Multiplying Powers of Ten

Lesson Overview

Year Group: Year 6
Subject Area: Mathematics
Curriculum Reference: Key Stage 2, Number – Multiplication and Division
Objective: Multiply whole numbers by 10, 100, and 1,000 confidently and understand the underlying place value relationship.
Time Allocation: 45 minutes
Class Size: 4 students

This lesson will incorporate hands-on activities, visual examples, and collaborative challenges to solidify students’ understanding of multiplying by powers of ten, all while fostering an energetic and engaging learning experience.

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Learning Outcomes

By the end of the lesson, students will:

1. Recognise and explain how digits shift place value when multiplying by 10, 100, and 1,000.
2. Accurately solve problems involving multiplying by these powers of ten in both standard and word problem formats.
3. Apply their learning to real-world situations, demonstrating understanding beyond procedural memorisation.

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Resources

• Mini whiteboards and markers
• Place value charts (pre-printed for each student)
• A set of base-10 manipulatives (blocks, rods, and cubes)
• Large inflatable die with "10," "100," and "1,000" labels on each face (or equivalent cards)
• Colour-coded number cards (e.g., 245, 78) for quick challenges
• A piece of blank A3 paper per group for a collaborative task

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Lesson Breakdown

1. Starter (5 minutes) – Place Value Warm-Up

Activity: "Shifting Digits Game"

• Write the number 45,678 on the board. Ask: "What happens to the digits when it’s multiplied by 10? By 100? By 1,000?"
• Let each student call out their prediction one at a time, giving a rationale. Reveal the answers step-by-step by shifting digits in real time on the board.
• Briefly recap that multiplying by powers of 10 moves digits to the left by 1 place (10), by 2 places (100), or by 3 places (1,000), while placeholders (zeros) appear for empty columns.

Conclude by recapping the link between multiplication and place value.

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2. Introduction (10 minutes) – Modelling and Interactive Teaching

Use the visual of a large place value chart displayed on the board or through classroom manipulatives:

• Direct teaching: Demonstrate how digits shift when multiplying by 10, 100, and 1,000. Use concrete examples such as 24 × 10, 24 × 100, and 24 × 1,000. Map how the base-10 blocks or rods physically "move" across columns, representing the decimal structure.
• Student practice: Provide each student with a mini place value chart and their own manipulatives. Give them simple numbers (e.g., "What’s 83 x 100?") to illustrate in real-time as you demonstrate.

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3. Key Activity (15 minutes) – Group Challenges

Task 1: "Roll and Multiply"

Each student rolls the inflatable die or pulls a power-of-ten card (10, 100, or 1,000).

1. Pick a number card from the deck (e.g., 167).
2. Multiply the number by the power of 10 rolled.
3. Write their answer on their whiteboard and explain how they applied place value shifts.
4. Rotate turns so each student rolls at least twice.

Extension: Introduce decimal numbers (e.g., 3.5 × 100) for advanced learners if appropriate.

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Task 2: "Real-World Multiplication"

Place an A3 sheet of paper on the desk. In pairs, students brainstorm and record scenarios where multiplying by 10, 100, or 1,000 might be useful in everyday life, e.g.:

• Counting costs for 10, 100, or 1,000 units of something in pounds (£).
• Multiplying distances (e.g., kilometres) or quantities in recipes.

Groups share their most creative example with the class. Use guiding questions to check understanding:

• “How did multiplying by 1,000 simplify the calculation?”
• “What would happen to the number if you divided instead?”

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4. Plenary (10 minutes) – Game-Based Recap

Game: "The Fastest Shift Challenge"

• Write a number (e.g., 523) on the board. Students take turns calling out the results of multiplying that number by 10, 100, or 1,000. (Teacher calls "10," "100," or "1,000" randomly to guide the game).
• Wrong answers get a fun "place value penalty" (e.g., explain where they went wrong).

Reflection Question: “Why does multiplying by these powers of ten always move numbers to the left?”

Use this final discussion to consolidate the conceptual reason for calculating using place value shifts.

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Differentiation

• Support: Provide pre-mapped examples on smaller place value charts for struggling learners or allow peer-led explanations during group work.
• Challenge: Involve decimals when multiplying by powers of ten, exploring how tenths, hundredths, and thousandths shift.

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Assessment

• Observing manipulation of resources (e.g., base-10 blocks or place value charts).
• Checking accuracy during whiteboard calculations and group challenges.
• Listening to well-reasoned answers for real-world problems.
• Using reflective questioning during plenary to gauge understanding.

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Homework (Optional)

Students create a mini-poster titled: "Why We Multiply by 10, 100, and 1,000." They should use diagrams or examples covered in class to explain their learning in their own words.

Bring posters back to display in class or share with peers.

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This highly interactive and engaging lesson ensures an excellent blend of hands-on exploration, conceptual clarity, and student ownership of learning outcomes.