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Lesson 1: Confident Column Method for Addition and Subtraction

National Curriculum Links

• Number – Addition, Subtraction, Multiplication and Division (Y6)
• Solve addition and subtraction multi-step problems in contexts
• Use formal written methods of columnar addition and subtraction

Learning Objectives

• Use the column method confidently for addition and subtraction of numbers up to 6 digits.
• Apply column addition and subtraction to solve word problems.
• Understand place value in calculations.

Success Criteria

• Set out column additions and subtractions neatly with place value correctly aligned.
• Accurately subtract using decomposition/borrowing.
• Solve word problems involving totals and differences using column method.

Starter (5 mins)

• Rapid-fire mental maths warm-up: quick addition and subtraction facts.
• Quick recall quiz: what is the value of each digit in a 5-digit number?

Main Teaching Activity (25 mins)

1. Model column addition:
   • Solve 364,258 + 245,739 on the board.
   • Emphasise place value and carrying digits across columns.
2. Model column subtraction:
   • Solve 625,438 - 274,186.
   • Demonstrate borrowing when the top digit is smaller.
3. Guided practice:
   • Student works through 5 calculations with scaffolded support.
   • Encourage explaining thinking aloud to consolidate understanding.
4. Contextual challenge:
   • Solve a multi-step word problem involving shopping bills using column method.

Plenary (5 mins)

• Discuss common difficulties and solutions.
• Student verbal reflection on how column method helps accuracy.

Independent Practice Worksheet

• 5 mixed addition and subtraction problems using column method.
• 2 word problems requiring column calculations.

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Lesson 2: Understanding and Simplifying Mixed Fractions

National Curriculum Links

• Number – Fractions (Y6)
• Compare and order fractions, including fractions >1.
• Add and subtract fractions with different denominators and mixed numbers.

Learning Objectives

• Recognise and represent mixed fractions.
• Convert improper fractions to mixed numbers and vice versa.
• Simplify mixed fractions where appropriate.

Success Criteria

• Correctly convert between improper fractions and mixed numbers.
• Add and subtract mixed fractions accurately.
• Simplify fractions to their lowest terms.

Starter (5 mins)

• Quick fraction recap: identify numerator and denominator.
• Whole class practice: visual fraction models—recognising parts of a whole and beyond.

Main Teaching Activity (25 mins)

1. Introducing mixed fractions:
   • Use visual models (fraction bars/circles) to demonstrate mixed numbers.
2. Conversion exercises:
   • Convert improper fractions like 17/5 to mixed numbers.
   • Convert mixed numbers back to improper fractions.
3. Adding/subtracting mixed fractions:
   • Demonstrate with unlike denominators, finding common denominators first.
4. Guided practice:
   • Adding 2⅓ + 4¾
   • Subtracting 5⅚ − 2⅖
5. Simplifying results:
   • Reduce fractions by common factors.

Plenary (5 mins)

• Student explains step-by-step how to add mixed fractions using an example.

Independent Practice Worksheet

• Convert 5 improper fractions to mixed numbers.
• Add and subtract 4 pairs of mixed numbers with unlike denominators.
• Simplify answers.

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Lesson 3: Calculating Percentages of Amounts

National Curriculum Links

• Number – Percentages (Y6)
• Solve problems involving the calculation of percentages (e.g., of quantities, measures).

Learning Objectives

• Calculate percentages of quantities using multiplication and division.
• Understand percentage as "parts per hundred".
• Solve real-life problems involving percentage discounts and increases.

Success Criteria

• Find 10%, 5%, 1% mentally.
• Calculate other percentages using known percentages.
• Solve percentage problems in contextual scenarios.

Starter (5 mins)

• Discuss everyday uses of percentages (sales, statistics).
• Quick mental calculation: Find 10%, 5%, and 1% of 200.

Main Teaching Activity (25 mins)

1. Demonstrate finding 10%, 5%, 1%:
   • Using dividing by 10, halving, and dividing by 100 methods.
2. Finding other percentages:
   • Calculate 15% by adding 10% + 5%.
   • Calculate 20%, 25% using fraction equivalents.
3. Solving word problems:
   • Example: Find 15% off a £120 jacket.
   • Increase £250 by 20%.
4. Guided practice:
   • Calculate percentages of varying quantities.
   • Solve 3 percentage context questions.

Plenary (5 mins)

• Reflect on strategies for mental maths using percentages.
• Student mini-presentation on their favourite strategy.

