Place Value Problems

Overview

• Year group: Year 4
• Duration: 60 minutes
• Class size: 30 students
• Curriculum links:
  • Mathematics Program of Study, Number – Number and Place Value, Year 4
  • Pupils should:
    • Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
    • Order and compare numbers beyond 1000
    • Solve number and practical problems involving place value, ordering, and rounding (National Curriculum, Key Stage 2)

Learning Objectives

• Consolidate understanding of place value in four-digit numbers
• Solve multi-step word problems involving place value
• Justify reasoning and explain thinking when solving place value problems

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Success Criteria

• I can identify the value of each digit in a four-digit number.
• I can solve word problems involving place value accurately.
• I can explain my methods and reasoning clearly.

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Resources

• Whiteboard and markers
• Place value charts (one per pair)
• Mini-whiteboards and pens for students
• Problem-solving question cards
• Place value counters or base-10 equipment (optional)
• Display of Bloom’s Taxonomy question stems

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Lesson Structure

1. Engaging Introduction (10 minutes)

Aim: Activate prior knowledge and build curiosity by presenting a mystery number challenge.

Activity:

• Display four digit cards on the board; ask pupils to guess the mystery number. Use clues linked to place value:
  • Clue 1: "My thousands digit is double my hundreds digit."
  • Clue 2: "The digit in the tens place is one less than the digit in the ones place."
  • Clue 3: "The number is greater than 3,000 but less than 4,500."

Questions (Whole Class – Targeting Bloom’s levels: Understand, Apply, Analyse):

• How did you interpret the clue about the thousands digit? (Explain understanding)
• Can you explain why the number must be between 3,000 and 4,500? (Justify reasoning)
• If we changed the hundreds digit, what effect would that have on the thousands digit? (Analyse)

AfL Moment:

• Observe students’ explanations to identify misconceptions about place value or inequalities.
• Use mini whiteboards for rapid concept check: “Write down your guess for the thousands digit.” Prompt immediate feedback.

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2. Modelling (15 minutes)

Aim: Demonstrate carefully scaffolded problem-solving to build pupil confidence and develop strategies.

Task 1 (Simple):
“Find the value of the digit 7 in 3,742.”

• Model how to identify place value using the place value chart.

Questions during modelling:

• How do we know that 7 is in the tens place? (Recall & Understand)
• Why does the position of the digit affect its value? (Explain)

Task 2 (Increasing Complexity):
“The number is 4,256. If I swap the hundreds and tens digits, what number do I get?
How does the value of the swapped digits change?”

• Model swapping digits using the chart, and calculate the difference between original and new number.

Questions during modelling:

• What changes and what stays the same after swapping? (Analyse)
• Why does swapping digits affect the number’s total value? (Explain reasoning)

Task 3 (Complex):
“A number has digits 3, 8, 5, and 2. The digit in the thousands place is less than twice the digit in the hundreds place. What could the number be? Write two possible numbers and explain your reasoning.”

• Walk through how to use inequalities and reasoning to narrow down options.

AfL Moments:

• Use mini whiteboards for pupils to write answers after each task. Rapid verbal feedback to check understanding.
• Pose "why" questions to individuals: "Why have you chosen this number? Can you explain your reasoning step-by-step?"

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3. Guided Practice (20 minutes)

Activity:

• Pupils work in pairs on a set of 4 word problems focusing on place value, presented on cards. Examples:

1. “The number has 4 thousands, 6 hundreds, 2 tens, and 9 ones. What number is it?”
2. “If the digit in the hundreds place is doubled, what happens to the number?”
3. “Sarah wrote a four-digit number. The thousands digit is one less than the hundreds digit. The tens digit is three times the ones digit. What could the number be?”
4. “Compare 4,582 and 4,258. Which is greater and why?”

Higher-order questioning prompts for pairs:

• Can you explain how you found the value of each digit?
• What strategies did you use to solve this problem?
• Are there any other numbers that could work here? Explain why or why not.
• How would the answer change if the tens and hundreds digits were swapped?

AfL Points:

• Circulate to listen to discussions, noting reasoning and use of place value knowledge.
• Use targeted questioning with struggling pairs to scaffold thinking.
• For pupils demonstrating stronger reasoning, challenge them to create their own problem for others to solve.

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4. Independent Challenge (10 minutes)

Task: Individually solve two multi-step place value problems:

• “A number is made up of digits that add up to 15. The hundreds digit is the smallest digit. What could the number be? Show all possibilities.”
• “You swap the digits in the ones and thousands place of 5,381. What is the new number? How much smaller or bigger is that number?”

Bloom’s focus: Apply, Analyse, Evaluate.

AfL: Review answers with a quick whole-class discussion. Select a few to explain their thought process aloud. Use mini whiteboards for some pupils to write their reasoning.

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5. Plenary (5 minutes)

Purpose: Reflect on learning and consolidate understanding through peer explanation.

Activity:

• Randomly select 3 pupils to explain one problem they solved and share their justification.
• Ask the class to vote (hands up) on which solution was most convincing and why.

Prompts to deepen thinking:

• What was the most challenging part of today’s problems?
• How does understanding place value help you solve these problems?
• How could you check your answers to make sure they are reasonable?

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Assessment for Learning (AfL) Summary

Stage	Method	Purpose	Example Use
Introduction	Mini-whiteboard quick-check	Gauge initial understanding	Identify place value errors
Modelling	Targeted questioning + mini-whiteboard	Check application of concepts	Justify digit values, reasoning for swaps
Guided Practice	Paired discussion + teacher questioning	Identify misconceptions, scaffold	Clarify reasoning & misconceptions
Independent Challenge	Class discussion + written reasoning	Assess deeper understanding	Evaluate solutions & reasoning
Plenary	Peer explanation and class voting	Consolidate learning & self-assess	Justify position of digits

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Differentiation

• Support: Use base-10 counters and place value charts, scaffolded question cards with sentence starters ("The digit in the ___ place means...").
• Challenge: Create more complex problems involving inequalities or digit manipulation; encourage explanation and creation of their own problems.

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This lesson plan ensures engagement with rich reasoning tasks, supporting pupils to deeply consolidate place value through careful questioning, collaborative work, and metacognitive reflection, all aligned tightly with the Year 4 National Curriculum expectations.