Year 6 Mathematics · AC9M6N06

Multiplying and Dividing Decimals by Powers of 10

Track changing digit value and factor multiples of ten

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Learning goalsSay it simply

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

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. 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 conceptTeach from the board

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.

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.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6N06 - Multiplying and Dividing Decimals by Powers of 10
Example 1

operation result digit-value change 4.275 × 10 42.75 each digit worth 10 times as much 4.275 × 100 427.5 100 times as much 4.275 ÷ 10 0.4275 one tenth as much

Example 2

2.4 × 300 → 2.4 × 3 × 100 → 7.2 × 100 → 720

Example 3

: 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

Example 4

: 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

Curriculum examplesCopied content

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.

Questions and answersWith answers

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.

Practice and reviewReady for practice
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.
Curriculum alignmentStart here

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

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. 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
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