Singapore Math guide to Standard and Foundation Mathematics for families and teachers outside Singapore. How Primary 5 and Primary 6 students take Mathematics at one of two levels, what each level covers, and how the PSLE examines and grades them.
From Primary 5, Singapore Mathematics has two subject levels.
Knowing how they work makes school reports and PSLE results much easier to read.
Every student follows the same syllabus from Primary 1 to Primary 4. At Primary 5 and Primary 6, subjects are offered at Standard or Foundation level, depending on the student’s Primary 4 school examination results.
Each level has its own content list, its own PSLE paper and its own grading scale.
This guide is useful for families and teachers who want to:
- understand what Standard and Foundation Mathematics mean at Primary 5 and 6;
- read a Singapore school’s subject-level recommendation with confidence;
- prepare a child who is moving into a Singapore primary school; or
- make sense of Singapore Math materials labelled Standard or Foundation.
Quick facts
Level: Primary 5 and Primary 6
Strand: All three strands: Number and Algebra, Measurement and Geometry, and Statistics
Official source: MOE Primary Mathematics Syllabus (2021), MOE subject-based banding, and SEAB PSLE syllabuses 0008 and 0038
Comes after: the common Primary 1 to 4 syllabus, including Graphs and Charts and Factors and Multiples
Leads to: secondary Mathematics, beginning with Integers and Real Numbers and Prime Factorisation, HCF and LCM
What Standard and Foundation Mean in Singapore Mathematics
MOE’s syllabus says that “The P1-4 syllabus is common to all students.”
Standard Mathematics “continues the development of the P1-4 syllabus”. It adds the Primary 5 and 6 topics found throughout this series, such as rate, ratio, algebra and circles.
Foundation Mathematics “re-visits some of the important concepts and skills in the P1-4 syllabus”. MOE describes its new concepts and skills as “a subset of the Standard Mathematics syllabus”.
So Foundation is not a separate subject with different topics. It revisits Primary 1 to 4 ideas, adds fewer new topics, and its PSLE paper assesses them in simpler contexts.
Levels are set subject by subject, so a student may take some subjects at Standard and others at Foundation.
MOE’s own guidance to parents states: “Taking subjects at the foundation level is not a disadvantage for your child.”
Where Standard and Foundation Sit in the Singapore System
The sequence below comes from MOE’s primary syllabus and subject-based banding pages.
- Primary 1 to 4: one common syllabus for all students.
- End of Primary 4: the school recommends a combination of subject levels, based on the Primary 4 school examination results.
- Students who pass 3 or more subjects are offered the 4 standard subjects.
- Students who pass 2 or fewer subjects are offered choices that include combinations of standard and foundation subjects, up to 4 foundation subjects.
- End of Primary 5: “Adjustments to the subject levels are made if needed.”
- End of Primary 6: students sit PSLE Mathematics (0008) or PSLE Foundation Mathematics (0038).
The two levels share much of their content, but not all of it.
| Content | Standard | Foundation |
|---|---|---|
| Order of operations and brackets | P5 | P5 |
| Factors and multiples | P4 | Revisited at P5 |
| Time and the 24-hour clock | P1 to P3 | Revisited at P5 |
| Multiplying fractions | P5 | P5 |
| Dividing fractions | P6 | P6 |
| Percentage, discount, GST and annual interest | P5 and P6 | P6 |
| Rate | P5 | P5 |
| Area of triangle | P5 | P6 |
| Volume of cube and cuboid | P5 and P6 | P5 and P6 |
| Ratio | P6 | Not included |
| Algebra | P6 | Not included |
| Circles | P6 | Not included |
| Parallelogram, rhombus and trapezium | P5 | Not included |
| Statistics | P6 average | P5 tables, bar and line graphs; P6 pie charts and average |
Ratio, algebra, circles, and the parallelogram, rhombus and trapezium do not appear in the Foundation content lists.
Both PSLE papers have the same calculator rule: Paper 1 does not allow calculators, and Paper 2 does.
| PSLE Mathematics (0008) | PSLE Foundation Mathematics (0038) | |
|---|---|---|
| Paper 1, no calculator | 1 h 10 min; 18 multiple-choice and 12 short-answer questions; 50 marks | 1 h; 20 multiple-choice and 8 short-answer questions; 46 marks |
| Paper 2, calculator allowed | 1 h 20 min; 5 short-answer and 10 structured or long-answer questions; 50 marks | 45 min; 10 short-answer and 4 structured questions; 34 marks |
| Total | 45 questions, 100 marks, 2 h 30 min | 42 questions, 80 marks, 1 h 45 min |
SEAB’s PSLE Foundation Mathematics (0038) syllabus gives the full format. Both syllabuses are marked “For Examination from 2026”.
