Decimal Power

Overview

Today students strengthen their understanding of decimal place value and use efficient strategies to add, subtract, multiply and divide with positive decimals. They also round to an appropriate accuracy and interpret results in a practical context.

Learning intentions

Students will be able to:

• explain what each digit in a decimal represents using place value
• round decimals to a given accuracy appropriate to a context
• solve addition, subtraction, multiplication and division problems with positive rational numbers (decimals) using efficient strategies
• interpret and justify whether a rounded answer is reasonable for the situation

Success criteria

• I can match digits to place values (tenths, hundredths, thousandths) and write decimals in expanded form.
• I can round a decimal to a specified number of decimal places and state the rounding rule used.
• I can choose an efficient strategy to calculate with decimals and check the reasonableness of my answer.
• I can explain what my final answer means in the real-world scenario.

Curriculum links

• Number — AC9M7N04: represent and interpret rational numbers (including decimals) on a number line and connect forms.
• Number — AC9M7N05: round decimals to a given accuracy and use estimation to check reasonableness.
• Number — AC9M7N06: use the 4 operations with positive rational numbers including decimals to solve problems using efficient calculation strategies.
• Number — AC9M7N09: use mathematical modelling to solve practical problems involving rational numbers and percentages, interpret solutions in context, and justify representation choices.

Lesson structure (60 minutes)

1. 0–5 min · Hook (decimal in the wild). Teacher displays a short prompt: “A drink costs $3.75. You pay with $5.00. How much change?” Students do a quick silent estimate and share their estimate only.

2. 5–15 min · Place value recap + mini modelling. Teacher uses a place value chart to show 3.75 and asks: “What is the 7? What is the 5?” Students complete:

• expanded form of 3.75 (3 + 0.7 + 0.05)
• locate 3.75 on a number line marked at whole numbers and tenths (teacher checks common misconceptions about tenths vs hundredths).

3. 15–28 min · Direct teach: efficient operations with decimals. Teacher models one example for each operation, emphasising a consistent strategy:

• Addition/subtraction: 8.2 + 1.35 and 10.5 − 2.17 (align decimal places; regroup if needed)
• Multiplication: 3.2 × 0.5 (rewrite as 16 × 0.1 × 0.5 or use “multiply as whole numbers then place the decimal”)
• Division: 6.3 ÷ 0.3 (turn into 63 ÷ 3, or use scaling) Students follow using the same structure on mini whiteboards, then explain one step in words to a partner.

4. 28–38 min · Rounding to accuracy + checking reasonableness. Teacher states the purpose: “We’ll round when the situation requires an estimate (like money, paint, time).” Students practise rounding:

• Round 12.346 to the nearest tenth, and to the nearest hundredth
• Round 3.75 to the nearest dollar, then to the nearest cent Teacher prompts checking: “Is your rounded answer close enough for the task? Would you expect it to be slightly bigger or smaller?”

5. 38–50 min · Practice task: real-world calculation. Teacher provides a context (on slides or handout): “A school is ordering classroom paint. Coverage is 7.5 m² per litre. The wall area is 63.2 m². Estimate the litres needed, then compute more accurately.” Students do:

• Estimate: round 63.2 to 1 decimal place (or nearest whole depending on the question) and divide by 7.5 to get an estimate.
• Accurate calculation: 63.2 ÷ 7.5.
• Decision: state how many litres to order using an appropriate rounding choice (e.g., round up to ensure enough paint). Teacher circulates to check decimal placement, division strategy, and the suitability of rounding for context.

6. 50–58 min · Assessment (individual). Students complete an assessment sheet (8–10 minutes work time + 1 minute check):

• A place value item: “Write 4.037 in expanded notation.”
• Two operations: one addition/subtraction and one multiplication/division with decimals.
• Rounding: “Round 18.256 to the nearest hundredth.”
• Reasonableness check: “Is 3.6 m² or 3.61 m² more reasonable for a measurement rounded to hundredths? Explain briefly.” Students show working and a short justification sentence for the rounding choice.

7. 58–60 min · Exit ticket (quick check). Exit ticket (2 questions):

• “Round 5.149 to 1 decimal place.”
• “Estimate 9.7 ÷ 0.5. Is your estimate an overestimate or underestimate? Why?” Students submit for immediate feedback.

Resources

• Place value chart (tenths/hundredths/thousandths) and markers
• Mini whiteboards and pens
• Teacher notes with worked examples for all four operations
• Number line (0 to 5 with tenths)
• Practice task sheet (paint coverage model)
• Individual assessment sheet with decimals and rounding items
• Exit ticket slips or digital form
• Calculator optional for the practice stage (teacher choice), emphasise estimation before using

Assessment

• Formative checks:
• Observe place value explanations during the 5–15 minute number line and expanded form tasks
• Monitor whiteboard calculations for correct alignment of decimal places and correct decimal placement after multiplication/division
• Listen for reasoning about why a rounded answer is suitable for the situation
• Summative check (58–60 minutes):
• Exit ticket responses for rounding accuracy and estimation reasonableness
• Collect/mark (50–58 minutes):
• Assessment sheet for computational accuracy, representation (expanded form), and justification for rounding

Differentiation

• Support:
• Provide sentence starters: “I rounded to … because …” and “My estimated answer is … so it should be an over/under estimate.”
• Offer a worked example template for each operation (align decimals, then compute; or multiply whole numbers and place decimals).
• Allow manipulatives (place value cards) for students who struggle with decimal place value.
• Extension:
• Add a second decision: “Would rounding to the nearest tenth or hundredth change the number of litres ordered? Explain.”
• EAL/SEN considerations:
• Use consistent terms: tenths, hundredths, thousandths; “round to” means “nearest …”
• Keep contexts concrete (money, paint coverage) and rephrase the problem aloud once before independent work.
• Calculation access:
• Permit calculator use in the accurate calculation step only, but require an estimate and rounding justification before any calculation.