Mental Maths Strategies
Build powerful mental maths skills using doubling, halving, and bridging through 10s and 100s to calculate quickly in your head.
Strategy 1: Doubling
Doubling means adding a number to itself. If you know your doubles, you can solve many problems faster. For example, 2 × 36 is the same as 36 + 36.
Quick Doubles
Double 15
30
Double 35
70
Double 48
96
Double 250
500
Tip: To double a two-digit number, double the tens and double the ones separately, then add. For example, double 37 = double 30 (60) + double 7 (14) = 74.
Strategy 2: Halving
Halving means dividing by 2, or finding half of a number. Halving is the opposite of doubling and is very useful for dividing and working with even numbers.
Halving in Steps
Example: Half of 86
Step 1: Half of 80 = 40
Step 2: Half of 6 = 3
Step 3: 40 + 3 = 43
Visual: Halving 64
Half of 64 is 32 because 32 + 32 = 64.
Strategy 3: Bridging Through 10s and 100s
Bridging means breaking a number into parts so you pass through a friendly number like 10, 100 or 1000. This makes adding and subtracting much easier.
Example: 47 + 36 (bridging through a ten)
Step 1: Start at 47. How far to the next ten? 47 + 3 = 50
Step 2: We used 3 of the 36, so we still need to add 36 − 3 = 33
Step 3: 50 + 33 = 83
Example: 263 + 58 (bridging through 100)
Step 1: 263 + 37 = 300 (bridge to 300)
Step 2: 58 − 37 = 21 left over
Step 3: 300 + 21 = 321
Strategy 4: Compensation (Round and Adjust)
Round one number to a friendly number, do the calculation, then adjust (add or subtract) to compensate.
Adding: 99 + 46
Round 99 up to 100.
100 + 46 = 146
We added 1 too many, so subtract 1.
Answer: 145
Subtracting: 532 − 198
Round 198 up to 200.
532 − 200 = 332
We subtracted 2 too many, so add 2.
Answer: 334
Key Vocabulary
Doubling
Adding a number to itself, or multiplying by 2.
Halving
Dividing by 2, or finding half of a number.
Bridging
Splitting a number so you pass through a friendly number (like 10, 100, 1000).
Compensation
Rounding to a friendly number, calculating, then adjusting the answer.
Worked Examples
Use doubling to solve 4 × 35.
Step 1: 4 × 35 = 2 × (2 × 35)
Step 2: Double 35 = 70
Step 3: Double 70 = 140
Answer: 140
Use bridging to solve 68 + 45.
Step 1: 68 + 2 = 70 (bridge to 70)
Step 2: 45 − 2 = 43 remaining
Step 3: 70 + 43 = 113
Answer: 113
Use compensation to solve 345 + 99.
Step 1: Round 99 up to 100.
Step 2: 345 + 100 = 445
Step 3: We added 1 too many, so 445 − 1 = 444
Answer: 444
Knowledge Check
Select the correct answer for each question.
Question 1
What is double 45?
Question 2
What is half of 74?
Question 3
Use bridging to solve 57 + 28. What is the answer?
Question 4
Use compensation to solve 256 + 99.
Question 5
Use doubling to solve 4 × 23.
Key Concepts Summary
- ●Doubling means multiplying by 2. Split into tens and ones to double big numbers.
- ●Halving means dividing by 2. Split into tens and ones to halve big numbers.
- ●Bridging means jumping to the next 10 or 100, then adding what is left over.
- ●Compensation means rounding to a friendly number, calculating, then adjusting.
- ●Choose the best strategy for each problem — there is often more than one way!