What is the CPA Method in SASMO? How to Transition Between Levels? How to Use CPA to Prepare for the New Season in Summer? With Examples

SASMO (Singapore Asian Schools Math Olympiad) is led by the Singapore mathematics system and covers grades G2–G12 across Asia-Pacific countries. It is held annually (in China, the exam is usually in April, with summer preparation for the following year). It is one of the few competitions for lower and middle grades (G2–G8) that treats the Singapore CPA pedagogy as a problem-solving methodology. Kangaroo leans towards fun visual puzzles, MathLeague leans towards American-style speed and deep problems, and AMC is pure abstract选拔. SASMO's differentiation lies in CPA: the questions are deliberately designed to follow the "Concrete → Pictorial → Abstract" three-stage progression. Especially in the G2–G6 range, many questions simply cannot be solved without drawing diagrams; forcing algebraic expressions反而 makes them more confusing. For domestic families, SASMO's value is not only as an Asia-Pacific credential (adding weight to applications for Singapore universities, Hong Kong universities, and Commonwealth countries at younger ages) but also as a way to learn Singapore's CPA "early math thinking training method" through the competition. This method supports the transition to G7+ Algebra far better than rote problem-drilling. This article breaks down what CPA is, how SASMO levels connect, how to use CPA to prepare for the new season in summer, and includes a complete example.

I. The CPA Pedagogy: Singapore Math's "National Treasure" and SASMO's Question-Setting Logic

1. The Three Stages of CPA

• C = Concrete: Use physical objects, counters, building blocks, or beans to "act out" the problem. For example, "5+3" is not written as "5+3="; instead, take 5 beans + 3 beans and count them to get 8. For young children (G1–G3), this is the first stage of learning math — they must be able to touch it, otherwise "5" is just a symbol to them.
• P = Pictorial: "Draw" the concrete objects — using bar models (Singapore math's signature tool), array diagrams, number lines, and pie charts to visualise quantitative relationships. This is the most critical stage of CPA and the core solution method for SASMO G2–G6 questions. If you can draw bar models, you can solve 70% of SASMO G2–G6 questions; if you cannot, forcing algebraic expressions can easily lead to confusion. Bar models are divided into "part-whole" and "comparison" types, and are a signature tool of Singapore math.
• A = Abstract: Turn the diagram into an equation — 5+3=8, 2x+3=11 — moving into symbolic operations. From G5+, students gradually transition from P to A, but even SASMO G7–G8 questions retain the design principle that "drawing a diagram lets you see the relationships faster."

2. Why SASMO Tests CPA Rather than Pure Calculation

The Singapore math system believes that "teaching A (abstract equations) directly to young children skips a crucial step; children memorize formulas and solve problems without understanding why." Therefore, the G1–G6 curriculum follows CPA throughout. As a competition led by the Singapore system, SASMO's question design continues this philosophy: G2–G4 questions can (and should) be solved using bar models; G5–G6 begins to include purely A-type questions, but the P stage remains a shortcut; G7+ moves closer to AMC style but still retains modelling thinking. This is different from Kangaroo's "look at the picture and choose the answer" — Kangaroo's pictures are decorative/contextual, while SASMO's pictures (bar models) are the problem-solving tool itself.

II. SASMO Level Progression: G2–G12 Tiers and Connection to the AMC Pathway

Level	Grades	CPA Weight	Core Topics	Progression Path
Grade 2–4	G2–G4	C→P dominant, A emerging	Four operations applications, bar model introduction, shape patterns, simple logic	Kangaroo B–C / MathLeague Elementary
Grade 5–6	G5–G6	P→A transition, deep bar model reasoning	Fractions, percentages, ratios, bar model solutions for chicken-rabbit, sum-difference, multiples, geometry area	AMC8 / MathLeague Middle
Grade 7–8	G7–G8	A dominant, CPA thinking as a safety net	Algebra introduction, advanced ratios, geometry (perimeter, area, volume), basic combinatorics	AMC8 High Score / AMC10
Grade 9–12	G9–G12	A dominant, close to AMC10/12	Functions, trigonometry, probability, number theory foundations	AMC10/12 / AIME

Guidance for families: For G2–G4 students first encountering an international math competition, SASMO is more "methodological" than Kangaroo — Kangaroo is play, SASMO is "play + learn CPA," which is more practical for subsequent school math and AMC transition. G5–G6 is the golden period for SASMO — bar models can solve chicken-rabbit, sum-difference, multiples, and fraction application problems, which are exactly the areas where students最容易崩 in school "word problems." Practicing with CPA once makes school word problems essentially solvable. From G7+, SASMO gradually becomes AMC-like; if aiming for AMC8/10, SASMO G7–G8 can serve as a supplement, but the main focus should still be on AMC.

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III. CPA Example: A Typical SASMO G4 Question Solved in Three Stages

Example: Xiaoming and Xiaohong have 28 marbles in total. Xiaoming has 4 more marbles than Xiaohong. How many does each have?

C Stage (Concrete): Take 28 beans (or counters) and have the child divide them into two piles, one pile with 4 more than the other. Try a few times until they find 12 + 16 = 28, difference 4. The child physically experiences that "the larger pile minus 4 equals the smaller pile" — a concrete perception.

P Stage (Pictorial, core of bar model): Draw two horizontal bars. The top bar (longer) represents Xiaoming, the bottom bar (shorter) represents Xiaohong. The top bar extends beyond the bottom by a small segment marked "4". The total length of both bars is marked "28". Next to the diagram, write: If we cut off the extra 4, the two bars become equal in length. The total length becomes 28 − 4 = 24. Each bar is 24 ÷ 2 = 12 (Xiaohong). Xiaoming = 12 + 4 = 16. This is the standard "comparison" bar model — SASMO G3–G5 has a very high proportion of such questions.

