Overview

Duration: 45 minutes
Class size: 1 student
Year group: Year 7 (age 11-12)
Curriculum link: National Curriculum for England
Focus: Using the column method for addition and subtraction of whole numbers, linking to developing fluency with written methods (Number – Addition and Subtraction (7N1)).

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Learning Objectives

By the end of the lesson, the student will be able to:

• Apply the column method confidently for addition and subtraction of 3-digit numbers with and without regrouping.
• Solve addition and subtraction problems using column method with accuracy.
• Develop fluency and understanding of place value in written calculations (NC ref: 7N1).

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Curriculum References

• Number – Addition and Subtraction (Year 7): Pupils extend calculation skills to larger numbers and practical problems, using formal written methods.
• Mathematical Fluency: Pupils consolidate fluency in addition and subtraction through written methods.
• Mathematical Reasoning: Develop problem-solving by explaining steps and checking answers.

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Success Criteria

• Writes calculations neatly using the column method.
• Carries digits correctly in addition and subtracts using borrowing when needed.
• Checks answers by inverse operations.

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Lesson Structure

1. Starter Activity (5 mins)

Mental maths warm-up: Rapid-fire oral questions on addition and subtraction of 2-digit numbers to regroup, e.g. 47 + 38, 75 - 29.
Purpose: Activate prior knowledge and place value awareness.

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2. Teacher Input (10 mins)

• Model step-by-step use of the column method for addition:
  Example: 346 + 289
  • Write numbers in columns (hundreds, tens, ones).
  • Add ones column first, carry if >9.
  • Add tens and hundreds columns similarly.
• Discuss common errors (forgetting to carry, aligning digits).
• Model subtraction with borrowing:
  Example: 634 - 287
  • Highlight borrowing from tens to ones, then hundreds to tens if needed.
• Ask student to explain each step back to teacher.

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3. Guided Practice (15 mins)

Activity: Student completes 5 addition and 5 subtraction questions using column method (see questions below).

• Student solves each problem.
• Teacher watches, asking probing questions if needed (e.g., “Why do we carry here?”, “How do you know if you need to borrow?”).
• Student checks each answer by performing inverse operation.

Questions & Answers:

1. 257 + 468 = 725
2. 634 + 275 = 909
3. 489 + 376 = 865
4. 722 + 159 = 881
5. 305 + 696 = 1001
6. 754 - 389 = 365
7. 601 - 273 = 328
8. 830 - 457 = 373
9. 715 - 298 = 417
10. 902 - 685 = 217

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4. Independent Practice (10 mins)

Set 5 mixed word problems involving addition and subtraction, requiring the column method for solution.
Student writes complete calculations and answers clearly.

Sample Problems:

1. A shop sold 365 pencils in the morning and 428 in the afternoon. How many pencils were sold in total?
2. There were 875 tickets for a concert. After selling 489, how many tickets remain?
3. A library had 720 books; they bought 238 more this month. How many books in all?
4. Peter had £832 and spent £449 on a bike. How much money is left?
5. A car travelled 485 miles on Monday and 627 miles on Tuesday. What was the total distance travelled?

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5. Plenary (5 mins)

• Review key learning points by asking the student to teach back one addition and one subtraction problem using the column method.
• Discuss usefulness of column method for handling larger numbers.
• Set a mini target: Practise neat setup and checking work as homework for fluency.

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Mixed Fraction Mastery

Overview

Duration: 45 minutes
Class size: 1 student
Year group: Year 7 (age 11-12)
Curriculum link: National Curriculum for England: Number – Fractions (7N2)
Focus: Understanding, adding, and subtracting mixed fractions.

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Learning Objectives

Upon completion, the student will be able to:

• Identify and convert between mixed fractions and improper fractions.
• Add and subtract mixed fractions with different denominators.
• Simplify answers and convert improper fractions back to mixed numbers where appropriate.

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Curriculum References

• Number – Fractions (Year 7): Extending understanding of fractions, including mixed numbers and improper fractions; addition and subtraction of fractions with different denominators.
• Problem Solving: Apply fraction work to real contexts.

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Success Criteria

• Converts mixed numbers to improper fractions correctly.
• Finds common denominators and adds/subtracts fractions accurately.
• Simplifies results and converts back to mixed numbers neatly.

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Lesson Structure

1. Starter Activity (5 mins)

Review proper vs improper fractions and mixed numbers with quick questions: e.g. convert ( 2\frac{3}{5} ) to an improper fraction.

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2. Teacher Input (10 mins)

• Explain and model converting mixed fractions to improper fractions.
• Demonstrate finding common denominators (e.g. between 3 and 5).
• Model addition and subtraction of mixed fractions step-by-step.
• Highlight simplifying final answers.

