Non-Calculator Paper Strategies

Thriving Without Technology

Paper 1 (Non-Calculator) tests your mental arithmetic, number sense, and mathematical reasoning. Here's how to excel.

Mental Arithmetic Essentials

Times Tables to 12×12

These must be instant. If you're not 100% confident:

• Apps like Times Tables Rock Stars
• Practice for 5 minutes daily
• Focus on the tricky ones: 7s, 8s, 9s

Powers and Roots to Know:

Powers of 2	Powers of 3	Powers of 5	Square roots
$2^1 = 2$	$3^1 = 3$	$5^1 = 5$	$\sqrt{4} = 2$
$2^2 = 4$	$3^2 = 9$	$5^2 = 25$	$\sqrt{9} = 3$
$2^3 = 8$	$3^3 = 27$	$5^3 = 125$	$\sqrt{16} = 4$
$2^4 = 16$	$3^4 = 81$	$5^4 = 625$	$\sqrt{25} = 5$
$2^5 = 32$	$3^5 = 243$		$\sqrt{36} = 6$
$2^{10} = 1024$			$\sqrt{49} = 7$

Prime Numbers to 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Multiplication Strategies

Grid Method for 2-digit × 2-digit:

$23 \times 47$

	40	7
20	800	140
3	120	21

$= 800 + 140 + 120 + 21 = 1081$

Multiplying by 5: Multiply by 10, then halve $48 \times 5 = 480 \div 2 = 240$

Multiplying by 25: Multiply by 100, then divide by 4 $36 \times 25 = 3600 \div 4 = 900$

Multiplying by 9: Multiply by 10, subtract the original $37 \times 9 = 370 - 37 = 333$

Division Strategies

Short Division (Bus Stop): Keep it neat, write remainders small, carry properly

Dividing by 5: Double and divide by 10 $135 \div 5 = 270 \div 10 = 27$

Dividing by 25: Multiply by 4 and divide by 100 $175 \div 25 = 700 \div 100 = 7$

Fraction Calculations

Adding/Subtracting:

1. Find the LCM of denominators
2. Convert each fraction
3. Add/subtract numerators
4. Simplify if needed

$\frac{2}{3} + \frac{3}{4} = \frac{8}{12} + \frac{9}{12} = \frac{17}{12} = 1\frac{5}{12}$

Multiplying: Multiply numerators, multiply denominators, simplify

$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Dividing (KFC — Keep, Flip, Change): Keep the first, flip the second, change to multiplication

$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

Percentage Calculations

Finding 10%: Divide by 10 Finding 1%: Divide by 100 Build up from these:

Find 17.5% of £240

10% = £24 5% = £12 2.5% = £6

17.5% = £24 + £12 + £6 = £42

Percentage increase/decrease: Original × multiplier

• Increase by 20%: × 1.2
• Decrease by 15%: × 0.85
• Increase by 5%: × 1.05

Checking Your Work

Inverse Operations:

• Did subtraction? Add to check
• Did division? Multiply to check

Estimation: Before detailed calculation, estimate the rough answer

Digit Sum (for divisibility by 9): Add the digits; if sum is divisible by 9, so is the original

Layout Matters

On non-calculator papers:

• Write clearly — examiners can't give marks for work they can't read
• Line up place values in column addition/subtraction
• Show all carrying/borrowing marks
• Don't squeeze too much into small spaces