Multiplying by 100

Lesson Overview

Duration: 60 minutes
Class size: 30 pupils
Year Group: Year 4
National Curriculum References:

• Mathematics: Number - Multiplication and Division
  • Year 4 programme of study: “Recall multiplication and division facts for multiplication tables up to 12 × 12.”
  • Develop efficient written methods of multiplication.
  • Understand place value and how it affects multiplying by powers of 10.

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Learning Objectives

By the end of this lesson, pupils will:

• Understand the effect of multiplying a number by 100 on its place value.
• Be able to multiply a two-digit or three-digit number by 100 confidently using knowledge of place value.
• Explain, in their own words, why multiplying by 100 shifts digits two places to the left.
• Apply reasoning and justify their answers using mathematical language.

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Success Criteria

Pupils will be successful if they can:

• Explain what happens to each digit’s place value when multiplying by 10 and then by 100.
• Multiply whole numbers by 100 using the correct place value shifts.
• Write clear explanations about the changes in digit value after multiplying by 100.
• Recognise and correct common misconceptions about multiplying by 100 (e.g., confusing adding zeros with multiplying).

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National Curriculum Links

• Number – Multiplication and Division
  Pupils should be taught to “multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers.”
• Number – Place Value
  Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones).

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Resources Needed

• Whiteboard and markers
• Mini whiteboards and pens for pupils
• Place value charts (optional visual aid)
• Printed worksheet with examples, misconceptions, and reasoning questions
• Place value counters or base ten equipment (optional)

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Lesson Structure

1. Introduction (10 minutes)

Hook: “The Mystery of the Moving Digits!”

• Begin by writing the number 47 on the board. Ask:
  “What happens if I multiply 47 by 10?”
• Recap: Multiplying by 10 shifts digits one place value to the left. The 4 moves from tens to hundreds, 7 moves from ones to tens; so 47 × 10 = 470.
• Use a place value chart or base ten blocks to show this visually.
• Then pose the question:
  “What do you think happens if I multiply 47 by 100 instead of 10?”

Whole class questioning:

• “Why do you think the digits move two places instead of one?” (Understanding)
• “Can someone explain away from just saying ‘because it’s 100’ what is actually happening to the digits or the place value?” (Explanation)
• “What would happen if we multiply by 1000? How does that relate to what we've just seen?” (Application)

Quick AFL:
Use mini whiteboards for pupils to write their prediction and reasoning. Collect a few examples for discussion. This checks initial understanding.

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2. Teaching & Modelling (20 minutes)

Step 1: Recap multiplying by 10 quickly

• Revisit: Multiplying by 10 adds one zero to the end for whole numbers and shifts digits one place value to the left.
• Write several examples on the board (e.g., 23 × 10 = 230, 5 × 10 = 50), modelling place value changes explicitly.
• AFL: Ask pupils to explain the place value change verbally or on mini whiteboards.

Step 2: Introducing multiplying by 100

• Explain multiplying by 100 is like multiplying by 10 twice or shifting place values two places to the left.
• Model the process with examples:
  • 47 × 100 = 4700
  • 3 × 100 = 300
  • 126 × 100 = 12,600

Write this example for pupils to copy into books:

Example	Explanation	Result
47 × 100	Move digits two places left (tens→thousands, ones→hundreds)	4,700

• Emphasise the rule: “When you multiply by 100, every digit moves two places to the left on the place value chart.”

Step 3: Common Misconceptions

• Discuss:
  • Confusing “adding two zeros” with actual multiplication (e.g., writing 47 → 470, not 4700).
  • Not adjusting the place value of digits properly with decimals (if applicable in questioning).
• Use deliberate mistakes for pupils to identify and explain why they're wrong.

Targeted whole class questioning using Bloom’s Taxonomy:

• Remembering: “What is the rule for multiplying by 100?”
• Understanding: “Why do the digits move two places on the place value chart?”
• Applying: “How would you multiply 85 by 100? What would happen?”
• Analysing: “If a digit moves two places left, what place value will it be in now?”
• Evaluating: “Someone says multiplying by 100 is just adding two zeros at the end — do you agree? Why or why not?”
• Creating: “Can you create your own number and show me what happens to it after multiplying by 100?”

AFL Checkpoint:
Ask three pupils to explain the rule and reasoning for multiplying by 100 aloud. Use questioning to probe deeper understanding, e.g., “Can you say more about what ‘two places to the left’ means?”

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3. Guided Practice (15 minutes)

• Pupils will work through 6 carefully designed questions on mini whiteboards or in books, showing multiplication by 100 alongside place value explanation.
• Example questions:
  1. Multiply 56 by 100 and explain what happens to each digit.
  2. Multiply 9 by 100 and write why the number changes as it does.
  3. Is 700 the answer to 7 × 100? Explain your thinking.
• Circulate to support, ask for explanations, and address misconceptions.

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4. Independent Practice (10 minutes)

• Pupils complete a short worksheet for detailed practice, including:
  • Multiplying a range of numbers by 100 (two and three-digit numbers).
  • Explaining in sentences the place value shifts.
  • One problem where pupils find an error in a given multiplication and explain why it’s wrong.

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5. Plenary (5 minutes)

• Recap the success criteria and use a “show me” strategy: pupils on mini whiteboards write one sentence explaining what happens to a number when multiplied by 100.
• Select a few pupils to share and explain their thinking.
• Ask reflective questions:
  • “Why is understanding place value important when multiplying by numbers like 10 or 100?”
  • “How can you check if your multiplication by 100 is correct?”
• Reinforce that multiplying by 100 is not just about adding zeros but understanding how digits shift place value.

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Assessment for Learning (AfL) Throughout

• Introduction: Use mini whiteboards for predictions and reasoning (formative).
• During teaching: Ask explanation questions linked to place value changes; listen and note misconceptions.
• Modelling: Pause regularly and ask pupils to explain steps aloud or write thinking.
• Guided practice: Work sampling and questioning to check for understanding & scaffold where necessary.
• Plenary: Pupils explain their thinking in writing; rapid assessment of overall grasp.

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WOW Ideas to Enhance Engagement

• Use physical place value charts with digits on cards that students can physically move two places to the left when representing multiplication by 100.
• Introduce a puzzle challenge:
  “I have a mystery number. When I multiply it by 100, the digits ‘shift’ places. Can you guess the original number if I tell you the answer is 3,800?” Encourage pupils to explain reasoning to solve the puzzle.
• Create a quick class chant or jingle explaining the rule for multiplying by 10, then 100.

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With this lesson plan, pupils will deepen their understanding of multiplying by 100, not just as a rote rule but as a place value concept that links fluently with the National Curriculum and the White Rose Maths Scheme thinking.