Example:
Add ( 1\frac{2}{3} + 2\frac{3}{5} )

• Convert to improper: ( \frac{5}{3} + \frac{13}{5} )
• Common denominator: 15
• ( \frac{25}{15} + \frac{39}{15} = \frac{64}{15} = 4\frac{4}{15} )

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3. Guided Practice (15 mins)

Student completes 6 adding and subtracting mixed fractions with differing denominators.

Questions & Answers:

1. ( 2\frac{1}{4} + 3\frac{2}{5} = 5\frac{13}{20} )
2. ( 4\frac{3}{7} - 2\frac{2}{7} = 2\frac{1}{7} )
3. ( 1\frac{5}{6} + 2\frac{1}{3} = 3\frac{1}{6} )
4. ( 5\frac{1}{2} - 3\frac{2}{3} = 1\frac{5}{6} )
5. ( 3\frac{4}{9} + 1\frac{5}{6} = 5\frac{7}{18} )
6. ( 6\frac{2}{3} - 4\frac{7}{12} = 1\frac{7}{12} )

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4. Independent Practice (10 mins)

Pose 3 word problems involving mixed fractions addition or subtraction.

Examples:

1. Sarah drank ( 1\frac{3}{4} ) litres of juice in the morning and ( 2\frac{2}{5} ) litres in the afternoon. How much did she drink in total?
2. A recipe needs ( 3\frac{1}{2} ) cups of flour, but only ( 1\frac{3}{4} ) cups have been added. How many more cups are needed?
3. Tom ran ( 5\frac{2}{3} ) miles on Monday and ( 3\frac{1}{4} ) miles on Tuesday. How far did he run in total?

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5. Plenary (5 mins)

Student explains in their own words the process for adding and subtracting mixed fractions, demonstrating with an example from the lesson. Teacher reinforces importance of denominator alignment and simplification.

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Percentage Challenge

Overview

Duration: 45 minutes
Class size: 1 student
Year group: Year 7 (age 11-12)
Curriculum link: National Curriculum for England: Number – Percentages (7N5)
Focus: Calculating percentages of amounts and understanding percentage problems.

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Learning Objectives

The student will be able to:

• Calculate percentages of given quantities.
• Solve increase and decrease problems involving percentages.
• Interpret percentage problems in real-life contexts.

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Curriculum References

• Number – Percentages (Year 7): Work with percentages, including finding percentages of quantities and solving problems involving percentage increase/decrease.
• Problem Solving: Apply percentages to real world problems such as money, quantities, and data.

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Success Criteria

• Accurately find percentages of quantities using fractions or decimals.
• Solve percentage increase and decrease problems confidently.
• Explain methods used for calculating percentages.

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Lesson Structure

1. Starter Activity (5 mins)

Quick revision: What is 10%, 25%, and 50% of 100? Discuss how percentages relate to fractions and decimals.

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2. Teacher Input (10 mins)

• Explain how to find a percentage of an amount by converting % to fractions or decimals.
• Model examples:
  • Find 15% of 240
  • Calculate increase of 20% on £45
• Use visual aids (e.g., grids or pie charts) to illustrate percentages if helpful.

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3. Guided Practice (15 mins)

Student attempts 8 questions with teacher support when needed.

Questions & Answers:

1. Find 30% of 200 = 60
2. What is 25% of 360? = 90
3. Increase 80 by 15% = 92
4. Decrease 150 by 40% = 90
5. If 40% of a number is 24, what is the number? = 60
6. Find 10% of 175 = 17.5
7. Increase £50 by 25% = £62.50
8. Decrease £90 by 10% = £81

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4. Independent Practice (10 mins)

3 problem-solving tasks involving percentages in real-life scenarios.

Examples:

1. A jacket costs £60. It is on sale with 30% off. What is the sale price?
2. A student scored 75% in a maths test of 80 marks. How many marks did the student get?
3. A population of a town increased from 20,000 to 22,000. What is the percentage increase?

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5. Plenary (5 mins)

Student summarises how to calculate percentages of amounts and solves a final quick question set by teacher. Discuss practical uses of knowing percentages.

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Mixed Fractions & Percentages

Overview

Duration: 45 minutes
Class size: 1 student
Year group: Year 7 (age 11-12)
Curriculum link: National Curriculum for England: Number – Fractions & Percentages
Focus: Linking mixed fractions and percentages through conversion and applications.

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Learning Objectives

• Convert mixed fractions to percentages and vice versa.
• Solve problems that combine use of mixed fractions and percentages.
• Explain reasoning clearly between fractional and percentage forms.

