⚡ Mental Math Strategies 🧠

Strong mental maths isn't magic — it's a set of powerful strategies that make calculations faster, safer and more reliable. Master these techniques and you'll be able to solve problems in your head, spot mistakes instantly, and tackle any exam question with confidence!

🔧 Partitioning
76 + 48 → (70+40) + (6+8) = 110 + 14 = 124
🎯 Rounding & Adjusting
99 + 64 → 100 + 64 − 1 = 163
🪞 Near Doubles
38 + 39 → 2 × 38 + 1 = 77

📋 BIDMAS — Order of Operations:

Always do operations in this order — never left to right!

Brackets Indices (powers & roots) Division Multiplication Addition Subtraction

÷ and × have equal priority — do them left to right. Same for + and −.

⚡ The Golden Rules:

📝 Worked Examples

Study each strategy — then try the drag exercises!

Example 1: BIDMAS — Order of Operations

Question: Work out (a) 3 + 4 × 2   (b) (5 + 3) × 4   (c) 20 − 3 × 4

(a) 3 + 4 × 2: Multiply first → 3 + 8 = 11   ✗ Wrong way: (3+4) × 2 = 14
(b) (5 + 3) × 4: Brackets first → 8 × 4 = 32
(c) 20 − 3 × 4: Multiply first → 20 − 12 = 8

Key rule: Multiplication and division ALWAYS before addition and subtraction — unless there are brackets!

Example 2: Partitioning and Rounding & Adjusting

Question: Calculate (a) 67 + 48 using partitioning   (b) 99 + 47 using rounding & adjusting

(a) 67 + 48: Split → (60 + 40) + (7 + 8) = 100 + 15 = 115
(b) 99 + 47: Round 99 up to 100 → 100 + 47 = 147, then subtract 1 → 146

Why? Because 99 = 100 − 1, so adding 99 is the same as adding 100 then taking away 1.

Example 3: Estimation and Checking

Question: Estimate 312 + 489, then calculate exactly.

Estimate: Round to nearest 100 → 300 + 500 = 800
Exact: 312 + 489 = (300 + 400) + (12 + 89) = 700 + 101 = 801
Check: 801 is very close to 800 ✓ — our estimate confirms the answer is reasonable.

Example 4: Using Known Facts to Derive New Facts

Question: Use the fact that 6 × 8 = 48 to work out (a) 60 × 8   (b) 600 × 8   (c) 6 × 80

(a) 60 × 8 = 6 × 10 × 8 = 48 × 10 = 480
(b) 600 × 8 = 6 × 100 × 8 = 48 × 100 = 4,800
(c) 6 × 80 = 6 × 8 × 10 = 48 × 10 = 480

Pattern: Every extra zero multiplies the answer by 10.

🔬 BIDMAS Expression Explorer

See how BIDMAS changes the answer! Cycle through each expression and spot which operation must happen first.

Expression 1 of 5

🧩 Drag 1: BIDMAS Order of Operations

Remember: multiplication before addition! Work out 3 + 4 × 2 correctly using BIDMAS.

11
14
18
3 + 4 × 2 =

(Hint: Multiply first → 4 × 2 = 8  |  Then add → 3 + 8 = ?)

🧩 Drag 2: Estimation by Rounding

Round each number to the nearest 100, then add. Estimate 347 + 589!

800
900
1000
347 + 589 ≈

(Hint: 347 rounds to 300, 589 rounds to 600  |  300 + 600 = ?)

🧩 Drag 3: Partitioning

Split 76 + 48 into tens and ones. Find the tens part first: 70 + 40 = ?

100
110
120
70 + 40 =

(Then add the ones: 110 + 6 + 8 = 110 + 14 = 124 ✓)

🧩 Drag 4: Rounding & Adjusting

Use rounding: 99 + 47 = 100 + 47, then adjust. What is the final answer?

144
146
148
99 + 47 =

(Hint: 100 + 47 = 147  |  We added 1 too many → 147 − 1 = ?)

🧩 Drag 5: Checking with Inverse Operations

If 24 × 6 = 144, which calculation can you use to check the answer? Drag the correct check!

144÷6
144×6
144+6
Check 24 × 6 = 144 using:

(The inverse of multiplication is division)

🧩 Drag 6: Known Facts → New Facts

If 7 × 8 = 56, use this fact to work out 700 × 8. Just multiply by 100!

560
5600
56000
700 × 8 =

(Hint: 7 × 8 = 56  |  700 = 7 × 100  |  56 × 100 = ?)

