Dividing by Powers

Overview

Grade: 6
Duration: 60 minutes
Class Size: 30 students
Unit: Mastering Place Value (Lesson 9 of 10)
Topic: Dividing Whole Numbers by Powers of Ten
Alberta Curriculum References:

Number - Number Concepts and Operations
- 6-NC4: Demonstrate an understanding of place value in whole numbers and decimals to thousandths, including the effect of multiplying and dividing by powers of 10.
- 6-NA1: Solve problems involving whole numbers and decimals, using mental math strategies and algorithms, including multiplication and division by powers of 10.

Learning Objectives (I can statements)

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

I can explain how dividing a whole number by 10, 100, or 1,000 shifts the place value.
I can divide whole numbers by 10, 100, and 1,000 using place value understanding.
I can solve word problems involving division by powers of ten.

Success Criteria

Students will:

Correctly identify the new place value of digits after division by powers of ten.
Accurately divide whole numbers by 10, 100, and 1,000 using place value shifting.
Demonstrate reasoning by explaining the relationship between division by powers of 10 and place value changes orally or in writing.
Solve at least 4 out of 5 word problems independently or with minimal support.

Materials Needed

Place value charts (printed and laminated per student or pair)
Whiteboards and markers for each student
Base-10 blocks (optional for concrete understanding)
Dyslexia-friendly worksheets (using sans serif font, larger spacing, and colour-coded place value columns)
Projector or interactive whiteboard
PowerPoint/slide showing examples and word problems
Math journal for reflection writing

Lesson Breakdown

1. Engage & Activate Prior Knowledge (10 min)

Begin with a quick review quiz game on place value shifts when multiplying by powers of 10 to consolidate previous lessons. (Example: Multiply 3,245 by 10, 100, 1,000)
Use an interactive place value chart on the whiteboard to visually show digits moving left when multiplying.
Pose the question: “What do you think happens to the digits when we divide by 10, 100 or 1,000?”
Collect student predictions to prime curiosity.

2. Explain - Direct Instruction (15 min)

Introduce the concept: dividing whole numbers by powers of 10 shifts digits to the right on the place value chart.
Model on the interactive board with examples:
- 4,000 ÷ 10 = 400
- 8,500 ÷ 100 = 85
- 63,000 ÷ 1,000 = 63
Use place value charts with arrows showing digit movement right by one, two, or three spaces depending on the power of 10.
Discuss what happens to zeroes and why sometimes digits “disappear” (e.g., 100 ÷ 1,000 = 0.1 – introduce decimals gently as “future learning”).
Use base-10 blocks to visually reinforce the division process for concrete learners.

3. Guided Practice (15 min)

Hand out dyslexia-friendly worksheets with problems involving division by 10, 100, and 1,000.
Students complete in pairs to encourage peer tutoring, supporting diverse learning needs.
Circulate and prompt students with questions: "Where does the 7 move? Why?"
Use whiteboards for students to write their answers and explain reasoning aloud.

4. Differentiation Strategies

For diverse learners or students with specific needs:
- Use colour-coded base-10 blocks and place value charts to reduce cognitive load.
- Provide sentence starters for explaining shifts (e.g., “When I divide by 10, the digits move…”).
- Use small group instruction for those struggling with concepts.
For advanced learners:
- Challenge them with multi-step word problems involving mixed operations (e.g., "If you divide 9,000 by 100 and then multiply by 10, what is the result?").
- Introduce decimal examples where division by 10 results in decimals.
- Prompt students to create their own word problems involving division by powers of 10.
Dyslexia-Friendly Reading Options:
- Ensure all printed materials use clear, sans-serif fonts (such as Arial or Comic Sans) with large font size (>14 pt).
- Use ample spacing and avoid crowding.
- Incorporate colour-coded place value blocks on worksheets to visually guide students.

5. Independent Practice (10 min)

Students complete an activity sheet independently that includes a mix of direct calculations and word problems.
Encourage them to draw place value charts to support their work.
Teacher monitors closely and provides targeted feedback.

6. Formative Assessment & Reflection (5 min)

Quick “exit ticket”: each student writes down one sentence explaining what happens to the number when dividing by powers of 10.
Alternatively, verbal exit ticket: students in turn say aloud an example and explain the place value shift.
Collect exit tickets for assessment of understanding.

Assessment

Formative: Observation during activities, whiteboard responses, exit tickets.
Summative suggestion (for lesson 10 or unit completion): Quiz on multiplying/dividing by powers of ten including both whole numbers and decimals.

Extension Activities

Use digital tools/apps that visually animate division by powers of 10 (e.g., interactive place value games).
Research historical number systems that don’t use place value and compare with our system for deeper understanding.
Explore real-life contexts: money conversions, metric system units (e.g., metres to centimetres, dividing by 100, etc.)

Teacher Notes

Reinforce language around place value (“shift right” means dividing, “shift left” means multiplying).
Encourage students to verbalise their thinking; the “I can explain” part supports metacognition.
Use positive reinforcement and provide immediate feedback to keep students engaged.
Monitor closely for students who struggle with place value concepts, as this underpins future decimal understanding.

Thank you for your dedication to deepening students' understanding of place value and division by powers of ten! This lesson balances visual, kinesthetic, and linguistic modes to support diverse learners while aligning closely with the Alberta Curriculum.

Teaching Instructions