Multiplying by Ten

Overview

This 60-minute lesson introduces Year 6 students to the concept of multiplying whole numbers by ten, building their understanding of place value shifts and numerical patterns. It aligns with the National Curriculum for England’s Maths Programme of Study for Key Stage 2, focusing on Number - Multiplication and Division.

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National Curriculum Links

• Year 6 Multiplication and Division:
  • “Multiply multi-digit numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers.” (Statutory requirement)
  • “Use their knowledge of the order of operations to carry out calculations involving the four operations.”
• Number and place value skills for Year 6:
  • “Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit.”
• Mathematical fluency:
  • Encouragement of efficiency and accuracy in mental calculation involving multiples of 10, 100, and 1000.

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Learning Objectives

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

• LO1: Recognise and explain how multiplying by 10 shifts digits one place to the left in whole numbers.
• LO2: Identify patterns in the place value system when multiplying by 10.
• LO3: Multiply whole numbers by 10 accurately using mental and written methods.
• LO4: Apply multiplication by 10 to solve simple problems in real-life contexts.

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Success Criteria

• I can describe how digits move in place value when multiplied by 10.
• I can multiply any whole number by 10 quickly and correctly.
• I can spot patterns when multiplying numbers by 10.
• I can solve word problems involving multiplication by 10.

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Resources

• Place value charts (large visual aids)
• Whiteboards and pens for each student
• Digit cards (0-9) for hands-on place value activities
• Mini interactive slide presentation to illustrate digit shifts
• Printed real-life scenario problem cards
• Number lines large enough for physical movement activity
• Timer or stopwatch

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Lesson Structure

1. Starter Activity (10 minutes)

Objective: Refresh understanding of place value.

• Begin with a quick mental warm-up asking students to write specific numbers (e.g., 34, 125, 9876) on their mini whiteboards and identify the value of each digit.
• Use digit cards with the class to build numbers on a place value chart in small groups.
• Ask: “What happens to the digits if we multiply this number by 10?” to spark curiosity.

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2. Introduction & Explanation (15 minutes)

Objective: Explain how multiplying by 10 moves digits and affects place value.

• Teacher uses a large place value chart and a number (e.g., 423) with digit cards.
• Demonstrate physically moving digits one place to the left when multiplied by 10 (e.g., 423 → 4230).
• Show the zero placeholder added in the units place.
• Use interactive slides to show multiple examples, including edge cases (e.g., multiples of 10, or numbers ending in zero).
• Emphasise vocabulary: ‘shift’, ‘place value’, ‘ten times larger’.

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3. Guided Practice (15 minutes)

Objective: Practice multiplying by 10, recognising patterns.

• Provide each student with a mini whiteboard.
• Call out random whole numbers (under 1,000 but including some three or four-digit numbers). Students write answers multiplying those numbers by 10.
• Discuss answers, highlighting the digit shift and added zero visually via place value charts.
• Introduce the idea that multiplying by 10 is the same as adding a zero on the right (for whole numbers), but clarify why this only works for whole numbers, and sometimes requires digit shifts to understand.
• Pattern spotting: Challenge students to predict the outcome before calculating (e.g., “What pattern do you notice in the units digit? The tens digit?”).

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4. Independent Application (15 minutes)

Objective: Apply multiplying by ten in problem-solving scenarios.

• Distribute real-life application problem cards with scenarios such as:
  • “If one packet has 15 pencils, how many pencils are in 10 packets?”
  • “A car travels 350 metres in each lap. How far does it travel in 10 laps?”
• Students solve problems individually or in pairs using multiplication by 10, writing full equations and explaining their reasoning.
• Circulate to assist and prompt use of place value language.

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5. Plenary & Assessment (5 minutes)

Objective: Consolidate learning and assess understanding.

• Quick oral quiz: Ask 5 questions where students have to mentally multiply by 10 and explain their answers.
• “What’s happening to the digits?” "Why does this method work?"
• Exit ticket: On a small slip, students write down one thing they learnt and one question they still have.

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Differentiation

• Support:
  • Use digit cards and place value charts for tactile learners.
  • Provide sentence starters for explaining digit movements (e.g., “When we multiply by 10, the ___ moves to the ___ place.”).
• Extension:
  • Challenge more able pupils to predict the result of multiplying by 10 for decimal numbers (to introduce the concept for the next lesson).
  • Investigate patterns in multiplying multiples of 10 by 10 (e.g., 30 x 10, 100 x 10).

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Assessment for Learning

• Formative checks through questioning and mini-whiteboard responses during guided practice.
• Observation during independent work to check use of mathematical language and accuracy.
• Review of exit tickets for understanding and misconceptions to feed into next lesson.

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Cross-Curricular Links

• Science: Measuring distances or quantities (e.g., calculating the length of objects multiplied by 10).
• Geography: Multiplying populations or distances by 10 to conceptualise scale.

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Teacher’s Notes

• Emphasise the conceptual understanding of place value shifts over rote repetition.
• Encourage use of precise mathematical vocabulary to improve fluency and confidence.
• This lesson sets a foundation; the next lesson will explore dividing by 10 and mental strategies with real-life contexts.

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End of lesson plan.