Problem Solving Mastery

Overview

Age Group: Year 4 (ages 8-9)
Duration: 60 minutes
Class Size: 30 pupils
Focus: Solve number and practical problems involving positive numbers
Curriculum Link:

• National Curriculum England
  • Mathematics Key Stage 2, Number - Number and Place Value
  • Pupils should be taught to:
    • Solve number and practical problems that involve increasingly large positive numbers (National Curriculum 2014, PoS: Years 3 & 4)
• White Rose Maths Scheme – Autumn 1: Number and Place Value

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Learning Objectives

By the end of the lesson pupils will be able to:

• Solve word problems involving positive whole numbers within 10,000
• Use the four operations (primarily addition and subtraction) to solve practical problems
• Demonstrate understanding of place value to support problem solving
• Explain their reasoning clearly, using appropriate mathematical language

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Resources Needed

• Whiteboards and pens (1 per pupil)
• Place value charts on the board and printed copies
• Number cards (0–9)
• Problem-solving worksheet differentiated into 3 levels (mild, spicy, hot)
• Counters or place value blocks for modelling
• Timer display
• Mini plenary visual aid (e.g., thumbs up/down, traffic lights cards)

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Lesson Structure

1. Starter / Introduction (10 minutes)

Aim: Engage pupils with place value discovery and hook into problem solving

• Hook: Start with a short interactive game: "Place Value Bingo"
  • Display random 4-digit numbers on the board.
  • Call out clues like “Show me the digit in the hundreds place,” “Point to the number with 2 in the thousands place.”
  • Use quick-fire questioning to ensure pupils consolidate place value knowledge.
• Questioning:
  • What does each digit in 4,305 represent?
  • If I changed the ‘0’ to a ‘7’, how would the number change?
  • How can we split this number into thousands, hundreds, tens and ones?
• AfL: Use mini whiteboards for immediate written responses to digit identification and place value questions.
  • Peer assess: Pupils swap boards with neighbours and mark correct/incorrect answers.

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2. Modelling and Guided Practice (20 minutes)

Aim: Model problem-solving using place value confidently, increasing difficulty stepwise

• Modelling 1 (Simple):

  • Write a problem on the board: “Sami has 3,405 marbles. He gives away 1,200 marbles. How many does he have left?”
  • Talk through identifying numbers, place values, and the operation (subtraction).
  • Use place value counters to represent the number physically.
  • Solve the problem step-by-step, verbalising thinking (“We subtract the thousands first...”)
  • Question: How can we check the answer?

• AfL: Use targeted questioning to check understanding (“What’s the value of the '2' in 1,200?”) and eliciting pupil explanations. Ask some pupils to model the problem on their mini whiteboards.

• Modelling 2 (Intermediate):

  • Present a two-step problem:
    "Jasmine’s school has 4,250 books. The library buys 780 more, but then 1,450 books are sent to another school. How many books does Jasmine's school have now?”
  • Demonstrate breaking this problem into parts, modelling addition first then subtraction.
  • Represent numbers on a number line or place value chart for clarity.
  • Emphasise estimation/reasonableness of answer.

• AfL: Cold call specific pupils to explain the steps. Use traffic light cards for pupils to self-assess their confidence with multi-step problems after modelling.

• Modelling 3 (Challenging):

  • Word problem requiring multi-step reasoning & decision making:
    “A fairground sells 2,675 tickets in the morning and 3,840 in the afternoon. They have 7,500 tickets to start. How many tickets are left at the end of the day? Explain how you worked it out.”
  • Encourage pupils to verbalise the strategy before working out the solution.
  • Model using a bar model or part-part-whole diagram to visualise the problem.
  • Highlight use of place value understanding for efficient mental calculation.

• AfL: Use open questioning and ask pupils to write a short explanation of their method on mini whiteboards. Conduct peer discussion to improve clarity of reasoning. Encourage pupils to explain to a partner.

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3. Independent / Paired Practice (20 minutes)

Aim: Pupils consolidate problem solving with scaffolded reasoning

• Pupils work in pairs or independently on differentiated worksheets:

  • Mild: Single operation word problems involving subtraction or addition under 4,000
  • Spicy: Two-step problems involving addition and subtraction up to 10,000
  • Hot: Multi-step, reasoning-heavy problems where pupils explain their thinking

• Teacher circulates to offer support and pose probing questions.

• Stop halfway for a brief ‘check-in’:

  • Use mini plenary questioning: “Who can share one tricky part?” “Who feels confident? Show me your green card!”

• Pupils encouraged to use manipulatives and place value charts if stuck.

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4. Plenary (10 minutes)

Aim: Reflect and reinforce learning with self and peer assessment

• Bring the class together. Present a reflective success criteria checklist:

  • I can identify place value in 4-digit numbers
  • I can decide which operation to use in a problem
  • I can work through multi-step problems logically
  • I can explain my thinking clearly

• Quick quiz on the board (true/false or multiple choice):

  • “If you add 200 to 3456, the answer is 3656.” (True)
  • “To find out how many books are left, you add all numbers together.” (False)

• Pupils respond with thumbs up/down for confidence and understanding.

• Final ‘Challenge Question’ for quick group work or brain teaser:

  • “There were 9,000 sweets in a jar. 4,763 were eaten. How many sweets are left now? What if 1,250 more were added afterwards?”

• End with sharing one new thing they learned or found tricky.

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Assessment for Learning (AfL) Points Summary

Timing	AfL Type	Purpose	Examples
Introduction	Mini whiteboards & peer marking	Check place value understanding	Quick quizzes on digit values
Modelling 1	Targeted questioning	Gauge individual comprehension	“What is the value of this digit?”
Modelling 2	Traffic light self-assessment	Check comfort with multi-step problems	Confident? Unsure? Need help?
Modelling 3	Written explanation on whiteboards	Assess reasoning and communication skills	Explain problem-solving method
Independent work	Observations & questioning	Identify misconceptions and scaffold	Prompt with “Why did you choose that operation?”
Plenary	Thumbs up/down and quiz	Reflect understanding and confidence	True/False questions

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Curriculum Links

Mathematics - Number and Place Value (Years 3-4)

• Count in multiples of 6, 7, 9, 25 and 1,000
• Find 1,000 more or less than a given number
• Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• Order and compare numbers beyond 1,000
• Solve number problems and practical problems involving these concepts (including addition and subtraction)

This lesson directly supports developing these competencies, emphasising problem solving using place value knowledge and operations within 10,000 aligned to Year 4 expectations.

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This detailed plan provides teachers with a clear pathway to engage pupils through active learning, scaffolded modelling, continuous AfL, and reflection – all based on proven approaches from the White Rose Maths scheme and National Curriculum. Using manipulatives and real-world contexts ensures relevance, while the multiple AfL layers allow teachers to adapt on the fly and maximise impact. This can transform a typical Maths lesson into an immersive and empowering mathematical journey.