Developing IP-Level Problem-Solving Habits
Download printable cheat-sheet (CC-BY 4.0)20 May 2025, 00:00 Z
“Real understanding means you can spot a pattern before the teacher points it out.”
You open your maths file at 10 pm, red pen ready, and stare at a page of un-done kinematics.
What one thing can you do in the next two minutes that improves the rest of the night?
This article answers that question seven times.
1 The IP Track at a Glance
- Length & goal Six years straight from Sec 1 to JC 2 (or IB Yr 6 / NUS High Yr 6).
- Skip an exam No O-Levels in Year 4; final credential is A-Level, IB Diploma or NUS High Diploma.
- Who gets in Top ≈ 10 % of each PSLE cohort—about four thousand students a year.
- Style More research and CCAs, but the syllabus is wider and moves faster.
The workload feels abstract only until the first common test hits.
The seven habits below are concrete guard-rails.
2 Seven Habits → Seven Micro-Routines
| Habit | Why it helps | 2-minute micro-routine | What it looks like |
| Spot Patterns | Cuts guess-work in algebra, graphs or titrations. | Dot & colour pass – put a ● next to anything that repeats ≥ 3× and give each recurring item its own highlighter colour. | Chem: three pink dots on identical 25.00 cm³ readings. |
| Build a Model | Turns a word wall into one clean diagram or equation. | One-sketch rule – draw one picture (strip diagram, free-body, flow chart) on a Post-it before writing any algebra. | Physics: sketch forces on a block before writing F = ma. |
| Break It Down | Keeps big problems from feeling overwhelming. | 1-3-5 break-plan – jot 1 recall, 3 atomic steps, then spend 5 min on step 1 only. | Essay: 1 thesis, 3 points, 5 min to draft intro. |
| Self-Check | Catches sign slips and unit mix-ups early. | Traffic-light margin – every 3 lines mark ✓ (green), ? (amber) or × (red). Stop at × and fix. | Math: find a sign error after × and redo two lines, not two pages. |
| Connect the Dots | Recycles tricks across subjects. | Analogy hunt – name two earlier topics with the same shape, then state one difference. | Bio: enzyme-rate curve vs physics resistance curve. |
| Big Picture First | Stops premature symbol-chasing. | Headline test – write the answer you expect in plain English first; replace words with symbols only when needed. | “Distance s after 3 s given u = 4 m/s, a = −1 m/s².” |
| Shuffle Practice | Builds recall under exam scramble. | Tiny interleave – pick one anchor topic and slip in 1–2 unrelated problems every 15 min. | Worksheet: Q1-4 kinematics, Q5 chem equilibrium, Q6 kinematics. |
3 Do-Along Worked Examples
3.1 Maths – Telescoping Series
Try first
Find \(Sₙ = Σₖ₌₁ⁿ 1∕[k(k+1)]\). Write the first three partial sums before reading the solution.
Solution
- Dot & colour – highlight the repeated 1 in the numerators.
- One-sketch – split each term: \(1/k − 1/(k+1)\).
- Terms cancel domino-style; only first and last survive.
- Result: \(1 − 1∕(n+1)\).
3.2 Physics – Same Question, Two Models
A stone is flicked up at 15 m/s. When does it return to the hand?
Pause & predict before checking the answers.
Model 1 (Kinematics) Solve \(0 = ut + 0.5at²\) → 3.1 s.
Model 2 (Energy) Use \(½mv² = mgh\). Find peak time, double it → 3.1 s.
3.3 Chemistry – Haber Pressure Trick
Self-Check Predict argon’s effect, then read.
Adding argon at constant pressure hardly shifts \(N₂ + 3H₂ ⇌ 2NH₃\): all partial pressures drop together, so the forward-to-back ratio stays the same.
4 Subject-Rotating Vignettes
| Habit | Maths | Physics | Lit ⁄ Humanities |
| Break It Down | Prove a vector identity via two lemmas. | Split airplane drag-lift Q into horizontal vs vertical tables. | Split a 12-mark DBQ into provenance ⁄ message ⁄ context. |
| Self-Check | After each derivative, swap x→0 to sanity-check. | After plugging numbers, estimate magnitude: ~10 m or 10 km? | Cover the quote; can you still paraphrase tone? |
Switching subjects shows the habit is general, not STEM-only.
5 Mini-Failure Story
Jia Hui lost 5 marks for writing m/s as a unit for acceleration.
She now writes the unit before the value, then back-fills numbers—traffic-light margin guards the habit.
6 7-Day Habit Sprint
| Day | Focus | Mission (≤ 15 min) |
| 1 | Traffic-light margin | Use it on tonight’s maths homework. |
| 2 | One-sketch rule | Apply to tomorrow’s chem worksheet. |
| 3 | Dot & colour pass | Re-annotate yesterday’s physics notes. |
| 4 | Headline test | Summarise an English essay before drafting. |
| 5 | Tiny interleave | Mix 2 bio MCQs into a math drill. |
| 6 | Analogy hunt | Link today’s graph to two past topics. |
| 7 | 1-3-5 break-plan | Plan weekend revision, photograph your sticky notes. |
Tick each box, post a pic to your class chat, tag a friend to try the next day.
7 Daily & Weekly Blueprint
- Weeknight micro-blocks 2 × 45 min problem sets + 15 min habit review.
- Weekend long block 3 h mix: past paper, CCA, rest.
- Journal in 30 s Habit used | snag point | tweak.
- Shuffle rule No two sessions in a row on the same subject.
8 Starter Toolkit (quick-demo links)
| Need | Free tool + setting | Habit reinforced |
| Graphs & motion | Desmos with Sliders template | Big Picture + Build Model |
| Flashcards | Anki + Cloze Overlapper add-on | Shuffle Practice |
| Past papers | TestPapersFree filter “common errors” | Self-Check |
9 Simple Practice Loop
- Pick one habit for the session.
- Work a mixed set.
- Journal the snag and the fix.
- Teach a friend before bedtime.
- Revisit the same set after 1, 7 and 21 days.
Small loops, spun many times, beat heroic overnight crams.
10 Read More
- How to Solve It — George Pólya
- Mathematical Problem Solving — Alan Schoenfeld
- Peer Instruction — Eric Mazur
