Dividing by Powers

Overview

This 60-minute session, designed for Year 7 students, concludes the unit "Mastering Powers of 10" focusing on dividing whole numbers and decimals by powers of 10. The lesson aligns with the National Curriculum for England’s mathematics programme of study, particularly Number - fractions (including decimals and percentages) and Number - multiplication and division, ensuring students deepen their understanding of place value and decimal manipulation.

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National Curriculum Alignment

• Number - multiplication and division:
  Use knowledge of multiplication and division facts to derive related facts (Y7 focuses on securing and extending previous understanding).
  Use place value, known and derived facts to multiply and divide mentally, including multiplying and dividing by 10, 100 and 1000, identifying the effect.

• Number - fractions (including decimals and percentages):
  Identify the value of digits to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places.

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Learning Objectives

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

• Divide whole numbers and decimals by 10, 100, and 1000 effectively and confidently.
• Accurately shift the decimal point to the left when dividing by powers of 10, articulating their reasoning.
• Demonstrate understanding of how division by powers of 10 affects the place value of digits.
• Apply their knowledge to solve a range of problems involving division by powers of 10, including word problems and practical activities.

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Resources Needed

• Whiteboard, markers
• Mini-whiteboards and pens for each student
• Place value charts (laminated A4), with decimal and whole number columns
• PowerPoint slides with visual examples and animations of decimal shifts
• Worksheets with differentiated exercises (basic, intermediate, challenge)
• Interactive decimal shift game (can be printed or digital if available)
• Exit ticket slips for quick assessment
• Number cards with whole numbers and decimals for group activities

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Lesson Structure

1. Starter Activity (10 minutes)

Mental recall and prior learning activation

• Begin with a quick recap quiz on multiplying by 10, 100 and 1000 using a mix of whole numbers and decimals on mini-whiteboards.
• Example questions:
  • What is 5 × 100?
  • What is 0.3 × 10?
• Briefly highlight the inverse nature of division and multiplication by powers of 10 to set context.

Purpose: Reactivate prior learning from lessons 1 and 2 to scaffold new learning.

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2. Introduction & Modelling (15 minutes)

Explicit teaching with visual aids

• Use PowerPoint animations to show how dividing by 10 shifts the digits one place to the left on the place value chart.
• Demonstrate examples with whole numbers first (e.g., 500 ÷ 10 = 50), then decimals (e.g., 3.2 ÷ 10 = 0.32).
• Emphasise language: "The decimal point moves one place to the left because dividing by 10 makes the number ten times smaller.”
• Model dividing by 100 and 1000 and relate the number of decimal shifts to the power of 10.

Key Questions:

• What happens to the digits?
• How does the place value change?
• Why does the decimal move left?

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3. Guided Practice (15 minutes)

Collaborative and hands-on learning

• Hand out laminated place value charts and number cards to pairs or small groups. Students use the cards to create numbers and then physically "move" the decimal point to the left to divide by 10, 100, and 1000.
• Provide a worksheet with clear instructions for students to work through, supported by the teacher circulating and providing immediate feedback.
• Include a mixture of calculations and word problems to contextualise division by powers of 10.

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4. Independent Practice (10 minutes)

Application and problem-solving

• Pupils complete differentiated worksheets covering:
  • Dividing whole numbers by powers of 10.
  • Dividing decimals by powers of 10.
  • Word problems involving context (e.g., measurements, money).
• Encourage students to annotate their working steps, especially how and why the decimal shifts.

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5. Plenary / Assessment (10 minutes)

Check understanding and consolidate

• Conduct a quickfire quiz using mini-whiteboards asking a mix of calculation and reasoning questions. For example:
  • Divide 46 by 10 — where does the decimal move?
  • If you divide 0.75 by 100, what is the result?
• Exit ticket: Each student writes an example question and answer they feel confident about, plus one thing they found tricky.

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Differentiation

• Lower ability: Use primarily whole numbers and focus on dividing by 10 only. Use more hands-on place value manipulations and visual aids.
• Middle ability: Include straightforward decimals with up to 2 decimal places and division by 10 and 100.
• Higher ability: Challenge students with decimals to three decimal places, division by 1000, and multi-step word problems involving division by powers of 10.

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Assessment and Feedback

• Ongoing formative assessment through questioning and mini-whiteboard responses.
• Teacher observation during guided practice and group activity.
• Mark and provide written or verbal feedback on independent worksheets.
• Use exit tickets to identify misconceptions or topics needing re-teaching.

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Extension Ideas / Homework

• Create a real-world decimal shifting investigation: students find prices or measurements at home and explore what happens when dividing by 10, 100, and 1000.
• Online or paper-based decimal shift puzzles – extending understanding with fun challenges.

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Key Vocabulary to Reinforce

• Divide
• Powers of 10
• Decimal point
• Place value
• Shift left
• Ten times smaller
• Quotient

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This lesson plan integrates visual, verbal, and kinesthetic learning strategies to engage all Year 7 learners, building fluency, conceptual understanding and confidence with dividing numbers by powers of 10 in line with the National Curriculum expectations.