How the Two Levels Work
1. One syllabus from Primary 1 to 4
Every student learns the same content in the first four years: whole numbers, the four operations, fractions, decimals, measurement, geometry and graphs.
2. A recommendation at the end of Primary 4
The school recommends a combination of subject levels based on the Primary 4 school examination results.
3. Two levels at Primary 5 and 6
Standard continues the Primary 1 to 4 development. Foundation revisits key Primary 1 to 4 ideas and adds a subset of the Standard topics.
4. A review at the end of Primary 5
MOE states that subject levels are adjusted at the end of Primary 5 if needed.
5. Two different PSLE papers
Standard students sit PSLE Mathematics (0008). Foundation students sit PSLE Foundation Mathematics (0038). The Foundation assessment objectives refer to “simple contexts” and “simple situations”.
6. Two grading scales
Standard subjects are graded from AL 1 to AL 8. Foundation subjects are graded A, B or C, and each grade maps to a Standard AL.
The school makes the recommendation and is the right place to ask about a particular child.
Worked Examples
These examples use the published formats and bands. Both are simple arithmetic, but they answer two questions families often ask.
Checking the paper totals
Question: Using the SEAB format, show that PSLE Foundation Mathematics is marked out of 80.
Step 1. Paper 1 Booklet A: 10 questions × 1 mark + 10 questions × 2 marks = 10 + 20 = 30 marks.
Step 2. Paper 1 Booklet B: 8 questions × 2 marks = 16 marks. Paper 1 total = 30 + 16 = 46 marks.
Step 3. Paper 2: 10 short-answer questions × 2 marks = 20 marks, plus 14 marks for 4 structured questions. Paper 2 total = 34 marks.
Check: 46 + 34 = 80 marks. The same method for 0008 gives 10 + 16 + 24 = 50 marks for Paper 1 and 10 + 40 = 50 marks for Paper 2, a total of 100.
Reading a PSLE Score
Question: A student has AL 3, AL 4 and AL 5 in three Standard subjects, and grade A in Foundation Mathematics. What is the PSLE Score?
Step 1. MOE maps Foundation grade A to AL 6.
Step 2. The PSLE Score is the sum of the ALs of the four subjects.
Step 3. 3 + 4 + 5 + 6 = 18.
Check: PSLE Scores range from 4 to 32, with 4 the best possible score, so 18 is within the range.
MOE publishes the bands on its PSLE scoring page.
| Standard AL | Raw marks | |
|---|---|---|
| AL 1 | 90 and above | |
| AL 2 | 85 to 89 | |
| AL 3 | 80 to 84 | |
| AL 4 | 75 to 79 | |
| AL 5 | 65 to 74 | |
| AL 6 | 45 to 64 | |
| AL 7 | 20 to 44 | |
| AL 8 | Below 20 | |
| Foundation grade | Mark band | Maps to Standard AL |
| A | 75 to 100 | AL 6 |
| B | 30 to 74 | AL 7 |
| C | Below 30 | AL 8 |
Common Mistakes
- Treating Foundation as a different subject. Families sometimes expect unfamiliar topics. Fix: MOE describes Foundation’s new content as a subset of Standard, so compare the two content lists.
- Assuming the level is fixed at Primary 4. MOE says adjustments are made at the end of Primary 5 if needed. Fix: ask the school how it reviews subject levels.
- Reading a Foundation grade as an AL. Grade A is not AL 1. Fix: use the mapping A to AL 6, B to AL 7 and C to AL 8.
- Comparing raw marks across the two papers. PSLE Mathematics is marked out of 100 and PSLE Foundation Mathematics out of 80. Fix: compare grades and ALs, not raw marks.
- Expecting calculators in every paper. At both levels, Paper 1 does not allow calculators. Fix: keep practising written and mental methods.
- Using the wrong practice material. Ratio, algebra and circles are not in Foundation Mathematics. Fix: check which level a practice book or paper was written for.
Teaching Standard and Foundation Mathematics Outside Singapore
- Labels on materials. Singapore materials for Primary 5 and 6 may be written for Standard or for Foundation. Check the level before you buy or assign them.
