Power of Place Value

Overview

Curriculum Area: Mathematics and Statistics
Level: Level 3 – The New Zealand Curriculum
Strand: Number and Algebra
Achievement Objective:
Students will be able to use their understanding of place value to multiply and divide whole numbers by 10, 100, and 1000.

Learning Intentions

By the end of this lesson, students will:

• Understand how the value of digits changes when multiplied or divided by 10, 100, and 1000.
• Recognise and apply the place value shifts with confidence.
• Begin to use strategies to solve problems involving multiplication and division by powers of 10.

Success Criteria

Students will:

• Correctly multiply and divide whole numbers by 10, 100, and 1000.
• Explain how and why digits shift places depending on the operation.
• Confidently identify the result of these operations without relying solely on a calculator or written algorithm.

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Resources Required

• Place Value Charts (laminated A3 paper per pair)
• Whiteboard markers and cloths
• Base-ten apparatus or place value dice
• ‘Power of 10’ cards (sets including x10, x100, x1000, ÷10, ÷100, ÷1000)
• Small whiteboards and pens
• Mini plastic cups labelled 1s, 10s, 100s, 1000s
• Counters or linking cubes
• Digital projector (for demonstration)
• Student Math Journals

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Lesson Breakdown – 60 Minutes

⏱ 10 minutes – Mihi & Maths Talk

Karakia/Mihi
Begin with a short karakia and class greeting to set a mindful tone.

Warm-Up Discussion: “What Happens When We Move?”
Pose a simple question to spark thinking:

“If you shift every digit in the number 345 one place to the left, what happens?”

• Explore quick number chats: 10, 100, and 1000.
• Emphasise value over digits.
• Use base-ten tools on the mat to show 123 → shift → 1230.

This primes their thinking and activates prior knowledge.

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⏱ 15 minutes – Discover: Exploring Patterns

Activity: Place Value Relay

1. Divide the 12 students into 4 groups of 3.
2. Each group gets a laminated place value chart, extras counters, and Power of 10 cards shuffled face down.
3. One student in each group draws a Power of 10 card and a whole number card (e.g. 27).
4. As a team, they model the operation using counters on the chart and call out the answer.
5. Other groups check using their own materials and give thumbs up/down to peer-check.

🎯 Teaching Focus During Activity:

• Observe language: Are students saying "move it to the left/right" or “add a zero” vs. “the digit value increases because of position”?
• Encourage explanatory talk: “Why did that happen?”

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⏱ 10 minutes – Explicit Teaching: Place & Power

Mini-Lesson: The Role of Place Value in Powers of 10

Gather students around the front. Using a projector or large whiteboard:

• Model the shifts with the number 56.
• Multiply by 10 → 560; underline each digit and narrate their movement.
• Use cups labelled 1s, 10s, etc., and physically ‘shift’ counters.
• Repeat the process for 56 ÷ 10 and highlight ‘moving right’ to decrease the value.

✅ Emphasise:
“It’s not about adding or taking away zeros — it’s shifting position based on powers of ten.”

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⏱ 15 minutes – Practise: Number Dig Gym

Independent or Paired Task

Students either work solo or in pairs (their choice) to complete "Number Dig Gym":

• Teacher reads out a challenge:
  “Multiply 83 by 100."
  “Divide 3,000 by 100.”
  “Your starting number is 4500. Multiply by 10 then divide by 100.”

Students write their working and answers on small whiteboards. After 2 minutes, they show it on the count of three.

• Mix correct answers with a reflective question:
  “How did you get that?” / “What happened to the digits after dividing?”

Repeat for 5 iterations.

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⏱ 5 minutes – Reflect & Connect

Math Journal Reflection

In their Maths Journals or on a digital device:

“What happens when we multiply a whole number by 10, 100, and 1000?
What did you notice about dividing?”

Encourage the use of diagrams or arrows to show movement of digits.

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Differentiation

Support for Diverse Learners:

• Use of tactile manipulatives (place value cups, counters).
• Visual demonstrations.
• Mixed-ability grouping to encourage peer learning.

Extended Learners:

• Provide larger numbers (in the tens of thousands).
• Challenge: Mix operations (e.g. ×10 then ÷1000).

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Māori & Pasifika Learner Considerations

Use contextually relevant numbers in activities such as Matariki events or quantities in Pacific traditional crafts. Integrate kupu Māori for mathematical terms (e.g., “tahi mano” for 1000). Emphasise oral sharing and whānau-based examples such as sharing kai to represent division.

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Assessment Opportunities

Formative assessment through:

• Observation of place value discussions
• Whiteboard responses during Number Dig Gym
• Journal entries that describe the shift process
• Peer explanations during group tasks

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Teacher Notes

• Consider incorporating student voice in the next lesson by asking:

  “What’s one question you still have about multiplying or dividing by 10, 100, or 1000?”

• This lesson sets a foundation for decimals in future sessions, where digit shifts also cross the decimal point.
• Anchor understanding in meaning, not just tricks. Avoid phrases like "just add a zero".

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Next Steps

In the next lesson:

• Transition into decimal place value, beginning with what happens when we divide by 10 or 100 and the result is no longer a whole number.
• Integrate real-world contexts (e.g. money, measurement) for application.

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Let us know how your class surprises you — these number shifts are magic in the minds of young explorers!