Dividing by Ten

Overview

• Year Group: Year 6
• Duration: 60 minutes
• Class Size: 20 students
• Unit: Mastering Tens: Multiply & Divide (Lesson 2 of 2)
• Focus: Dividing whole numbers by ten and understanding place value shifts
• National Curriculum Links:
  • Number – Multiplication and Division:
    • Pupils should be taught to divide numbers up to 4 digits by a one-digit number using formal written methods and mental strategies (NC 2014, Y6)
  • Number – Place Value:
    • Recognise the place value of each digit in numbers up to 10,000,000 (including decimals up to three decimal places) and use this to understand number operations (NC 2014, Y6)

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Learning Objectives

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

1. Understand that dividing a whole number by 10 shifts digits one place to the right in the place value system.
2. Divide a variety of whole numbers by 10 using both mental strategies and concrete representations.
3. Explain why dividing by ten affects the place value of digits.
4. Solve increasingly challenging problems involving division by 10 and justify their answers verbally and in writing.

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Resources

• Whiteboard and markers
• Place value charts (for every 2-3 pupils)
• Base-10 blocks or place value counters (tens, ones)
• Individual whiteboards and pens for students
• Worksheets with division by 10 problems
• “Place Value Shift” interactive slides or printed number grids
• Mini-group discussion prompt cards

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Lesson Structure

Starter (10 minutes)

• Recap: Quickly revisit the previous lesson on multiplying by 10. Use a couple of mental multiplication examples (e.g., 24 × 10 = ?). Focus on the concept of shifting digits left.
• Think-Pair-Share: Ask pupils, “If multiplying by 10 shifts digits to the left, what do you think happens when we divide by 10?” Record initial ideas on the board.
• Learning Goal Share: Explain that today they will explore how dividing by 10 shifts digits to the right and why.

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Introduction (15 minutes)

• Concrete Model Demonstration:
  • Using base-10 blocks, show the number 240. Demonstrate dividing by 10 by grouping the blocks into 10 equal groups, emphasising transformation: 240 ÷ 10 = 24.
  • Use the place value chart to physically move the digit '2' from hundreds to tens, '4' from tens to ones, explaining the shift.
• Visual Slide: Present place value chart with number lines to show digit shifts when dividing by 10.
• Guided Practice:
  • Write numbers like 3,500; 1,720; and 860 on the board. Ask students to predict the answer to dividing by 10.
  • Confirm by moving digits on the place value chart or working out the division mentally.

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Main Activity (25 minutes)

Activity 1: Hands-On Practice (15 minutes)

• In pairs, pupils use place value counters and mini place value charts.
• Give each pair numbers like 520, 4,010, 980, 6,340.
• Task: Physically divide each number by 10 using counters and write down the answer.
• Circulate and support by asking guiding questions, e.g., “What happens to each digit when you divide by 10?”

Activity 2: Problem-Solving and Group Discussion (10 minutes)

• Split class into four groups (5 pupils each).
• Give them problem cards with questions such as:
  1. “A shop sold 730 pencils in one day. How many packs of 10 pencils could they fill?”
  2. “If 2,450 is divided by 10, what is the value of the digit ‘4’ now?”
  3. “Explain in your own words what happens to the place value when dividing by 10.”
• Groups discuss and record answers.
• Select one group to present their solution and explanation to the class.

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Plenary (10 minutes)

• Quick Quiz: Use individual whiteboards for quickfire questions:
  • Divide numbers such as 120, 650, 4,300 by 10.
  • Identify the place value changes of specific digits after division.
• Class Discussion: Reflect on any misconceptions, e.g., “Does dividing by 10 always mean the number gets smaller?” (Explain exceptions such as decimals or zero).
• Self-Assessment: Pupils rate their understanding on a smiley-face scale (1-3) and write one sentence describing what they learned today.

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Assessment & Differentiation

• Formative:
  • Observe pupil discussions and question responses during activities.
  • Use plenary quiz answers to check for understanding.
• Summative:
  • Worksheet tasks completed during class (e.g., divide by 10 problems with place value reasoning).
  • Group problem explanations provide evidence of depth of understanding.
• Support:
  • Provide extra place value scaffolds and step-by-step guidance for those who need it.
  • Visual aids and manipulatives to reinforce concepts.
• Challenge:
  • Ask more able learners to divide decimal numbers by 10 (e.g., 43.6 ÷ 10).
  • Extend problem-solving with real-life contexts, such as money division (e.g., £540 ÷ 10).

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National Curriculum Alignment

• Mathematics Programmes of Study - Number – multiplication and division (Y6):
  • Use their knowledge of place value and number facts to multiply and divide numbers mentally, including dividing whole numbers and those involving decimals by 10.
• Number – place value (Y6):
  • Recognise the place value of each digit in numbers up to 10,000,000 and decimals to three decimal places and use this understanding to carry out calculations including division.
• Mathematical reasoning and problem-solving:
  • Use discussion and explanation to consolidate understanding of number operations.

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Teacher Notes & Tips

• Emphasise the conceptual link between multiplication and division by 10 — they are inverse operations affecting place value oppositely.
• Encourage pupils to verbalise the “digit shift” concept; this deepens numerical fluency rather than just focusing on rote answers.
• Use physical manipulatives liberally; concrete understanding in Year 6 solidifies abstract number work, especially for certain learners.
• Include real-life contexts (e.g. money, measurements) whenever possible to make the maths meaningful.

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By delivering this lesson, pupils will build a strong conceptual foundation for dividing by 10, preparing them for more complex division and decimal number work ahead.