Paper 1 is coming. One hour thirty minutes. Eighty marks available. And absolutely no calculator allowed.
I'm Aadam, and I've been tutoring GCSE students for over five years at SHLC. Here's what consistently surprises students: Paper 1 (non calculator) is where the most marks are lost, not because it's harder, but because students have become so dependent on calculators that basic mental arithmetic feels impossible under pressure.
Research shows that students often find the time pressure worse on non calculator papers compared to calculator papers. They get bogged down in lengthy calculations and lose track of time. But Paper 1 accounts for one third of your total marks, making it absolutely critical to master.
In this guide, I'm revealing the ten essential non calculator skills you must have automatic before your mocks, why each one matters, and exactly how to build fluency.
Why Non-Calculator Skills Matter
Let's be clear about what's at stake. Paper 1 is worth 80 marks out of 240 total. That's 33.3% of your entire GCSE Maths grade. If you struggle on Paper 1 through weak mental arithmetic, you're potentially losing 20, 30, even 40 marks.
Remember: each grade improvement is worth around £23,000 in lifetime earnings. Paper 1 performance directly affects which grade you achieve.
Research also shows that strong mental maths develops number sense and logical thinking skills that benefit all areas of mathematics. Students who can manipulate numbers mentally spot patterns faster and make fewer errors on calculator papers too.
Skill 1: Long Multiplication and Division
Why it's tested on Paper 1: You can't punch 327 × 48 into a calculator, so examiners test whether you can multiply large numbers by hand using column methods.
What you must master:
- Multiplying any two numbers using the column method (including decimals)
- Long division with remainders and decimal answers
- Checking answers by estimation
Common mistakes:
- Misaligning columns when multiplying decimals
- Forgetting to carry digits
- Not showing working clearly
- Dividing the wrong way around
How to build fluency: Practice 5-10 long multiplication and division problems daily until the method is automatic. Use Corbett Maths 5-a-Day Foundation Plus which regularly includes these calculations.
Start with whole numbers, then progress to decimals. The method is identical, you just need to count decimal places carefully.
Check your answers by estimation: 327 × 48 should be roughly 300 × 50 = 15,000. If your answer is 5,000, something's wrong.
Time saving tip: Use the area model for multiplication if column method feels unclear. Break numbers into parts and multiply each part, then add results.
Skill 2: Fraction Arithmetic (All Four Operations)
Why it's tested on Paper 1: Calculators can handle fractions, so Paper 1 specifically tests whether you can add, subtract, multiply and divide fractions without digital help.
Research shows fractions are the number one topic students struggle with on non calculator papers, with over 40% losing marks on basic fraction operations.
What you must master:
- Adding/subtracting fractions (finding common denominators)
- Multiplying fractions (numerators × numerators, denominators × denominators)
- Dividing fractions (keep, change, flip method)
- Simplifying fractions fully
- Converting between mixed numbers and improper fractions
- Finding fractions of amounts
Common mistakes:
- Adding fractions without common denominator (1/3 + 1/4 ≠ 2/7)
- Multiplying denominators when adding
- Not simplifying final answers
- Mixing up multiplication and division methods
How to build fluency: Create fraction flashcards and drill them daily:
- 1/2 + 1/3 = ?
- 2/5 × 3/4 = ?
- 3/4 ÷ 2/3 = ?
Practice finding common denominators mentally for common fractions (halves, thirds, quarters, fifths, sixths, eighths, tenths).
Use Maths Genie fraction topics to work systematically through each operation type.
Time saving tip: Memorise equivalent fractions: 1/2 = 2/4 = 3/6 = 5/10. When you see 1/2 + 3/10, immediately convert to 5/10 + 3/10 = 8/10 = 4/5. No written working needed for common denominators.
Skill 3: Percentage Calculations (Without Calculator)
Why it's tested on Paper 1: Percentages test proportional reasoning. Paper 1 questions specifically use percentages that can be calculated mentally or with simple methods.
