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Four Operations: Fast & Accurate

Maths · Y4 OC Prep
Year 4 OC
Lesson Guide
Explanation
No calculators in the OC test — your head is the calculator, and shortcuts are its speed. Three power moves: ADD FRIENDLY (398 + 267 → 400 + 267 − 2 = 665), SUBTRACT BY COUNTING UP when numbers are close (703 − 598: gap is 2 + 103 = 105, no borrowing circus), and MULTIPLY BY SPLITTING (5 × 106 = 500 + 30 = 530 — a favourite OC-style multiplication!).
Your Turn
Speed run: 499 + 356, 902 − 895, 4 × 208. Check: 855, 7, 832.
Watch Out
Fix-up direction: if you ADDED 2 extra, take 2 away. Rushed fix-ups going the wrong way are the top mental-maths error.
Explanation
Bigger numbers bow to the same splitting idea. 7 × 36: split 36 into 30 + 6, giving 210 + 42 = 252. Division splits too — but into chunks the divider likes: 96 ÷ 4 = (80 + 16) ÷ 4 = 20 + 4 = 24. And learn the 25s trick: since four 25s make 100, 6 × 25 = 600 ÷ 4 = 150. OC time rewards whoever splits smartest.
Your Turn
Split and solve: 6 × 43, 84 ÷ 6, 8 × 25. Check: 258, 14, 200.
Watch Out
For division, split into chunks the divider FITS INTO (80 and 16 for ÷4) — splitting 96 as 90 + 6 makes ÷4 harder, not easier.
Explanation
OC style: 6 goats eat 18 kg of hay a week; 3 ponies also eat 18 kg. How much hay for 3 goats AND 6 ponies? The master plan: find ONE animal's share first. One goat: 18 ÷ 6 = 3 kg. One pony: 18 ÷ 3 = 6 kg. Now rebuild: 3 × 3 + 6 × 6 = 9 + 36 = 45 kg. 'Divide down to one, multiply up to many' — this unit-rate plan unlocks a whole family of OC questions.
Your Turn
5 pencils cost 60c. How much do 8 pencils cost? Check: one pencil 12c → 8 × 12 = 96c.
Watch Out
Don't compare group totals directly — 6 goats and 3 ponies eating the same 18 kg means each pony eats MORE, not the same.
Explanation
OC money questions make you shop cleverly. OC style: cat food comes as 500 g for $1.50 or 2 kg for $5 — buy EXACTLY 3 kg as cheaply as possible. Compare per-kilo prices: small box $3/kg, big box $2.50/kg — big is cheaper. Use it: one big box covers 2 kg for $5, leaving 1 kg = two small boxes = $3. Total $8. The word 'exactly' is the constraint — two big boxes would be 4 kg, too much!
Your Turn
Juice: 1 L for $2 or 3 L for $5. Cheapest way to exactly 5 L? Check: 3L + 1L + 1L = $5 + $4 = $9 (vs five 1L = $10).
Watch Out
'Exactly' forbids overshooting. Without it, overshooting with cheap big packs might win — read the constraint word.
Explanation
Arithmetic speed is built like fitness: short daily training. Five minutes of mixed questions every day beats an hour once a week. Two rules while you train: accuracy before speed (a fast wrong answer scores zero — speed grows naturally from correct repetition), and keep an error list — most students repeat the same three mistakes, and naming yours is how you stop them. Treat the exercise set below as your first timed drill: note your time, then beat it next week.
Your Turn
One-minute burst: 25 × 4, 640 ÷ 8, 397 + 46, 512 − 199, 7 × 15. Check: 100, 80, 443, 313, 105.
Watch Out
In drills, a wrong answer you understand beats a right answer you guessed. Always find out WHY an answer went wrong.
Step 1: Introduction
Step 1 of 5
The OC arithmetic toolkit Add friendly, fix up: 398 + 267 = 400 + 267 − 2 = 665 round to the nearest friendly number, then repair Subtract by counting up: 703 − 598 → 2 + 103 = 105 close numbers? find the gap, skip the borrowing Multiply by splitting: 5 × 106 = 5 × 100 + 5 × 6 = 530 break the awkward number into easy pieces These three shortcuts solve most OC arithmetic in your head.
Split, times-table, reassemble 7 × 36 = 7 × 30 + 7 × 6 = 210 + 42 = 252 96 ÷ 4 = (80 + 16) ÷ 4 = 20 + 4 = 24 6 × 25 = 6 × 100 ÷ 4 = 150 Split awkward numbers along place value (36 = 30 + 6), or split to friendly chunks (96 = 80 + 16, both divisible by 4). 25s trick: ×25 = ×100 ÷ 4. Four 25s make 100!
OC style: goats and ponies 🐐 6 goats eat 18 kg of hay per week. 🐴 3 ponies eat 18 kg of hay per week. How much hay for 3 goats and 6 ponies? Step 1 — find ONE animal's share (the unit rate): 1 goat: 18 ÷ 6 = 3 kg · 1 pony: 18 ÷ 3 = 6 kg Step 2 — rebuild the new group: 3 × 3 + 6 × 6 = 9 + 36 = 45 kg ✓ Divide down to ONE, multiply up to MANY. Works every time.
Cheapest way to exactly 3 kg small box 500 g for $1.50 = $3 per kg big box 2 kg for $5 = $2.50 per kg — cheaper! Need EXACTLY 3 kg, lowest price: Use the cheap big box: 2 kg ($5). Remaining: 1 kg. 1 kg = two 500 g boxes = $3. Total: $5 + $3 = $8 — check no cheaper combo exists! Big packs are usually cheaper per kg — but 'exactly' limits your choices.
Train like an athlete 🏃 Daily 5-minute drill beats weekly 1-hour cram. Ten mixed questions, timed, every day. Watch your time fall. Accuracy FIRST, speed second. A fast wrong answer scores zero. Slow-and-right becomes fast-and-right. Know your enemy: YOUR common errors. Keep an error list — most people repeat the same 3 mistakes. The exercises below are your first timed drill. Go!
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