Multiplying Decimals

Overview

This 39-minute, teacher-led session focuses on multiplying decimals by 10, 100, and 1,000, designed specifically for a Year 6 student. The lesson strictly follows the National Curriculum for England Mathematics Programmes of Study for Key Stage 2, specifically addressing the learning objective to "use understanding of place value to multiply and divide whole numbers and decimals by 10, 100, and 1,000" (KS2 Number – Multiplying and Dividing).

National Curriculum Links

• Mathematics Programmes of Study: Number — Multiplication and Division (Year 6)
• Pupils should be taught to:
  • Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.
  • Multiply and divide numbers by 10, 100 and 1,000 giving answers up to three decimal places.

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Learning Objectives

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

• Understand how multiplying by 10, 100, and 1,000 affects the place value of decimals.
• Multiply decimals by 10, 100, and 1,000 accurately using place value shifts.
• Explain the reasoning behind multiplication by powers of 10 in relation to decimals.

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Resources Needed

• Whiteboard and marker
• Place value chart (including units, tenths, hundredths, thousandths)
• Number cards with decimals (e.g., 0.3, 4.56, 0.078)
• Mini whiteboard and pen for student
• Printable worksheet with progressively challenging questions
• Number line (optional for visualising shifts)

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Lesson Structure

1. Introduction and Recap (5 minutes)

• Begin with a quick mental warm-up: Ask the student to multiply whole numbers by 10, 100, and 1,000 (e.g., 3 × 10, 45 × 100).
• Recap the place value system, emphasising the position of digits before and after the decimal point: units, tenths, hundredths, thousandths.
• Show examples on place value chart to visualise how digits move when multiplied by 10, 100, and 1,000.
• Reference NC point: "Recognise the place value of each digit in numbers up to three decimal places."

2. Teacher Explanation and Modelling (10 minutes)

• Demonstrate multiplying decimals by 10: Use a simple decimal like 0.4. Write 0.4 × 10 on the board.
• Illustrate that multiplying by 10 moves digits one place to the left. Show how 0.4 becomes 4.0.
• Repeat with 100 (2 places left) and 1,000 (3 places left).
• Write several examples: 0.56 × 100 = 56, 0.078 × 1,000 = 78.
• Link back to place value chart each time to reinforce understanding.
• Explain that if the digit moves past the decimal point, zeros may be added accordingly (e.g., 4.5 × 10 = 45.0).

3. Guided Practice (10 minutes)

• Give the student mini whiteboard and number cards with decimals.
• Call out decimals and multiplication by 10, 100, or 1,000. Example: "Multiply 0.32 by 1,000."
• Student writes answers, then explains reasoning aloud.
• Correct errors immediately, reinforcing place value shifting.
• Mix in some mental checks, for example asking if multiplying by 1000 will increase or decrease the number.

4. Independent Task (8 minutes)

• Provide a printed worksheet with 12 questions, arranged in increasing difficulty:
  • Multiply decimals by 10 (e.g., 0.7 × 10)
  • Multiply decimals by 100 (e.g., 0.045 × 100)
  • Multiply decimals by 1,000 (e.g., 0.006 × 1,000)
  • Include application questions (e.g., “A bottle contains 0.25 litres of juice. How much juice is there if you multiply by 1000?”)
• Student completes independently while teacher monitors and offers support if needed.

5. Plenary and Assessment (6 minutes)

• Review key learning points: How place value shifts affect decimals when multiplied by 10, 100, 1,000.
• Ask the student to verbalise one example in full, explaining the place value shift and the answer.
• Quick quiz: Ask 3 oral questions to confirm understanding (e.g., "What is 0.89 × 10? Why?").
• Use mini whiteboard to get immediate written responses for visual assessment.

6. Extension Challenge (Optional if time permits)

• Introduce very small decimals and encourage the student to predict the answer before calculating.
• Example: Multiply 0.007 by 1,000. Discuss how the decimal point moves three places to the right and what that means for the number.

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Assessment & Feedback

• Formative assessment through guided practice and plenary questioning.
• Summative assessment via worksheet completion, which will be reviewed for accuracy and understanding.
• Provide immediate verbal feedback correcting misconceptions, focusing on errors related to place value shifts.
• Celebrate successes by highlighting correct reasoning and effective use of place value knowledge.

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Differentiation & Personalisation

• Since the class is of 1 student, adapt the pace according to their grasp of the concept.
• Use visual aids more extensively if the student benefits from seeing number patterns physically.
• Provide supportive scaffolding for struggling moments, including revisiting relevant prior knowledge of multiplication or decimals.
• For more advanced understanding, extend to multiplying decimals by powers of 10 beyond 1,000 or link to division by 10, 100, 1,000 to reinforce inverse operations.

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Notes for the Teacher

• Encourage the student to think aloud to surface their understanding and misconceptions.
• Use consistent terminology aligned with the National Curriculum: “place value,” “decimal point,” “multiply by 10, 100, 1,000.”
• Model good mathematical language and use it in feedback.
• Keep the lesson interactive and visual to maintain engagement in a one-to-one setting.

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This highly focused, curriculum-aligned session will ensure mastery of decimal multiplication by powers of 10 and lays a solid foundation for later concepts such as efficient multiplication and division of decimals.