What you must master:
- Finding 10%, 50%, 25% of amounts mentally
- Finding any percentage using building blocks (e.g., 15% = 10% + 5%)
- Percentage increase/decrease
- Expressing one amount as a percentage of another
- Reverse percentages
The mental shortcuts you need:
- 10% → divide by 10
- 50% → divide by 2
- 25% → divide by 4
- 1% → divide by 100
- 5% → find 10% then halve it
- 15% → find 10% then add 5%
Common mistakes:
- Using wrong base for percentage change
- Calculating 20% by doing ÷ 20 instead of finding 10% × 2
- Not converting percentages to decimals when needed
How to build fluency: Practice finding these percentages of common amounts:
- 15% of £80
- 35% of 200
- 12% of £250
Break every percentage into building blocks: 35% = 10% + 10% + 10% + 5% 12% = 10% + 1% + 1%
Drill reverse percentages specifically, as these cause most errors: "A price after 20% discount is £64. What was the original price?" Think: £64 = 80% of original. So 10% = £8. Therefore 100% = £80.
Skill 4: Simplifying Fractions and Ratios
Why it's tested on Paper 1: Calculators can simplify these, so Paper 1 tests whether you can find highest common factors and simplify without digital help.
What you must master:
- Finding highest common factor (HCF) of two numbers
- Simplifying fractions to lowest terms
- Simplifying ratios to lowest terms
- Converting ratios to fractions
- Sharing amounts in given ratios
Common mistakes:
- Not simplifying fully (writing 4:6 instead of 2:3)
- Only dividing numerator when simplifying fractions
- Missing common factors beyond obvious ones
How to build fluency: Learn to spot common factors quickly:
- Even numbers → divide by 2
- Numbers ending in 5 or 0 → divide by 5
- If digits sum to multiple of 3 → divide by 3
Practice prime factorisation for finding HCF: 24 = 2³ × 3 36 = 2² × 3² HCF = 2² × 3 = 12
For ratios, divide all parts by the same number repeatedly until no common factor remains.
Use Physics and Maths Tutor to find every past paper question on simplifying fractions and ratios.
Skill 5: Working with Indices (Powers and Roots)
Why it's tested on Paper 1: Examiners can test index laws with neat numbers that don't require calculators, revealing whether you truly understand how powers work.
What you must master:
- Calculating squares up to 15²
- Calculating cubes: 2³, 3³, 4³, 5³, 10³
- Square roots of perfect squares
- Cube roots of perfect cubes
- Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ
- Index laws: aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- Index laws: (aᵐ)ⁿ = aᵐⁿ
- Negative indices: a⁻ⁿ = 1/aⁿ
- Fractional indices: a^(1/2) = √a, a^(1/3) = ³√a
Common mistakes:
- Adding indices when multiplying (thinking 2³ × 2⁴ = 2¹²)
- Not knowing squares beyond 12²
- Mixing up square roots and cube roots
How to build fluency: Memorise perfect squares up to 15²:
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
Memorise cubes:
2³ = 8
3³ = 27
4³ = 64
5³ = 125
10³ = 1000
Create index law flashcards and test yourself daily until automatic.
For fractional indices, remember: the denominator is the root, the numerator is the power. 8^(2/3) = (³√8)² = 2² = 4
Skill 6: Standard Form Without Calculator
Why it's tested on Paper 1: Standard form tests understanding of powers of 10 and place value. Paper 1 uses manageable numbers that don't require calculator manipulation.
What you must master:
- Converting ordinary numbers to standard form
- Converting standard form to ordinary numbers
- Multiplying standard form numbers
- Dividing standard form numbers
- Adding/subtracting standard form (requires same power of 10)
Common mistakes:
- Writing 340 as 340 × 10⁰ instead of 3.4 × 10²
- Forgetting to adjust power when moving decimal point
- Adding indices when multiplying numbers (not just the powers)
How to build fluency: Remember: standard form is a × 10ⁿ where 1 ≤ a < 10
To convert 45000 to standard form:
- Move decimal 4 places left: 4.5
- Each move left adds 1 to the power: 10⁴
- Answer: 4.5 × 10⁴
To multiply in standard form: (3 × 10⁴) × (2 × 10⁵) = (3 × 2) × (10⁴ × 10⁵) = 6 × 10⁹
Practice with SHLC past papers which include worked solutions showing every step clearly.
