Decimal Multiplication

Overview

Today students will solve decimal multiplication problems by using place value partitioning and efficient mental strategies, then check whether their answers are reasonable. This builds on earlier work with multiplication and place value, and connects multiplication to arrays and algorithms.

Learning intentions

Students will be able to:

• solve multiplication problems involving decimals by partitioning numbers into place value parts
• explain strategies (e.g., splitting into hundreds/tens/ones and tenths/hundredths)
• choose an efficient method for one- or two-digit multipliers
• use estimation to check the reasonableness of answers

Success criteria

• I can multiply decimals by one- or two-digit numbers using place value (e.g., 3.24 × 8).
• I can show my thinking (parts method/array or written algorithm) and label place values.
• I can estimate first and explain if my exact answer is reasonable.
• I can use digital tools (calculator/spreadsheet) to verify, not replace, my reasoning.

Curriculum links

• Number — multiplication of larger numbers by one- or two-digit numbers; choose efficient calculation strategies; use digital tools where appropriate; check reasonableness of answers - Number — interpret and compare decimals using place value understanding ## Lesson structure (60 minutes)

1. 0–5 min · Warm-up: quick estimates

• Teacher displays: “Estimate first, then compute: 2.4 × 6”
• Students do a silent estimate (e.g., 2.4 is close to 2.5; 2.5 × 6 = 15), then compute on mini-whiteboards.

2. 5–12 min · Mini-teach: place value partitioning

• Teacher models with a short worked example: 3.24 × 8.
• Students watch and then complete a second example together: 1.6 × 7 by thinking of 1.6 = 1 + 0.6 and using (1×7) + (0.6×7).

Key teaching points (say and display):

• Split the decimal into place value parts (ones, tenths, hundredths).
• Multiply each part by the whole number.
• Add partial products, keeping track of decimal places using place value (not guesswork).
• If there is a two-digit multiplier, use breaking apart (e.g., 16 = 10 + 6) and add results.

3. 12–22 min · Guided practice: parts method

• Teacher places three problems on the board, one at a time, and ticks a strategy checklist: “Estimate → Partition → Multiply parts → Add → Check”.
• Students work in pairs; teacher circulates and prompts students to verbalise place value decisions.

Problems (appropriate difficulty for Year 5):

• A: 0.7 × 12
• B: 4.35 × 8
• C: 2.6 × 15 (use 15 = 10 + 5)

Teacher prompts:

• “What does the ‘7’ in 0.7 represent?”
• “Where will your decimal point land when you add the partial products?”
• “How do you know your answer is sensible?”

4. 22–30 min · Efficiency choice: strategy comparison

• Teacher shows two solution sketches for one problem: 3.05 × 6.
• Students compare methods in a short discussion: partitioning vs. a simplified written algorithm using place value.
• Students vote: which is easier and why, and what might go wrong (e.g., losing track of decimal places).

Target reasoning:

• 3.05 × 6 = (3×6) + (0.05×6) where 0.05×6 = 0.30, so total 18.30.

5. 30–46 min · Independent task: decimals around the classroom

• Teacher distributes a worksheet or task card set with 6 questions:
• Mix of one-digit and two-digit multipliers
• Include at least one with tenths only (e.g., 2.4 × 13), one with hundredths (e.g., 1.25 × 8), and one with whole number part (e.g., 6.3 × 12).
• Students complete Questions 1–4 independently first, then choose either Q5 or Q6 (choice supports differentiation).
• Students must include:
• an estimate written at the top
• a worked method with clear place value
• a final reasonableness check

6. 46–55 min · Formative check: quick share and correction

• Teacher selects 2–3 student exemplars (anonymous) showing different strategies and common errors (e.g., treating decimals like whole numbers).
• Students discuss: “What is correct? What needs adjusting? How can we check?”

Common misconception to address:

• “Forgetting that tenths/hundredths are parts of 1, so partial products must be positioned accordingly.”

7. 55–60 min · Exit ticket

• Students complete one problem independently:
• “Estimate and calculate: 5.4 × 13. Then write one sentence: Is your answer reasonable? Why?”
• Collect for quick marking.

Resources

• Mini-whiteboards, markers, erasers
• Board/visualiser for worked examples and strategy steps
• Worksheet/task cards with decimal multiplication questions (including tenths and hundredths)
• Number line or place value grid (tenths/hundredths shading) for teacher reference
• Digital tools: class calculator or student tablets (for checking only)
• Estimation reference card (e.g., rounding rules and “close-to” benchmarks like 0.5, 1, 2.5, 5)

Assessment

• Formative during warm-up: accuracy of estimate and final computation (listen for strategies)
• Guided practice checks: observe whether students partition decimals correctly and explain place value decisions
• During independent task: use a quick checklist
• estimate present
• partial products shown with place value
• reasonableness check included
• Exit ticket: assess correctness and the quality of the reasonableness explanation

Differentiation

• Support:
• Provide a partially completed example modelled on the worksheet (with place value headings: ones/tenths/hundredths).
• Sentence starters for reasoning: “My answer is reasonable because…”, “I estimated by rounding…”.
• Use a place value grid for students who need the decimal parts physically represented.
• Extension:
• Include a challenge question: “Which strategy is most efficient for 7.02 × 9: partitioning or splitting 9 into factors? Explain.”
• Ask students to create a similar problem for a partner with a decimal including hundredths and a two-digit multiplier.
• EAL/SEN considerations:
• Reduce language load by using consistent labels (ones, tenths, hundredths; estimate; calculate; check).
• Allow explanation orally or with diagram plus a short written sentence.
• Procedure adjustments:
• For students needing more time, require Questions 1–3 only, but still include estimate and reasonableness check for those.