A Stage (Abstract): Let Xiaohong have x marbles, Xiaoming have x + 4. x + (x + 4) = 28 → 2x = 24 → x = 12, Xiaoming = 16. Comparing the three stages, the child can explain "why we subtract 4 and then divide by 2" — this is true understanding, not memorizing the sum-difference formula "(sum + difference)/2 = larger number".

Another example: SASMO G5 fraction bar model question

Problem: "A barrel of oil has 2/5 used, and 12 litres remain. How many litres were originally in the barrel?"

P Stage (bar model, part-whole type): Draw a horizontal bar representing the whole barrel. Divide it into 5 equal parts. Shade 2 parts and label them "used". The remaining 3 parts are labelled "12 litres" → each part = 4 litres → whole barrel = 5 parts = 20 litres. Without drawing a diagram, a G5 student might easily reverse the numerator and denominator when writing "12 ÷ (1 − 2/5)". With the diagram, it's clear at a glance. For SASMO G5–G6 fraction/percentage word problems, the bar model is the standard solution — far more reliable than memorizing "given a part, find the whole = part ÷ corresponding fraction".

IV. How to Use CPA to Prepare for the New Season in Summer (2026 April Exam has passed; prepare for the 2027 April New Season)

5. G2–G4 Segment (C→P dominant): Summer June–August

• 2 sessions per week, 30–40 minutes each.
• ① C-stage play: Use counters/Lego/beans to play with concrete versions of "sum-difference" and "multiples" (e.g., "You have 2 more than me, we have 10 total, how many each?" — act it out).
• ② P-stage drawing bar models — this is the core: Singapore math G1–G3 textbooks (e.g., My Pals Are Here! Math / Maths No Problem! — both series are available in China) have bar model practice problems. Practice 5–8 per week, divided into "part-whole" and "comparison" types.
• ③ A-stage equation writing: For each P-stage problem, write an equation. Have the child explain how the C→P→A three stages correspond.
• Over the summer, work through 2–3 sets of SASMO G2–G4 past papers (untimed). The key is to see whether the child can draw diagrams. For problems they cannot diagram, demonstrate with a bar model — this is more useful than just giving the answer.

6. G5–G6 Segment (P→A transition): Summer

• 3 sessions per week, 45 minutes each.
• ① Deep bar model reasoning: Use bar models for all fraction/percentage/ratio problems. SASMO G5–G6 high-frequency失分 areas: "given part find whole", "given whole find part", "remaining after two changes" — practice the bar model templates for these three types until熟练.
• ② Four classic Singapore system word problem types: Chicken-rabbit, sum-difference-multiple, age, and travel — work through them using P→A.
• ③ Introduction to geometry area: Perimeter/area/volume formulas + bar model辅助 understanding (e.g., "rectangle length:width = 3:2, perimeter 30, area?" — draw a bar model to first find length and width).
• ④ Practice SASMO G5–G6 past papers: 3–5 sets, timed (G5–G6 usually 30 questions/90 minutes, sample). For G5–G6 students aiming for AMC8, the best combination is SASMO + AMC8 G1–15 mixed practice — SASMO builds modelling thinking, AMC8 builds speed.

7. G7+ Segment (A dominant): Summer

• For G7+, SASMO question types are already close to AMC8/10. CPA is no longer the main focus, but "modelling thinking" still helps with application problems (e.g., rate, concentration, work — drawing line diagrams is more stable than forcing equations).
• The main summer focus should be on AMC8/10. SASMO G7–8 past papers can be used for maintenance and as an Asia-Pacific credential supplement; there is no need to prepare separately.

V. Appendix: How to Practice the CPA Three Stages at Home (Parent-Executable Checklist)

Stage	Home Materials	Practice Sources
C (Concrete)	Counters/beans/Lego/ten-frame grids	Singapore system G1–G3 textbook exercises + SASMO G2–4 past papers
P (Pictorial)	Whiteboard + coloured markers (for colour-coded bar models)	Singapore system G2–G4 bar model specialisation + SASMO G3–6
A (Abstract)	Scratch paper + equation notebook	SASMO G5–8 + AMC8 G1–15

SASMO's true value is not in the "Asia-Pacific certificate" itself, but in the CPA methodology. Children who thoroughly practice bar models in G2–G6 will transition much more smoothly to Algebra in G7+ than those who only drill calculation workbooks — because "the ability to turn textual relationships into diagrams" is a prerequisite for setting up algebraic equations. A common mistake made by domestic families is to "jump straight to calculation drills in G2–G4, skipping C and P" — resulting in disastrous performance on G5 word problems and fractions, and taking much longer to catch up on CPA later.

Over the summer, if G2–G4 are just starting out, do not rush into SASMO past papers. Use counters + bar models to work through "sum-difference / multiples / fraction introduction" in three stages, then move on to past papers in August. For G5–G6 who already have a basic understanding of bar models, spend the summer deepening bar models for fractions/percentages/ratios + practicing 3–5 sets of SASMO G5–G6 past papers. Aiming for Gold (Top 5%) in April 2027 is an achievable target.

Final piece of advice: If your child says "I don't know how to do" a SASMO problem, do not rush to explain the equation. First ask, "Can you draw it?" If they can draw it, they can solve it. If they cannot, it means the first two stages of CPA haven't been mastered — it's not that they're bad at math.