the program, and by listening to how a child explains a drawing. A child who can draw the bar model for a new problem, and say what each part stands for, has understood more than one who only gets the answer.

7 Strengths and criticisms

Strengths

  • Coherent and focused. The US National Mathematics Advisory Panel (2008) held up Singapore's standards as an example of developing proficiency in a small number of important topics.
  • The bar model is one picture that keeps paying off, from 2nd-grade word problems to ratio and percent in middle school.
  • Objects and drawings come first, which matches the 2021 federal practice guide's advice to use concrete and semi-concrete representations, a recommendation it rates as having strong evidence.
  • Singapore math came to the US through homeschoolers as well as schools, so home editions with a parent's guide are easy to find.

Criticisms and watch-outs

  • There is little rigorous outcome research on the programs themselves. The What Works Clearinghouse reviewed studies of Singapore Math several times and found none that met its standards, so it could draw no conclusion either way.
  • It asks a lot of the adult. Without the objects, the drawings and the talk, it becomes one more workbook.
  • Blocks and drawings help only if children are led from them to numbers. The Advisory Panel stressed that students must eventually move to abstract symbols.
  • Math in Focus was rated by EdReports in 2021 as not meeting expectations for Common Core alignment in most grades (as of November 2026). That measures fit to US standards and how they are sequenced, not whether children learn math well with it.

8 What the research says

The direct evidence on Singapore programs is thin. A 2015 What Works Clearinghouse update looked at seven new studies and found that none met its design standards, so it could make no conclusion about effectiveness; earlier reviews ended the same way. In England, two trials of Mathematics Mastery, a program influenced by Singapore's approach, found small positive effects that were not statistically significant on their own and amounted to about a month of extra progress when combined. The approach's main parts have better support than the brand names do. The 2021 federal practice guide for students who struggle rates the use of concrete and semi-concrete representations as strong evidence, and a 2013 meta-analysis of manipulatives found they can help, but only under certain conditions, such as clear guidance from the teacher. No study has shown that Singapore math fails; there are simply too few strong studies to say how much it helps.

9 How to try it

  1. Pick one word problem a day and solve it three ways: with objects from the kitchen table, with a drawing, then with numbers.
  2. Teach the bar model on easy problems first. Sam has 5 apples and gets 3 more deserves a bar too, so the habit is in place when problems get harder.
  3. Play number bonds: hold up 10 fingers, hide some, and ask how many are hidden. Do the same with 7, 8 and 9.
  4. Ask how do you know? after every answer, and let your child explain with a drawing.
  5. If you choose a program, read the teacher's guide for a lesson before you teach it; the student pages alone leave out the objects and the questions.

10 Using Peabody with it

  • Virtual base-ten blocksBlocks to drag and trade on a screen or projector, for the concrete step when real blocks aren't to hand.
  • Number bondsA part-part-whole diagram for any whole to 20, the same picture Singapore programs use for taking numbers apart.
  • Fraction barsStacked bars from halves to twelfths that work like the bar model for fractions.
  • Numbers, on the kids' siteShort practice by grade with a worked example; it does not draw bar models, so keep those on paper.

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11 Programs that follow it

Programs and materials often named with this approach: Primary Mathematics, Dimensions Math, Math in Focus, Maths — No Problem!.

Questions people ask

What is a bar model in Singapore math?
A bar model is a drawing of rectangles that stand for amounts in a word problem. A longer bar is a bigger amount, and a bracket with a question mark marks what you need to find. Children draw it before they write an equation, so they can see which operation the problem needs.
What does concrete–pictorial–abstract mean?
It is the order in which a new idea is taught: first with real objects a child can move (concrete), then with a picture of them (pictorial), then with numbers and symbols alone (abstract). The aim is that the symbols mean something because the child has already seen and drawn them.
What is the difference between Primary Mathematics, Dimensions Math and Math in Focus?
All three follow Singapore's approach. Primary Mathematics is the original series, for grades 1 to 6. Dimensions Math is Singapore Math Inc.'s newer series, from Pre-K to 8th grade. Math in Focus is a separate program made by Marshall Cavendish and sold to US schools by Houghton Mifflin Harcourt.
Does Singapore math work?
The honest answer is that it has not been tested well. The What Works Clearinghouse found no studies of it that met its standards. Its main methods, objects and drawings before symbols, and a focus on fewer topics, are backed by broader research, and a related program in England showed a small gain of about a month's progress.

Sources

  • Mastery math: Teach one topic in small connected steps until it is secure, keep the whole class together, and only then move on.
  • Problem-based math: Children work on a well-chosen problem first, share their ways of solving it, and the teacher then draws out the math.
  • Math fact fluency: Knowing addition and multiplication facts by heart, built from strategies first and then short practice, as one strand of math, not all of it.
  • Spiral math: New topics in small pieces, and every day's practice mixes in problems from earlier lessons so nothing is learned once and dropped.
  • Montessori: Children choose their own work from hands-on materials in a mixed-age room, with the teacher as guide and the materials showing mistakes.
  • Every approach in the curriculum guide

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