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Curriculum References

• Number – Fractions and Percentages (Year 7): Understand equivalences between percentages and fractions, including mixed fractions.
• Mathematical Communication: Argue mathematically about conversions and problem-solving steps.

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Lesson Structure

1. Starter Activity (5 mins)

Refresh converting simple fractions (e.g., ( \frac{1}{2}, \frac{3}{4} )) to percentages.

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2. Teacher Input (10 mins)

• Model conversion of mixed fractions to improper fractions, then to decimals, then to percentages.
• Example: Convert ( 2\frac{1}{4} ) to a percentage:
  • ( 2\frac{1}{4} = \frac{9}{4} = 2.25 )
  • ( 2.25 \times 100 = 225% )
• Model reverse conversion of percentages to mixed fractions.

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3. Guided Practice (15 mins)

Student completes 6 conversions between mixed fractions and percentages and answers true/false reasoning questions.

Questions & Answers:

1. ( 1\frac{1}{2} = 150% ) (True)
2. Convert ( 3\frac{2}{5} ) to percentage: ( 3\frac{2}{5} = \frac{17}{5} = 3.4 = 340% )
3. ( 225% = 2\frac{1}{4} ) (True)
4. Convert 125% to mixed fraction = ( 1\frac{1}{4} )
5. ( 4\frac{1}{2} ) as a percentage = 450%
6. 80% is equal to ( \frac{4}{5} ) (True)

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4. Independent Practice (10 mins)

Apply conversions to word problems:

1. A recipe requires ( 1\frac{1}{3} ) cups of sugar. Express this as a percentage of 1 cup.
2. A class has 120% the number of boys compared to girls. Express this in terms of mixed fractions.
3. A car’s fuel efficiency increased from ( 2\frac{1}{2} ) miles per litre to 300% of the original. What is the new efficiency?

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5. Plenary (5 mins)

Student explains one conversion example and identifies real-life situations where knowing this skill helps (e.g., cooking, finance).

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Percentage Problems Mixed

Overview

Duration: 45 minutes
Class size: 1 student
Year group: Year 7 (age 11-12)
Curriculum link: National Curriculum for England – Number (Percentages and Problem solving)
Focus: Complex percentage problems including reverse percentages and multi-step problems.

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Learning Objectives

• Solve reverse percentage problems (finding original amount).
• Tackle multi-step problems involving percentage increase/decrease.
• Apply percentages confidently in real-world scenarios.

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Curriculum References

• Number – Percentages (Year 7): Solve problems involving percentages including reverse percentages (7N5).
• Reasoning and Problem Solving: Use strategies to tackle multi-step percentage problems.

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Success Criteria

• Correctly identify what is given and what is unknown in percentage word problems.
• Use efficient strategies to find original values from percentage changes.
• Explain solutions clearly and check answers where possible.

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Lesson Structure

1. Starter Activity (5 mins)

Quick quiz: If 80 is 40% of a number, what is the number? Discuss key vocabulary like “original amount” and “percentage of.”

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2. Teacher Input (10 mins)

• Explain strategies for reverse percentage problems:
  • Use equation: original × percentage = given amount
• Model multi-step problems involving increase/decrease followed by further percentage changes.
• Draw flow diagrams where helpful to visualise steps.

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3. Guided Practice (15 mins)

Student works through 7 problems with teacher support.

Questions & Answers:

1. 80 is 40% of what number? (Answer: 200)
2. After a 20% increase, an item costs £72. What was the original price? (Answer: £60)
3. A population decreased by 30% to 14,000. What was the population before? (Answer: 20,000)
4. A jacket is reduced by 25% to £45. What was the original price? (Answer: £60)
5. A quantity is increased by 10% then decreased by 20%. If final amount is 792, what was original? (Answer: 880)
6. The price of a car increased twice, first by 15% then by 10%. If final price is £12,650, what was original price? (Answer: approx. £10,000)
7. The population grew from 15,000 to 16,200. What is the percentage increase? (Answer: 8%)

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4. Independent Practice (10 mins)

Two multi-step challenges:

1. A laptop originally cost £650. It was first discounted by 10%, then a further 15%. Find the final price.
2. A town’s population decreases by 12%, then increases by 25%. The final population is 22,000. Find the original population.

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5. Plenary (5 mins)

Student summarises problem-solving method for reverse and multi-step percentage problems. Discuss real-life applications such as shopping discounts and population growth.

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This 5-lesson series offers robust, curriculum-linked, expertly scaffolded teaching for Year 7 students focusing on column method, mixed fractions, and percentages, with rich questioning, real-world problem-solving, and formative assessment throughout for mastery and confidence.