Skill 7: Mental Arithmetic and Estimation
Why it's tested throughout Paper 1: Every calculation requires either exact mental arithmetic or estimation to check reasonableness of answers.
What you must master:
- Adding/subtracting mentally with numbers up to 1000
- Multiplying single digits instantly (times tables to 12 × 12)
- Dividing two digit numbers mentally
- Rounding to significant figures and decimal places
- Estimating calculations before working them out
Times tables you MUST know instantly: All times tables from 2 × 2 to 12 × 12 without thinking. If you pause on 7 × 8, you're losing time throughout Paper 1.
Check out my guide on mastering times tables in hours for a systematic approach to building fluency.
Estimation technique: Round numbers to 1 significant figure before calculating: 327 × 48 ≈ 300 × 50 = 15,000
This lets you spot errors. If your actual calculation gives 1,500, you know something's wrong.
How to build fluency: Use Corbett Maths 5-a-Day Numeracy questions daily. These specifically target mental calculation skills.
Practice mental addition of three digit numbers by breaking into parts: 387 + 245 = (300 + 200) + (80 + 40) + (7 + 5) = 500 + 120 + 12 = 632
Skill 8: Tree Diagrams With Fractions
Why it's tested on Paper 1: Tree diagrams require multiplying and adding fractions. They test both probability understanding and fraction arithmetic simultaneously, making them perfect for non calculator assessment.
What you must master:
- Drawing tree diagrams systematically
- Multiplying along branches (combined probabilities)
- Adding across outcomes (total probability of event)
- Working with fractions throughout
- Simplifying final probability answers
Common mistakes:
- Adding probabilities when should multiply
- Multiplying when should add
- Not simplifying final answers
- Branches not summing to 1
How to build fluency: Remember the rules:
- AND means multiply (probability of A AND B)
- OR means add (probability of A OR B)
All branches at each stage must sum to 1. Use this to check work: If first outcome is 2/5, second outcome must be 3/5.
Practice tree diagrams with replacement and without replacement. Paper 1 typically includes at least one tree diagram question.
Use my digital revision planner to track whether you're confident with tree diagrams (green), improving (amber), or still struggling (red).
Skill 9: Algebraic Manipulation (Expanding, Factorising, Simplifying)
Why it's tested on Paper 1: Basic algebra doesn't require calculators. Paper 1 tests whether you can manipulate algebraic expressions fluently.
What you must master:
- Collecting like terms
- Multiplying terms (3a × 4b = 12ab)
- Expanding single brackets: 3(2x + 5) = 6x + 15
- Expanding double brackets: (x + 3)(x + 5) = x² + 8x + 15
- Factorising expressions: 6x + 9 = 3(2x + 3)
- Factorising quadratics: x² + 5x + 6 = (x + 2)(x + 3)
Common mistakes:
- Trying to simplify unlike terms (2a + 3b ≠ 5ab)
- Sign errors when expanding brackets with negatives
- Not fully factorising (taking out 2 when could take out 4)
How to build fluency: Practice expanding brackets with grid method initially:
x +3
x x² +3x
+5 +5x +15
Sum all cells: x² + 3x + 5x + 15 = x² + 8x + 15
For factorising quadratics, find two numbers that multiply to give c and add to give b in x² + bx + c.
x² + 7x + 12: need two numbers that multiply to 12 and add to 7. Factors of 12: 1×12, 2×6, 3×4 3 + 4 = 7 ✓ Answer: (x + 3)(x + 4)
Skill 10: Exact Answers (Surds and π)
Why it's tested on Paper 1: When you can't use a calculator, questions often require exact answers in terms of surds or π rather than decimal approximations.
