Multiplying Decimal Fractions

Overview

In this tenth lesson of the unit, students connect decimal multiplication to place value, area models and partitioning. They use estimation and reasoning to decide whether a product is sensible, building on prior work with decimal place value, fractions and multiplication strategies.

Learning intentions

• WALT multiply decimal fractions to hundredths.
• WALT use models, partitioning and place-value reasoning to solve multiplication problems.
• WALT choose an appropriate mental or written strategy.
• WALT estimate and check the size of a product.

Success criteria

• I can multiply decimals to hundredths accurately.
• I can represent a decimal multiplication using a grid, partitioning or another suitable strategy.
• I can explain how place value affects the product.
• I can check whether my answer is a sensible size.

Curriculum links

• Mathematics and Statistics — Number: multiplicative thinking, decimal place value and operations.
• Mathematics and Statistics — Number: connecting fractions, decimals and multiplication.
• Mathematics and Statistics — mathematical practices: representing, explaining, choosing strategies and checking reasonableness.
• Mathsteasers: challenging higher-order thinking questions that deepen understanding for advanced learners.

Lesson structure (60 minutes)

1. 0–7 min · Hook and estimate. Teacher displays a rectangle labelled 0.4 by 0.3 and asks, “Will its area be greater or less than 0.4? How do you know?” using the opening estimation slide. Students make an individual estimate, justify it to a partner and share the key idea that multiplying by a number less than one reduces the result.

2. 7–18 min · Model the meaning. Teacher uses a hundredths grid on the area-model teaching slides to model (0.4 \times 0.3), then connects the 12 shaded hundredths to (0.12). Teacher models a second example, (0.6 \times 0.25), showing that 6 tenths of 25 hundredths is 15 hundredths. Students annotate the model and explain what each factor represents.

3. 18–28 min · Connect strategies. Teacher demonstrates (0.34 \times 0.2) by partitioning (0.34 \times (0.1+0.1)), then links this to multiplying as whole numbers and reasoning about two decimal places. Students solve two guided examples on the guided modelling and strategy worksheet, first drawing or using a grid and then recording a suitable written or mental strategy.

4. 28–43 min · Paired practice. Teacher distributes the guided modelling and strategy worksheet and conferences with pairs, prompting: “What do you know about the size of the answer?”, “Which place-value columns are involved?” and “How can you check it?” Students complete a progression of problems, including (0.3 \times 0.7), (0.4 \times 0.25), (1.2 \times 0.06) and (2.35 \times 0.4). They must show a model, partitioning or written strategy for selected questions and record an estimate beside each answer.

5. 43–53 min · Reasoning challenge. Teacher presents the comparison prompts on the reasoning challenge slides: “Which is larger: (0.8 \times 0.6) or (0.8 \times 0.9)? Explain without calculating both fully” and “A student says (0.7 \times 0.4=2.8). What mistake might they have made?” Students discuss in pairs, write a clear explanation and compare methods with another pair. Invite several students to explain how the factors’ size helps predict the product.

6. 53–60 min · Plenary and exit check. Teacher revisits the learning intentions using the plenary and exit-check slide. Students complete an exit response: solve (0.24 \times 0.3), show or describe one strategy, and state why the answer must be less than (0.24). Collect responses to identify who needs further modelling in the next lesson.

Resources

• the decimal multiplication slide deck
• the guided modelling and strategy worksheet
• Hundredths grids or squared paper
• Mini-whiteboards and pens
• Pencils, rulers and highlighters
• Projector or interactive display
• Calculators for checking only, if appropriate

Assessment

• Listen during the hook and modelling discussion for correct use of decimal and place-value language.
• Check worksheet representations, estimates and explanations, not only final answers; conference with students who misplace the decimal point.
• Use the exit response to assess accuracy, strategy choice and understanding that multiplying by a factor less than one reduces the product.

Differentiation

• Provide pre-drawn hundredths grids, colour-coded tenths and hundredths, worked examples and a step-by-step template: estimate, represent, multiply, place value, check.
• Begin support students with simpler factors such as (0.2 \times 0.3) and (0.4 \times 0.5), and allow oral explanations, partner rehearsal or use of squared paper.
• Use explicit vocabulary and sentence starters for EAL learners: “My product is ___ because ___”; “The answer is less than ___ because ___.”
• Extend confident students to investigate products of two decimals, such as (0.36 \times 0.24), and explain generally why multiplying by a number between zero and one can reduce a result. Ask them to create a product close to, but less than, 0.1 and justify it.