Multiplying Decimal Numbers

Overview

In this ninth lesson of the unit Decimal Fractions and Operations, students develop reliable methods for multiplying decimals by whole numbers. They connect repeated addition, arrays, money and measurement representations to place-value reasoning before recording efficient symbolic calculations.

Learning intentions

• WALT multiply decimals by whole numbers using representations, repeated addition and place value.
• WALT estimate products and use estimation to check whether an answer is sensible.
• WALT explain how the decimal point is placed in a product.
• WALT communicate and compare different mathematical strategies.

Success criteria

• I can model a decimal multiplied by a whole number using an array, money or measurement.
• I can calculate the product accurately using a place-value strategy.
• I can estimate the product before calculating and check my answer afterwards.
• I can explain why the decimal point is in its position.

Curriculum links

• Mathematics and Statistics — Mathsteasers: challenging higher-order thinking questions that deepen understanding for advanced learners.
• Mathematics and Statistics — Mathsteasers / Alignment: mathematical challenge is connected to relevant textbook and unit content.
• Mathematical thinking and communication: students represent, reason, justify, compare strategies and explain generalisations.
• Number learning: students use place value and multiplicative reasoning with decimal fractions.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Open with the opening estimation slide showing 4 × 2.6 alongside four groups of 2.6, and ask, “Will the answer be closer to 8, 10 or 12? How do you know?” Students independently estimate, then share a related multiplication fact from prior lessons, such as (4 \times 26) or (4 \times 0.6).

2. 7–17 min · Build the representation. Use the representation and modelling slides to model (3 \times 1.4) as three groups of 1 whole and 4 tenths, using a place-value chart and money notation ($1.40). Teacher records repeated addition: (1.4 + 1.4 + 1.4 = 4.2), then connects this to (3 \times 14 = 42) tenths, or 4.2. Students build and explain a second example, (5 \times 0.7), using a place-value chart or a quick drawing.

3. 17–27 min · Gradual move to symbols. Display the worked examples in the place-value strategy slides. Explicitly model: estimate first, multiply as whole-number digits, then use place value to rename the result. For (6 \times 2.35), students identify 235 hundredths, calculate (6 \times 235 = 1410), and rename 1410 hundredths as 14.10, or 14.1. Emphasise that the decimal point is not “just moved”; the product is renamed according to the unit being counted. Students complete two guided examples on the guided modelling and practice worksheet and justify each decimal placement to a partner.

4. 27–43 min · Collaborative problem solving. Distribute the decimal multiplication problem-solving worksheet. In pairs, students solve a progression of problems using at least two representations for selected questions: an array, repeated addition, money or measurement. Include contexts such as 4 lengths of 1.25 m, 6 items costing $0.75, and 8 groups of 0.6 L. Students estimate before calculating, record a method, and circle the step that proves the decimal placement. Teacher conferences with pairs, asking, “What unit are you counting?” and “How does your estimate help?”

5. 43–53 min · Place-value generalisation. Use the pattern and challenge slides and the place-value slider. Students investigate examples such as (2.4 \times 10), (2.4 \times 100) and (2.4 \times 1,000), then test a decimal with two or three decimal places. They use the slider to show how each digit changes place and explain the pattern in words. Invite students to identify when a zero is needed as a placeholder.

6. 53–60 min · Plenary and exit check. Return to the discussion and exit-question slide. Students compare two statements: “To multiply by 10, add a zero” and “To multiply by 10, each digit becomes ten times its value.” They decide which is more accurate and explain why. Students complete the final question on the independent exit-ticket section: estimate and calculate (7 \times 1.08), then explain the decimal point using place value.

Resources

• the complete decimal multiplication slide deck
• the decimal multiplication worksheet
• the Standard Form Place Value Slider
• Place-value charts
• Base-ten materials or decimal grids
• Coins and notes, or a money model
• Rulers or metre strips
• Mini-whiteboards and pens
• Calculators for checking, not for first attempts

Assessment

• Listen for whether students describe the product in tenths or hundredths rather than relying on a rule about “moving the decimal”.
• Check worksheet representations, estimates and explanations during pair work; note students who need support with renaming units.
• Use the exit question to identify whether students can connect a correct calculation to a place-value explanation. Revisit misconceptions in the next lesson.

Differentiation

• Support: provide place-value charts, decimal grids, money and measurement models; begin with one-decimal examples and use repeated addition before moving to symbolic recording.
• Provide sentence starters: “I estimated ___ because…”, “There are ___ hundredths, so…”, and “The decimal point is placed here because…”.
• For EAL learners and students needing additional support, pre-teach product, tenths, hundredths, estimate and rename with visual examples; pair them with a supportive peer and reduce the number of questions without reducing the reasoning demand.
• Extension: students generalise multiplying decimals by 10, 100 and 1,000, including numbers with trailing or placeholder zeroes, and create a misleading worked example for a partner to diagnose and correct.