What you must master:
- Simplifying surds: √50 = √(25×2) = 5√2
- Adding/subtracting surds: 3√5 + 2√5 = 5√5
- Multiplying surds: √3 × √5 = √15
- Rationalising denominators: 1/√2 = √2/2
- Leaving answers in terms of π
- Calculating with π: 2πr, πr², 4πr²
Common mistakes:
- Trying to add unlike surds (√2 + √3 ≠ √5)
- Not simplifying surds fully
- Giving decimal approximations when exact answer required
- Using 3.14 instead of π symbol
How to build fluency: Learn perfect squares to identify simplifiable surds:
√4 = 2, √9 = 3, √16 = 4, √25 = 5
√36 = 6, √49 = 7, √64 = 8, √81 = 9
√100 = 10, √121 = 11, √144 = 12
To simplify √72: 72 = 36 × 2 √72 = √(36×2) = 6√2
For circle questions, always leave answer with π unless told to use a value: Area = πr² not 3.14r²
Systematic Practice Strategy
Knowing which skills matter is useless without systematic practice. Here's the method I use with students at SHLC:
Weeks 1-2: Diagnostic and Prioritisation Complete a full Paper 1 past paper under timed conditions. For each lost mark, identify which of these ten skills caused the error.
Rank skills from weakest (1) to strongest (10).
Weeks 3-8: Targeted Skill Building (one skill per week, starting with weakest) For each skill:
- Complete 20-30 isolated practice questions
- Time yourself to build speed
- Mark carefully and review every error
- Retest after 3 days to verify retention
Use Maths Genie to find topic-specific questions for each skill.
Weeks 9-12: Integration Practice Complete full Paper 1 papers weekly under timed conditions. Your target:
- Foundation: 50+ marks for grade 4, 60+ for grade 5
- Higher: 60+ marks for grade 7, 70+ for grade 8-9
Track scores to verify improvement. Use my mock exam marking service every 4 weeks for expert feedback.
Daily Maintenance: Corbett Maths 5-a-Day keeps skills sharp between intensive practice sessions.
Time Management on Paper 1
Paper 1 is 90 minutes for 80 marks. That's roughly 1 mark per minute, plus 10 minutes for checking.
Research shows students find time pressure worse on non calculator papers because lengthy calculations consume time quickly.
Time management strategy:
- Questions worth 1-2 marks: 1-2 minutes maximum
- Questions worth 3-4 marks: 3-4 minutes maximum
- Questions worth 5+ marks: 5-7 minutes maximum
- Final 10 minutes: checking
If you've spent 5 minutes on a 2 mark question and you're stuck: MOVE ON. Write what you know, mark the question, return if time allows.
Don't let one difficult question consume 15 minutes whilst easier marks slip away elsewhere.
For Parents: Supporting Non-Calculator Skills
Remove Calculator Dependency For homework that doesn't explicitly require a calculator, remove access to it. This forces mental arithmetic practice.
Drill Basic Skills Daily 5 minutes of times table practice or fraction calculations daily builds fluency faster than hour-long weekly sessions.
Use Everyday Opportunities Shopping, cooking, journey planning all involve mental maths. Ask your child to calculate:
- 20% off £45 in a shop
- How long till we arrive if it's 90 miles at 60mph
- Double this recipe that serves 4 to serve 8
Check Understanding, Not Just Answers Ask "How did you get that?" forces explanation, revealing whether they truly understand or just memorised a method.
Know When Extra Help Is Needed If these skills remain shaky despite practice, your child might need teaching, not just reminders.
At SHLC, I work systematically through non calculator skills, identifying exactly where gaps exist and filling them efficiently.
The Bottom Line
Paper 1 accounts for one third of your total GCSE Maths marks. Strong non calculator skills aren't optional, they're essential.
These ten skills consistently determine whether students excel or struggle on Paper 1. Master them, and 70+ marks becomes achievable. Neglect them, and you're leaving 30-40 marks on the table.
Students who build genuine fluency with these skills don't just improve Paper 1 scores. They develop number sense that improves performance on calculator papers too. They spot errors faster, estimate better, and work more efficiently throughout all three papers.
Remember: each grade improvement is worth around £23,000 in lifetime earnings. Paper 1 skills directly affect which grade you achieve.
Start practising today. Build these skills systematically. And watch your Paper 1 confidence transform.
Struggling with Paper 1 non calculator skills? Get in touch with SHLC to discuss how targeted support can build the fluency you need to excel.