Mental Math Strategies Every Student Should Know

1. Number Bonds (Making 10)

Number bonds are pairs of numbers that add up to a target - usually 10. Knowing these pairs instantly is the foundation of all mental addition and subtraction.

• The bonds to 10 are: 1+9, 2+8, 3+7, 4+6, 5+5. Memorise these until they are automatic.
• How to use them: To add 8 + 5, think "8 needs 2 to make 10, take 2 from 5, leaving 3. So 10 + 3 = 13."
• Extend to bonds of 20, 100, and 1,000. If you know 3 + 7 = 10, you know 30 + 70 = 100 and 300 + 700 = 1,000.

2. Doubles and Near Doubles

Doubles are easy to remember and give you a shortcut for nearby problems.

• Doubles facts: 6 + 6 = 12, 7 + 7 = 14, 8 + 8 = 16. Practise up to 20 + 20.
• Near doubles: 6 + 7 = double 6 plus 1 = 13. Or 15 + 16 = double 15 plus 1 = 31.
• Subtraction doubles: 14 – 7 = 7 (half of 14). This works for any even number.

3. Compensation (Rounding and Adjusting)

When a number is close to a "friendly" number (like 10, 20, 50, or 100), round it first, then adjust.

• Addition: 47 + 29 > think 47 + 30 = 77, then subtract 1 > 76.
• Subtraction: 83 – 19 > think 83 – 20 = 63, then add 1 > 64.
• Multiplication: 6 × 19 > think 6 × 20 = 120, then subtract 6 > 114.
• This strategy works best when one number ends in 8 or 9 (or 1 or 2 for subtraction).

4. Breaking Apart (Decomposition)

Split a hard problem into two or three easier ones using place value.

• Addition: 56 + 37 > (50 + 30) + (6 + 7) > 80 + 13 > 93.
• Multiplication: 7 × 14 > 7 × 10 + 7 × 4 > 70 + 28 > 98.
• Subtraction: 72 – 35 > 72 – 30 = 42, then 42 – 5 = 37.
• This strategy teaches children to think about numbers in terms of tens and ones, strengthening place value understanding.

5. Counting On and Counting Back

For small additions or subtractions, counting on from the larger number is the simplest strategy - especially for younger students.

• Counting on: 48 + 3 > start at 48, count 49, 50, 51. The answer is 51.
• Counting back: 63 – 4 > start at 63, count 62, 61, 60, 59. The answer is 59.
• Counting up (for subtraction): 52 – 47 > start at 47 and count up to 52: 48, 49, 50, 51, 52 > that is 5 jumps.
• Use a number line to visualise the jumps until the strategy becomes automatic.

6. Multiplication Mental Shortcuts

• ×2: Double the number. 2 × 37 = 74.
• ×4: Double twice. 4 × 16 > double 16 = 32 > double 32 = 64.
• ×5: Multiply by 10 then halve. 5 × 18 > 180 ÷ 2 = 90.
• ×9: Multiply by 10 then subtract the original. 9 × 7 > 70 – 7 = 63.
• ×11 (two digits): For a number like 11 × 23 > 2 _ 3, middle digit is 2+3=5 > 253.

How to Practice Mental Math Daily

• Number talks: Spend 5 minutes each day solving one problem mentally and discussing strategies. No pencils, no paper.
• Estimation jar: Fill a jar with objects. Estimate how many, then count. This builds number intuition.
• Car maths: Add up digits on number plates. Estimate distances. Calculate arrival times.
• Play games: Card games like "Make 24" or digital maths games provide thousands of micro-practice opportunities.
• Start easy, build up: Master strategies with small numbers before tackling two- and three-digit calculations.