Tutor's Crash Course · P4 Singapore · Bar Modelling
Bar Modelling, Decoded
The closed set of templates + the decision rule. For Felix → Valen (P4).
The one idea that unlocks everything:
The bar IS the number. Length = quantity.
Draw a bar for each thing, label every part, read the answer off the bar.
Teach Valen one line: "Draw a bar for each thing, label it, read the answer off the bar."
1 · The Master Templates
Only 3 problem types, plus a units layer that sits on top. Pick the template first — the drawing is then just slotting numbers in.
| # | Template | When? | Signature words |
|---|
| A | Part–Whole | groups join / split | total, altogether, in all, left, remaining |
| B | Comparison | one thing more/less than another | more than, fewer than, as many as, difference, cost |
| C | Before–After | something changes partway | gave, lost, bought, spent, won, transferred, after |
| +D | Units layer | "x times" / fraction of an amount | twice, 3 times, as many, half, ⅓ of… |
D is NOT a 4th problem type — it's a layer on top of A, B or C (the "units" trick). This one fact removes the most confusion.
🗺️ The Classifier (what Valen learns to say out loud)
READ. Underline the numbers. Circle ONE action word.
joined / total / left → Part–Whole 1 bar, cut
more/less than, difference → Comparison 2 stacked bars
gave / spent / lost / after → Before–After draw twice
times / as many / fraction → add UNITS equal parts
2 · How to Draw Each One
APart–Whole
BComparison
CBefore–After
DUnits
A · Part–Whole
- Draw ONE long bar = the total.
- Cut it into segments = the parts. Label each.
- Unknown total? Add the parts. Unknown part? Total − known parts.
Ali has 45 stamps, Bala has 38. How many in all?
83 stamps · 45 + 38 = 83
B · Comparison
- Two bars, one above the other, left-aligned.
- The longer bar pokes out by the difference. Mark it.
A bag costs $45. A wallet costs $12 less. How much is the wallet?
← $12 less →
45 − 12 = 33
⭐ P4 classic — Sum + Difference
Two numbers add to 100. One is 20 more than the other. Find both.
← 100 →
2u = 100 − 20 = 80 → u = 40 (small) · big = 60
C · Before–After (the transfer model)
- Draw the bar for the START. Then an arrow / a second "after" bar.
- Show the changed piece being moved or crossed out.
- Golden rule: find what stayed the same (total? one person?) — that's your bridge.
Tom gave 8 marbles to Jerry. Tom now has 5 more than Jerry. How many more did Tom have at first?
Before
After (give 8 → Tom −8, Jerry +8)
Tom had 5 + 8 + 8 = 21 more at first
The "8 given" appears twice — lost by Tom, gained by Jerry. That's the 2X rule.
D · Units method (the master key)
Pick the smallest amount → call it 1 unit (1u).
Express every other quantity as a multiple of 1u.
Write one equation from the total / difference / after-relationship.
Solve for 1u → multiply to answer.
Ali and Bala have 120 stickers. Ali has 3× as many as Bala. How many each?
4u = 120
1u = 120 ÷ 4 = 30 → Bala = 30 · Ali = 90
3 · The Named Recipes (P4 exam traps)
Learnable rules, not luck. When Valen can name the recipe, he stops guessing.
① Sum + Difference — the #1 P4 model
"Two things total X, one is Y more." → 2u = X − Y, each = u. Drill this to reflex.
② "More than the rest"
The "more" is added to the remainder, not the whole. Draw carefully — this one silently trips kids.
③ Constant difference
Both quantities change by the same amount → the difference never changes. That's your Before–After bridge.
④ The 2X transfer rule
"Gave X to him" → X appears twice (lost by one, gained by other). Difference shifts by 2X.
⑤ Fraction of the remaining amount
"Spent ⅓ of what was left" → re-split the remainder bar, not the original.
4 · Practice — Classify Quick Quiz
Read it, tap the template. This trains the decision rule itself.
5 · 4-Session Plan for Valen
SESSION 1 · Foundation + Part–Whole
Bar = number. Part–Whole only. 10 warm, 5 unknown-total, 5 unknown-part. He can name the template at the end.
SESSION 2 · Comparison + Units + Sum&Diff
Comparison bars, more/less/diff. Introduce 1u with simple "3× as many" totals. Drill Sum + Difference until automatic.
SESSION 3 · Before–After
Simple gave/spent/lost transfers, two-drawing habit. Teach the 2X rule explicitly. Pure reasoning, no units yet.
SESSION 4 · Mixed bag + classify
15 past-paper sums. He must write the template name
before solving. Debrief misfires: classified wrong? drew wrong? computed wrong? → tells you what to re-teach.
6 · Where to Get the Worksheets