Decimal Rules Sprint

Overview

This lesson continues “Mastering Maths Concepts” by building practical fluency for multiplying and dividing decimals, using place value and patterns so students can choose efficient strategies. Students will also use a quick check to recognise when answers should terminate (end) rather than continue forever.

Learning intentions

Students will:

• apply the rules for multiplying decimals using place value
• apply the rules for dividing decimals by making the divisor a whole number
• estimate to check whether an answer is reasonable
• recognise terminating versus recurring decimal results using digital tools

Success criteria

Students can:

• explain how many decimal places to place after multiplication
• rewrite a division with a decimal divisor as an equivalent division with a whole number divisor
• use estimation to identify incorrect answers
• determine whether a decimal result should terminate or recur (with support)

Curriculum links

• Mathematics — Number: recognise terminating and recurring decimals, using digital tools as appropriate - Mathematics — Number: use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate - Mathematics — Number: use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts ## Lesson structure (30 minutes)

1. 0–4 min · Retrieval hook Teacher writes two rapid prompts on the board: “What is 0.6 × 0.5?” and “What is 2.4 ÷ 0.6 (approx.)?” Student answers quickly, then shares their estimate method (rounding to nearest whole number or tenth).

2. 4–10 min · Direct teaching: multiplying decimals Teacher models:

• Move to “ignore decimals” by treating 0.23 × 0.4 as 23 × 4, then place decimals back.
• Show counting decimal places: total decimal places in the product equals (decimals in first factor + decimals in second factor).
• Example: 0.23 × 0.4 → 23 × 4 = 92, and 2 (from 0.23) + 1 (from 0.4) = 3 decimal places → 0.092. Student completes a guided pair: 1.2 × 0.35 and explains the decimal-place count aloud.

3. 10–18 min · Direct teaching: dividing decimals Teacher demonstrates the “scale-up” method: multiply both numbers in the division by the same power of 10 so the divisor becomes a whole number.

• Example: 3.6 ÷ 0.12 Multiply by 100 → (3.6 × 100) ÷ (0.12 × 100) = 360 ÷ 12 = 30.
• Emphasise: multiply numerator and divisor by the same factor, so the value stays unchanged. Student practices: 2.8 ÷ 0.7 and 5.4 ÷ 0.09, stating the scale-up factor (×10 or ×100) before calculating.

4. 18–24 min · Check & reason: estimating and decimal behaviour Teacher sets a short “reasonableness check” routine:

• Estimate by rounding (e.g., 0.7 ≈ 1, 0.35 ≈ 0.4)
• Compare estimate to computed answer
• If needed, use a calculator to distinguish terminating vs recurring decimals. Student calculates one problem fully and checks with estimation:
• 0.75 ÷ 0.25 Then asks: “Should this terminate or recur?” Student confirms using a digital tool and notes the result ends.

5. 24–29 min · Mini task: mixed operations (real context) Teacher provides a simple context relevant to Year 8: “A student buys 0.8 kg of fruit for $3.50 per kg. What is the cost?” (multiplication) “They have $10 and want to split the cost equally among 4 friends. How much does each friend pay?” (division by a whole number is a rational division step) Student solves in two stages, recording calculations and one sentence explaining the strategy used.

6. 29–30 min · Exit ticket Teacher gives:

• a) 0.06 × 0.5 =?
• b) 4.5 ÷ 0.9 =?
• c) Predict: does 1 ÷ 3 end or recur? (terminating or recurring) Student submits answers, using a sentence for (b) describing how they removed the decimal from the divisor.

Resources

• Whiteboard and markers
• Printed mini task/exit ticket sheet
• Calculator or phone/tablet calculator (teacher-controlled if needed)
• Base-ten place value chart or paper for counting decimal places
• Scaffolding cards: “Multiplication decimal places” and “Division scale-up method”
• Rounding strips (tenth/whole number rounding guidance)

Assessment

• Teacher observes students’ reasoning during multiplication decimal-place counting and division scale-up factor choice.
• Formative checks:
• quick questioning during examples (“How many decimal places now?” “What did you multiply by to make the divisor a whole number?”)
• compare student estimates to actual answers before finalising
• Exit ticket: correct answers plus a brief explanation for division method and a terminating/recurring prediction for 1 ÷ 3.

Differentiation

• Support:
• Provide sentence starters: “First I ignore the decimals…”, “I count decimal places…”, “I multiply by 10/100 so the divisor is…”
• Use a worked example template for division with a decimal divisor.
• Challenge/extension within the lesson:
• Ask for an alternative method: for multiplication, also use area/partition reasoning; for division, compare scale-up vs converting to a fraction.
• EAL/SEN considerations:
• Keep language consistent: “scale-up”, “decimal places”, “same value” and encourage the student to point to the place-value locations rather than rely only on terminology.
• Independent pacing for a class of 1:
• Move quickly through guided steps; allow extra time for the exit ticket if needed and reduce practice amount if accuracy is low.