Decimal Problem Solving

Overview

This is lesson 11 of 15 in the unit Number Connections: Fractions, Decimals, Percentages. Students apply decimal knowledge to realistic problems involving money, sports statistics and distance, while explaining their reasoning and checking whether answers are sensible.

Learning intentions

• WALT solve and communicate solutions to decimal problems.
• WALT identify relevant information and choose an appropriate operation.
• WALT represent decimal thinking clearly using equations, diagrams and words.
• WALT evaluate whether an answer makes sense in its context.

Success criteria

• I can identify the important information and the question.
• I can select and use an appropriate operation.
• I can show clear working and explain my strategy.
• I can check whether my answer is reasonable and includes a suitable unit.

Curriculum links

• Number: use place value and decimal knowledge to solve addition, subtraction, multiplication and division problems.
• Number: connect fractions, decimals and percentages in familiar contexts.
• Mathematical processes: reason, represent, communicate and justify mathematical ideas.
• Use mathematical and statistical information to make decisions and check the reasonableness of results.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and connect Open with the problem-solving hook and learning intention. Display: “A class shop sells three items for $2.40, $1.75 and $0.85. How could we work out the total, and how can we check it?” Students estimate first, then share what information is relevant. Emphasise that an estimate is a useful reasonableness check, not just a guess.

2. 5–12 minutes – Model a problem-solving routine Use the worked-example slides to model the class-shop problem. Think aloud through: understand the problem, choose an operation, solve, communicate and check. Record the equation vertically, align decimal points, include the dollar sign, and compare the exact answer with the estimate. Ask: “What might go wrong if the decimal points are not aligned?”

3. 12–15 minutes – Guided strategy rehearsal Pairs discuss the sports-statistics example in the guided discussion slide: “A player ran 2.35 km in one session and 1.8 km in another. How far altogether?” Students identify the operation, predict whether the answer will be greater than 3 km, and explain how they would represent 1.8 as 1.80. Take two responses before students begin independent work.

4. 15–30 minutes – Paired problem solving Distribute the decimal problem-solving worksheet to pairs. Students solve a selection of class-shop, sports-statistics and distance problems, showing an estimate, equation, working and written answer for each. Circulate and ask: “Which words or quantities helped you choose the operation?” and “How do you know your answer is reasonable?” Run a teacher-led group for students needing simplified language, visual data or operation prompts.

5. 30–39 minutes – Compare and communicate solutions Display the compare-solutions and discussion slides. Pairs select one completed problem and compare their method with another pair’s method. Invite students to explain different valid representations, such as a number line, expanded notation, a column algorithm or repeated addition. Discuss errors constructively, including misplaced decimal points and answers without units.

6. 39–45 minutes – Review and exit response Use the plenary and exit-question slide. Students complete the final worksheet problem independently: “A 5 km route has 2.65 km completed in the morning and 1.7 km in the afternoon. How much remains?” They must estimate, solve and write one sentence explaining whether the answer makes sense. Invite two students to share different checking strategies.

Resources

• the decimal problem-solving teaching deck
• the decimal problem-solving worksheet
• Whiteboard and pens
• Place-value charts or decimal grids
• Mini-whiteboards and markers
• Pencils, rulers and highlighters
• Optional calculators for checking, not replacing, working

Assessment

• Observe whether students identify relevant information, select an operation and align decimal place values.
• Review worksheet working and explanations for accurate calculations, units and reasonableness checks.
• Use the final response to identify students needing further support with operation choice, decimal representation or checking strategies.

Differentiation

• Support: provide simplified wording, highlighted key information, visual data, place-value charts and operation prompts such as “Are the amounts being combined, compared or shared?”
• Teacher-led group: solve one problem together using the routine Understand–Choose–Solve–Explain–Check, with students using mini-whiteboards for each stage.
• EAL and SEN: pre-teach terms such as total, difference, distance and remaining; read problems aloud, offer sentence frames, and allow oral explanations before written responses.
• Extension: students design a realistic decimal problem with at least two constraints, such as a fixed budget or maximum distance, then compare two possible solutions and justify which is more efficient or sensible.