Independent Practice Worksheet

• 8 percentage calculation questions.
• 3 applied problems with discounts and mark-ups.

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Lesson 4: Mixed Problems – Column Method, Fractions and Percentages

National Curriculum Links

• Number – Consolidation of Y6 objectives
• Use all skills to solve multi-step problems.

Learning Objectives

• Integrate column method, fractions, and percentage skills fluently.
• Approach complex word problems with multiple steps.
• Double-check and reason about answers.

Success Criteria

• Identify which mathematical skill to apply to each problem.
• Plan and carry out calculations stepwise.
• Explain answers clearly.

Starter (5 mins)

• Quick quiz revisiting key terms: decimal, fraction, percentage, addition, subtraction.

Main Teaching Activity (30 mins)

1. Model problem-solving approach:
   • Read a multi-step problem: "A shop has 450 apples. 25% are sold in the morning. In the afternoon, 2⅓ boxes with 12 apples each are sold. How many apples left?"
   • Break down into percentage and mixed fraction multiplication using the column method where needed.
2. Student practice:
   • Solve 3 multi-step word problems involving mixed skills.
3. Peer discussion:
   • Explain strategies used to a mini-audience.

Plenary (5 mins)

• Share one challenging part and how it was overcome.
• Emphasise methodical working.

Independent Practice Worksheet

• 5 multi-step word problems involving addition/subtraction, fractions, percentages.

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Lesson 5: Assessing Mastery and Reasoning

National Curriculum Links

• Mathematical Reasoning and Problem Solving (Y6)
• Reason mathematically and check solutions.

Learning Objectives

• Demonstrate mastery of column method, mixed fractions, and percentages.
• Reason about answers using self-assessment and explanation.
• Solve unfamiliar problems confidently.

Success Criteria

• Complete a mixed skill assessment worksheet.
• Show working clearly in all problems.
• Identify mistakes and correct them where necessary.

Starter (5 mins)

• Warm-up with quick mental maths percentage and fraction recall.

Main Teaching Activity (30 mins)

• Timed assessment:
  • 10 calculation questions (column addition/subtraction, fraction conversion, percentage).
  • 5 reasoning questions asking “Explain why…” or “Which method would you use…?”
• Teacher provides immediate verbal feedback and hints on common errors observed.

Plenary (10 mins)

• Reflective peer review of work.
• Discuss strategies for checking work and problem-solving confidence.

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Resources – Worksheet Samples with Answers

Lesson 1 Worksheet: Column Method

1. 54,273 + 18,149 = 72,422
2. 96,507 − 38,294 = 58,213
3. 217,361 + 384,629 = 602,990
4. 560,000 − 249,875 = 310,125
5. Word Problem:
   "Sara had £8,457 and spent £3,219 on a bike. How much left?"
   Answer: £8,457 − £3,219 = £5,238

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Lesson 2 Worksheet: Mixed Fractions

1. Convert 22/7 to mixed: 3⅁₁⁄₇
2. Convert 4⅘ to improper: 24/5
3. Add 1⅓ + 2⅝ = 3⅞
4. Subtract 5⅖ − 3⅖ = 2
5. Simplify 15/20 = 3/4

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Lesson 3 Worksheet: Percentages

1. 10% of 360 = 36
2. 5% of 140 = 7
3. Find 25% of 320 = 80
4. 15% of £200 = £30
5. Increase £180 by 20% = £216
6. Reduce £150 by 10% = £135
7. 8% of 250 = 20
8. Calculate 50% of 86 = 43

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Lesson 4 Worksheet: Mixed Problems

1. A bag has 120 sweets. 20% are eaten. How many left?
   Answer: 96 sweets left.
2. 3⅔ litres of juice shared equally into 5 bottles. How many litres each?
   Answer: ⅔ litres per bottle.
3. A jacket costing £60 is reduced by 25%. New price?
   Answer: £45.
4. Add 2345 and 4568 using column method.
   Answer: 6913.
5. Subtract 7⅕ − 4⅗.
   Answer: 2⅚.

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Lesson 5 Worksheet: Assessment Sample

Mixed calculations combining above question types. Teacher marks and reviews.

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This set of five detailed and progressive lesson plans embeds fluency, problem-solving, reasoning, and application in Year 6 students closely aligned to the National Curriculum (England) mathematical standards. Each lesson integrates concrete examples, varied activities, and consolidation exercises tailored for a one-to-one teaching environment, maximising personalised support and progress.