Lesson 8 of 10: Multiplying Whole Numbers by Powers of Ten

Grade: 6

Duration: 60 minutes

Class Size: 30 students

Unit Title: Mastering Place Value

Alberta Curriculum Reference:

• Number - Number Concepts:
  • 6.N.2 - Represent, compare, and describe whole numbers (up to 100 000) and decimals (to thousandths).
  • 6.N.3 - Use place value to multiply and divide whole numbers by powers of 10 and explain the effect.

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Learning Objectives

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

• I can multiply whole numbers by 10, 100, and 1,000.
• I can explain how multiplying by powers of ten affects the place value of digits in a number.
• I can demonstrate shifting of digits in whole numbers when multiplied by powers of ten using visual and numerical strategies.

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Success Criteria

Students will demonstrate success when they:

• Multiply whole numbers by 10, 100, and 1,000 accurately (e.g., 23 × 100 = 2,300).
• Explain the relationship between place value and movement of digits in a multiplication by powers of ten.
• Use base-ten blocks, place value charts, or diagrams to visualize the multiplication process.
• Complete a short formative assessment with at least 80% accuracy.

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Materials Needed

• Whiteboard and markers
• Place value chart handouts (dyslexia-friendly font: OpenDyslexic or Arial)
• Base-ten blocks or virtual manipulatives (interactive app/tablet if available)
• Multiplication by powers of ten activity sheets with visual aids
• Mini whiteboards for student responses
• Timer or stopwatch
• Extension task sheets for advanced students
• Sentence starters and graphic organizers

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Lesson Sequence

1. Warm-up & Review (10 minutes)

Activity: Quick place value review

• Write several 4- and 5-digit numbers on the board (e.g., 4,372; 25,609).
• Ask students "What value does the digit 3 have in 4,372?" and "What happens if we multiply 4,372 by 10?"
• Use "I can..." statements:
  • I can identify place value in whole numbers.
  • I can explain digit value changes when multiplying by 10.

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2. Introduction to Multiplying by Powers of Ten (10 minutes)

Concrete-Pictorial-Abstract (CPA) approach:

• Show physical base-ten blocks representing a number (e.g., 43) and then attaching ten times as many blocks to show multiplication by 10.
• Use a place value chart to shift digits left one place for ×10, two places for ×100, and three places for ×1,000.
• Model multiplying 43 by 10, 100, and 1,000 on the whiteboard using expanded form:
  • 43 × 10 = (40 + 3) × 10 = 400 + 30 = 430
• Dyslexia-friendly: Use colour-coding for place value columns and clear spacing.

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3. Guided Practice (15 minutes)

• Distribute place value charts and manipulatives.
• In pairs, students multiply numbers (up to 5 digits) by 10, 100, and 1,000 using charts and blocks.
• Encourage students to verbalize their thinking aloud:
  • "When I multiply by 1,000, each digit moves three places to the left."
• Circulate to assess understanding and provide individual support.

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4. Independent Practice (15 minutes)

• Students complete a worksheet that includes:
  • Multiplying whole numbers by 10, 100, and 1,000.
  • Explaining the effect in writing or using a place value chart.
• Support: Provide a checklist for students with dyslexia and sentence starters like:
  • "When I multiply by 10, the digits ______."
  • "The place value of the digit _____ increases because ____."
• Use mini whiteboards for quick formative checks on select problems.

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5. Extension Activities (for advanced learners)

• Explore multiplying by higher powers of ten (10,000 or 100,000).
• Introduce problems combining multiplication by powers of ten with multi-digit numbers (e.g., 348 × 1,000).
• Challenge: Write real-world word problems involving multiplication by powers of ten and solve using place value reasoning.

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6. Reflection & Closing (10 minutes)

• Summarize key learning points using “I can…” statements for class discussion:
  • I can multiply whole numbers by 10, 100, and 1,000.
  • I can explain how digits move left depending on the power of ten.
• Exit ticket question: Write one example of a number multiplied by a power of ten and describe what happens to the digits.
• Address any misconceptions noticed during practice.

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Differentiation Strategies

• For Struggling Learners:

  • Use tactile manipulatives extensively (base-ten blocks).
  • Provide step-by-step visual guides and place value charts with coloured columns.
  • Allow verbal or drawing-based responses instead of writing.

• For English Language Learners:

  • Use visual supports and key vocabulary cards (e.g., “place value,” “digit,” “multiply,” “power of ten”).
  • Pair with a buddy or small group for peer explanations.

• For Students with Dyslexia:

  • Use dyslexia-friendly fonts and high-contrast materials.
  • Provide audio instructions or recorded explanations (if technology permits).
  • Offer extra processing time and support with written explanations.

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Assessment & Evaluation

• Formative:

  • Observation during pair work and guided practice.
  • Mini whiteboard responses and exit tickets.
  • Worksheet completion with immediate feedback.

• Summative (later in the unit):

  • Include problems multiplying whole numbers by powers of ten in a unit test.

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Teacher Reflection Notes

• Were all students able to visualize and explain the digit shifts?
• Did manipulatives support learner understanding?
• Did differentiation meet diverse learning needs effectively?
• What could be improved for next time?

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Summary

This lesson empowers students with the understanding of how multiplying by powers of ten changes place value by shifting digits – a critical foundational skill in the Alberta Grade 6 mathematics curriculum. Using a balanced CPA approach, paired activities, and dyslexia-friendly materials, students deepen comprehension and develop confidence through hands-on and visual learning.