Quick Math · grades 4–9
Mental Math.
Fast arithmetic with logic, not memorization. Short videos, animated lessons, and instant practice — built on four simple ideas: think left-to-right, break numbers apart, use friendly numbers, and count the gap.
Foundations
The two habits every fast calculator shares.
Addition
Three logical ways to add anything in your head.
- A1
Add the big parts first
Split both numbers into tens and ones, add each, recombine: 58 + 34 → 80 + 12 → 92.
- A2
Add in friendly chunks
Keep one number whole and add the other a chunk at a time: 145 + 38 → 175 → 183.
- A3
Round and fix
Round to a friendly number, add the easy way, then give back the difference: 297 + 58 → 357 − 2.
Subtraction
Three logical ways to subtract anything in your head.
Multiplication
Break numbers apart, and the shortcuts that lean on round numbers.
- M1
Break it apart
The master move (distributive law): 7 × 14 → 7×10 + 7×4 → 70 + 28 = 98.
- M2
×10, ×5, ×50, ×25
Shortcuts from place value and halving: ×5 = ×10 ÷ 2, ×25 = ×100 ÷ 4.
- M3
×9 and ×11
×9 = ×10 − itself; the famous two-digit ×11 middle-digit pattern.
- M4
Double and halve
Reshape a product into an easy one: 16 × 25 → 8 × 50 → 4 × 100 = 400.
- M5
Squaring & close pairs
Square anything ending in 5 instantly; multiply close pairs with 10² − 2².
Division
Un-multiply: break the dividend, halve, factor, and read the radar.
- D1
Break the dividend
Division is un-multiplying: 96 ÷ 4 → 80÷4 + 16÷4 → 20 + 4 = 24.
- D2
Halving & ×5 tricks
÷2, ÷4, ÷8 are just halving; ÷5 = ×2 ÷ 10.
- D3
Factor the divisor
Two easy divisions beat one hard one: ÷6 = ÷2 ÷3, ÷12 = ÷3 ÷4.
- D4
Divisibility radar
Quick rules for 2, 3, 5, 6, 9, 10 — know it divides before you start.
Capstone
Pick the best method, then race the clock.
Level Up · grades 7–9
Bigger numbers, sharper tools — building on everything so far.
- L1
Two-digit × two-digit
The cross method: 23 × 47 → 800 + 140 + 120 + 21 = 1081.
- L2
Square any number
Anchor at a ten: 47² → 50 × 44 + 3² = 2209.
- L3
×99 and ×101
Lean on 100: 47 × 99 → 4700 − 47 = 4653.
- L4
Percent of a number
Build from 10% and 5%: 15% of 240 → 24 + 12 = 36.
- L5
Divisible by 7 or 11?
The alternating-sum test for 11 and the double-and-subtract test for 7.
- L6
Estimate & sanity-check
Round, multiply, and catch silly mistakes: 38 × 42 ≈ 1600.
Decimals
Add, subtract, multiply, and divide decimals — the point is just a guide.
- DEC1
Add decimals
Line up the points; add whole parts and decimal parts: 3.4 + 2.8 → 6.2.
- DEC2
Subtract decimals
Take away the whole part, then the decimal part: 6.2 − 2.8 → 3.4.
- DEC3
Multiply decimals
Ignore the point, multiply, then count the places: 0.3 × 0.4 → 0.12.
- DEC4
Divide decimals
Shift both to make the divisor whole: 4.8 ÷ 0.6 → 48 ÷ 6 = 8.