Year 6 Mathematics · AC9M6N04

Adding and Subtracting Decimals

Use place value, efficient strategies, estimation and digital verification

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students align place values, rename when regrouping, choose mental or written strategies and compare exact results with purposeful estimates.

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: apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers
Key conceptTeach from the board

Calculate 18.375 + 6.84 by aligning place values

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

tensonestenthshundredthsthousandths18375684025215

Write 6.84 as 6.840 to align equal place values. Placeholder zeros clarify structure without changing value.

Choose an efficient subtraction strategy

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

32.00 − 9.875written regrouping
19.95 + 7.60compensation: 20 + 7.60 − 0.05
48.6 − 19.9subtract 20, then add 0.1
digital toolverify after setup and estimation

Estimate before calculating: 18.375 + 6.84 is about 18.4 + 6.8 = 25.2, so 25.215 is reasonable.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6N04 - Adding and Subtracting Decimals
Example 1

tens ones tenths hundredths thousandths 1 8 3 7 5 6 8 4 0 2 5 2 1 5

Example 2

32.00 − 9.875 written regrouping

Example 3

: applying estimation strategies to addition and subtraction of decimals to at least thousandths before calculating answers or when a situation requires just an estimation

Example 4

: applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredths

Curriculum examplesCopied content

AC9M6N04: apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers

  • E1: applying estimation strategies to addition and subtraction of decimals to at least thousandths before calculating answers or when a situation requires just an estimation
  • E2: applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredths
  • E3: working additively with linear measurements expressed as decimals up to 2 and 3 decimal places; for example, calculating how far off the world record the athletes were at the last Olympic games in the women’s long jump or shot-put and comparing school records to the Olympic records
  • E4: deciding to use a calculator as a calculation strategy for solving additive problems involving decimals that vary in their number of decimal places beyond hundredths; for example, 1.0 - 0.0035 or 2.345 + 1.4999

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Add 18.375 and 6.84.
  • Subtract 32 − 9.875.
  • Use compensation for 48.6 − 19.9.
  • Estimate first.
  • Explain placeholder zeros.

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
Decimal points not alignedAlign place values, not final digits.
Zeros added to the left or inside incorrectlyOnly trailing placeholder zeros preserve a decimal’s value.
Estimate omittedUse it to detect misplaced decimal points.
Calculator result accepted without contextCheck operation, input and magnitude.
Curriculum alignmentStart here

Learning goal

Students align place values, rename when regrouping, choose mental or written strategies and compare exact results with purposeful estimates.

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: apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers
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