Build and annotate the model
Represent adding and subtracting decimals and label the important parts, quantities or choices.
Learning goals
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
- Represent
- Reason
- Calculate
- Interpret
- 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 concept
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.
Worked examples
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.
Curriculum elaborations explicitly taught
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.
Common misconceptions
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.
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
- 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.
Curriculum wording and references
Australian Curriculum v9.0
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
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: Adding Decimals: Example 1
Khan Academy — Add decimals by aligning equal place values; subtraction and checking are developed in the written lesson.
As you watch: Why should tenths line up with tenths rather than just lining up the last digits?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Estimate and calculate 12.45 + 3.8. Explain how a place-value chart can help you check the result.
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 Apply knowledge of place value to add and subtract decimals...
Mapped skill: 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
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 | AC9M6N04 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6N04 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-RN-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: AC9M6N04 — Adding and Subtracting Decimals
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