- Placement and grade levels. Singapore levels do not convert neatly into grades elsewhere. The Singapore Math Placement guide and the Singapore Math Grade Levels guide explain why.
- Moving into a Singapore school. Subject levels are recommended by the school. Families relocating should ask the school directly how a new student’s levels are decided.
- Calculator rules. The same rule applies at both levels: no calculator in Paper 1, calculator allowed in Paper 2.
- Prerequisites. Foundation Mathematics revisits Primary 1 to 4 ideas such as fractions, decimals, factors and time. Those same foundations matter for every Primary 5 and 6 topic, at either level.
How to Support Either Level at Home
A clear picture of the level makes home practice more useful.
- Find out from the school which level your child is taking in Mathematics.
- Read the content list for that level on MOE’s syllabus page.
- Check the Primary 1 to 4 foundations: place value, multiplication tables, fractions and decimals.
- Practise some questions without a calculator, as in Paper 1, and some with one, as in Paper 2.
- Show working, even on short-answer questions, because a correct method can earn 1 mark when the answer is wrong.
- Near the end of Primary 5, talk to the school about how the year has gone.
The level describes the course, not the limit of a child’s thinking.
Try These
- A Standard Mathematics raw mark is 82. What AL is it?
- Which Standard AL does Foundation grade B map to?
- A student’s four subjects have ALs of 2, 3, 4 and 7. What is the PSLE Score?
- Which of these topics is not in Foundation Mathematics: rate, ratio or average?
Answers
- AL 3, because 82 lies in the band 80 to 84.
- AL 7.
- 16, because 2 + 3 + 4 + 7 = 16.
- Ratio. Rate is in Primary 5 Foundation and average in Primary 6 Foundation.
What Comes Next
- At Primary 6, Standard Mathematics students meet Ratio and Algebra in Primary 6.
- Both levels include Average at Primary 6.
- The secondary pages of this series begin with Integers and Real Numbers.
- MOE explains secondary subject levels on its Full SBB page.
Understanding the two levels helps families plan practice that matches the course.
Frequently Asked Questions
When do Singapore students start Standard or Foundation Mathematics?
At Primary 5. The level depends on the Primary 4 school examination results, and it can be adjusted at the end of Primary 5 if needed.
Is Foundation Mathematics easier?
It covers fewer new topics. MOE describes its new content as a subset of Standard, and its PSLE paper assesses it in simpler contexts.
Can a student take Standard in some subjects and Foundation in others?
Yes. Students who pass 2 or fewer subjects at the end of Primary 4 are offered choices that include combinations of standard and foundation subjects.
Which topics are in Standard but not in Foundation?
Ratio, algebra, circles, and the parallelogram, rhombus and trapezium.
Are calculators allowed in PSLE Foundation Mathematics?
Yes in Paper 2, no in Paper 1. The rule is the same as for PSLE Mathematics.
How is Foundation Mathematics graded at PSLE?
With grades A, B or C. For the PSLE Score, these map to AL 6, AL 7 and AL 8.
Helpful Reading
- Singapore Mathematics | International Edition: Graphs and Charts
- Singapore Mathematics | International Edition: Ratio
- Singapore Mathematics | International Edition: Calculators
- How PSLE Mathematics Paper 2 Works | Revised 2026 Format
- Why Mathematics Often Becomes Harder in P5 and P6
- How to Make Sense of the PSLE Mathematics Syllabus
- MOE Subject-Based Banding for Primary School
- SEAB PSLE Formats Examined in 2026
Two Levels in Singapore Mathematics
One syllabus to Primary 4.
Two levels from Primary 5.
A review at the end of Primary 5.
Two papers, two grading scales, one PSLE Score.
Foundation revisits. Standard extends.
The school recommends, and the school can explain.
Families who understand the system can ask better questions and plan calmer practice.
Ask Bukit Timah Tutor
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If your child is learning Singapore Mathematics at home, in an international school or in a Singapore school, and you are unsure where to begin with this topic, send us a short message with the student’s level and one example of the work.
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Singapore Mathematics | International Edition is a Bukit Timah Tutor guide series for families and teachers outside Singapore. It is not a textbook and is not affiliated with MOE, SEAB or any publisher. Syllabus details were checked against MOE and SEAB documents in October 2026. Always confirm current requirements with your school.
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