Build and annotate the model
Represent multiplying and dividing decimals by powers of 10 and label the important parts, quantities or choices.
Learning goals
Learning goal
Students explain how each digit’s place value changes under multiplication or division by 10, 100 and 1 000, then extend this to factors such as 30, 400 and 0.1-related contexts.
Success criteria
- I can represent or identify the concept.
- I can explain the underlying relationship.
- I can select an appropriate strategy or feature.
- I can apply it in a new context.
- I can justify and verify the response.
Teaching routine
- Represent
- Reason
- Calculate
- Interpret
- Verify
Curriculum focus: multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers
Key concept
Track 4.275 through ×10, ×100 and ÷10
Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.
operationresultdigit-value change4.275 × 1042.75each digit worth 10 times as much4.275 × 100427.5100 times as much4.275 ÷ 100.4275one tenth as much
The decimal point is a fixed notation reference; explain changing digit values rather than saying the point physically moves.
Worked examples
Factor multiples of powers of ten
Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.
2.4 × 300→2.4 × 3 × 100→7.2 × 100→720
For 48 ÷ 0.6, scaling both numbers by 10 gives 480 ÷ 6 = 80; this preserves the quotient.
Curriculum elaborations explicitly taught
AC9M6N06: multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers
- E1: applying place value knowledge, including that the value of the digit is 10 times smaller each time a place is moved to the right, and known multiplication facts, to multiply and divide a decimal by powers of 10
- E2: applying and explaining estimation strategies in multiplicative situations involving a decimal greater than one that is multiplied by a two- or three-digit number, using a multiple of 10 or 100 when the situation requires just an estimation
- E3: explaining the effect of multiplying or dividing a decimal by 10, 100, 1000 … in terms of place value and not the decimal point shifting
Use the central and application models above to connect each elaboration to the same underlying concept.
Common misconceptions
Add zeros rule used with decimalsUse place value; zeros may be placeholders, not a universal rule.
Decimal point said to moveDigits change place value relative to the fixed point.
Factor 300 treated as 3Include the factor of 100.
Division estimate omittedCheck quotient magnitude before accepting.
Classroom activities
Compare and reason
Use the application model to compare two cases, explain the relationship and identify a likely error.
Transfer and verify
Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.
Revision Notes and quick mastery check
Check understanding
- Calculate 4.275 × 100.
- Calculate 72.5 ÷ 10.
- Solve 2.4 × 300.
- Solve 48 ÷ 0.6.
- Explain digit-value change.
Evidence of mastery
- Represent or identify the concept
- Explain the underlying relationship
- Select an appropriate strategy or feature
- Apply it in a new context
- Justify and verify the response
Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.
Curriculum wording and references
Australian Curriculum v9.0
AC9M6N06: multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers
The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.
Resources and next steps
Teacher Slides
Project the fixed, branded four-page teaching sequence.
Open Classroom ViewHomework
Use the printable activity for written practice.
Open HomeworkPractice and Test
Use supported Practice first, then the separate Test when ready.
Open PracticeOpen Test
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Multiply and Divide by Powers of 10
Math Antics — Explain multiplication and division by powers of ten through place-value changes.
As you watch: What happens to the value of each digit when a number is multiplied by 100?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Calculate 3.24 × 100 and 324 ÷ 1000. Explain the place-value changes, then find 3.24 × 200.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Multiply and divide decimals by multiples of powers of 10...
Mapped skill: multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6N06 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6N06 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-MR-01 + MA3-MR-02 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M6N06 — Multiplying and Dividing Decimals by Powers of 10
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