📝 Practice Questions

Show all your working and use the best mental strategy for each question!

  1. Work out 3 + 4 × 2 using BIDMAS.
  2. Work out (5 + 3) × 4 using BIDMAS.
  3. Work out 20 − 3 × 4.
  4. Round 347 to the nearest 100.
  5. Round 2,650 to the nearest 1,000.
  6. Estimate 49 + 63 by rounding to the nearest 10.
  7. Estimate 312 + 489 by rounding to the nearest 100.
  8. Use partitioning to find 76 + 48.
  9. Use rounding and adjusting to find 99 + 64.
  10. Use near doubles to find 38 + 39.
  11. If 9 × 7 = 63, write down two related division facts.
  12. Use a known fact to find 80 × 60.  (Hint: use 8 × 6)
  13. Work out 5 + 3² × 2.  (Remember: indices before multiplication!)
  14. Use compensation to find 64 − 29.  (Hint: subtract 30, then add 1)
  15. Estimate 51 × 19 by rounding both numbers to the nearest 10.
  16. Work out 2 × (14 − 6) + 3².
  17. If 456 + 237 = 693, write the inverse calculation that checks this.
  18. Estimate 4.8 × 3.2 by rounding both to the nearest whole number.
  19. Work out 100 − (3 × 4 + 8).
  20. Use partitioning to find 134 + 257.
  1. 11  (4 × 2 = 8, then 3 + 8)
  2. 32  (brackets first: 5+3=8, then 8×4)
  3. 8  (3 × 4 = 12, then 20−12)
  4. 300
  5. 3,000
  6. 110  (50 + 60)
  7. 800  (300 + 500)
  8. 124  (70+40=110, 6+8=14, 110+14)
  9. 163  (100+64=164, −1=163)
  10. 77  (2×38+1 = 76+1)
  11. 63 ÷ 9 = 7  and  63 ÷ 7 = 9
  12. 4,800  (8×6=48, ×100=4,800)
  13. 23  (3²=9, 9×2=18, 5+18)
  14. 35  (64−30=34, +1=35)
  15. ≈ 1,000  (50 × 20)
  16. 25  (14−6=8, 2×8=16, 3²=9, 16+9)
  17. 693 − 237 = 456  (or 693 − 456 = 237)
  18. ≈ 15  (5 × 3)
  19. 80  (3×4=12, 12+8=20, 100−20)
  20. 391  (100+200=300, 30+50=80, 4+7=11, 300+80+11)

🔥 Challenge: Word Problems

Show all your working — use mental strategies wherever you can!

  1. A baker makes 4 trays of cookies. Each tray has 6 rows with 8 cookies in each row. Estimate, then calculate the exact total number of cookies.
  2. Use BIDMAS to work out: 50 − 4 × (3 + 2).
  3. A school trip costs £15 per pupil. There are 29 pupils. Estimate the total cost, then calculate the exact amount.
  4. Work out 3² + 4² and explain which operation you carry out first.
  5. A shop has 198 apples and receives a delivery of 304 more. Use rounding to estimate the total, then find the exact answer.
  6. Use rounding and adjusting to find 63 − 28.
  7. A rectangle has a length of 42 cm and a width of 19 cm. Estimate the area, then calculate exactly.
  8. If 36 × 25 = 900, use this known fact to find 360 × 25.
  9. Work out 2 × (14 − 6) + 3². Show each step using BIDMAS.
  10. Estimate 68 × 52 by rounding to the nearest 10. Then calculate the exact answer.
  1. Estimate: 4×6×8=192. Exact: 192  (4×6=24, 24×8=192)
  2. 30  (brackets: 3+2=5, then 4×5=20, then 50−20=30)
  3. Estimate: £15×30=£450. Exact: £435  (£15×29 = £15×30−£15 = £450−£15)
  4. 25  (indices first: 3²=9, 4²=16, then add: 9+16=25)
  5. Estimate: 200+300=500. Exact: 502
  6. 35  (63−30=33, +2=35 — we subtracted 2 extra so add 2 back)
  7. Estimate: 40×20=800 cm². Exact: 798 cm²  (42×20=840, −42=798)
  8. 9,000  (360=36×10, so 360×25 = 900×10)
  9. 25  (brackets: 14−6=8; indices: 3²=9; multiply: 2×8=16; add: 16+9=25)
  10. Estimate: 70×50=3,500. Exact: 3,536  (68×50=3,400, 68×2=136, 3,400+136)
Created by Mr Josh