Solving Time Problems

National Curriculum Links

• Mathematics Programme of Study (Year 4):
  • "Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks."
  • "Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days."
• Aligned with White Rose Maths Scheme (Block: Time, Week 3), focusing on problem-solving with time conversions.

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Learning Objectives

By the end of the lesson, children will:

• Understand and apply the conversions between hours and minutes and minutes and seconds.
• Solve word problems involving time conversions.
• Explain their reasoning using mathematical vocabulary related to time.

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Success Criteria

I can:

• Convert hours to minutes and minutes to seconds accurately.
• Use my knowledge of time to solve problems involving more than one step.
• Explain my methods and justify my answers clearly.
• Check my answers to see if they are reasonable.

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Lesson Overview (35 minutes)

Time	Activity	Purpose
5 mins	Engaging Introduction with Whole-Class Discussion	Activate prior knowledge and hook interest.
10 mins	Guided Modelling & Targeted Questioning	Step-by-step worked examples with layered questioning and AfL.
15 mins	Independent Task with Increasing Complexity	Practice converting and problem-solving.
5 mins	Plenary: Prove It Reasoning & Self-Assessment	Consolidate learning and reflect.

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Detailed Lesson Plan

Engaging Introduction (5 minutes)

Starter Activity: Display a large analogue clock showing 2:45. Ask:

• "If we know that 1 hour is 60 minutes, how many minutes have passed since 1 o'clock?"
• "Can you explain how you worked this out?"

Use think-pair-share: children discuss answers with a partner before sharing with the class.

Targeted Whole-Class Questions:

• "Why is 60 minutes equal to 1 hour?"
• "How might this help us when solving time problems?"
• "What are some different units of time we use daily?"

Misconceptions to watch for:

• Confusing 24-hour and 12-hour clocks.
• Forgetting that minutes and seconds require different conversions (not just changing numbers).
• Treating unit conversions as simple addition or subtraction rather than multiplication/division.

Active Reasoning: Encourage pupils to explain reasons behind their conversion methods.

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Guided Modelling and Questioning (10 minutes)

Example to Copy in Books:
Example 1:
“How many minutes are there in 3 hours?”

• 1 hour = 60 minutes
• So, 3 hours = 3 × 60 = 180 minutes

Example 2:
“If a film lasts 2 hours and 30 minutes, how many minutes is that in total?”

• 2 hours = 2 × 60 = 120 minutes
• Total = 120 + 30 = 150 minutes

Use layered questioning on each example:

• Remembering: "What is the conversion factor between hours and minutes?"
• Understanding: "Why do we multiply the number of hours by 60?"
• Applying: "Can you think of another example where you would need to do this?"
• Analysing: "If we reversed the process, how would we convert minutes back to hours?"
• Evaluating: "Is 150 minutes closer to 2 or 3 hours? How do you know?"
• Creating: "Can you write your own time conversion problem for a friend to solve?"

AfL Point: After modelling Example 2, ask pupils to use mini whiteboards to:

• Write the total minutes for 1 hour 45 minutes
• Teacher circulates, checking for understanding and correcting misconceptions.

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Independent Task with Increasing Complexity (15 minutes)

Task Stage	Description	Challenge & Scaffold
Stage 1 – Simple conversions	Convert given hours into minutes e.g., 4 hours, 1hr 15m to minutes	Scaffold with number lines, step reminders.
Stage 2 – Multi-step problems	Solve word problems with hours and minutes, e.g., “School starts at 9:00 am and ends at 3:15 pm. How many minutes is the school day?”	Prompt them to break down hours and minutes separately.
Stage 3 – Applying to new contexts	Convert and solve problems involving minutes and seconds, e.g., “A race lasts 3 minutes 45 seconds. How many seconds is that?”	Extra challenge: Pupils create their own time problem.

Targeted Questions for Reasoning:

• "Explain why you multiplied or added those numbers to find your answer."
• "How did you check your answer was correct?"
• "If you had to explain this method to a friend, what would you say?"

Misconceptions to Anticipate:

• Adding hours and minutes directly without conversion.
• Confusing units and adding seconds to minutes without conversion.
• Not aligning the parts of a word problem logically before calculating.

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Plenary – Prove It/Reasoning Question (5 minutes)

Prove it: Display this problem on the board:
“Jane ran for 1 hour 20 minutes. Tom ran for 80 minutes. Who ran for longer? Explain your answer.”

Use sentence stems:

• “I think ______ ran longer because _______.”
• “I know this because _______.”
• “My calculation shows _______.”

Verbal reasoning timer:

• 30 seconds to think silently.
• Pupils share their answer aloud with their partner.
• Select 3-4 pupils to share with the class—stress use of time vocabulary accurately.

Self-assessment: Ask pupils to tick the success criteria they have achieved today and write one thing they want to improve next time.

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Assessment for Learning (AfL) Throughout

Stage	AfL Strategy	Purpose
Introduction	Think-Pair-Share	Informal check of prior knowledge.
Modelling	Mini whiteboards for quick conversion problems	Immediate feedback on understanding.
Guided Practice Task	Verbal explanations using sentence stems	Check depth of pupil reasoning.
Independent Work	Teacher circulates, uses questioning	Identify misconceptions early.
Plenary	Peer explanation & self-assessment	Consolidate learning and self-reflect.

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Differentiation and Inclusion

• Support:
  • Pre-printed number lines and conversion charts.
  • Adult support for pupils with SEND.
  • Practical, visual aids with clocks and timers.
• Challenge:
  • Create multi-step problems involving several conversions.
  • Include word problems requiring 24-hour clock understanding.

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Resources Needed

• Large analogue clock display or interactive clock tool.
• Mini whiteboards and pens.
• Printouts of word problems/tasks.
• Timer for verbal reasoning.
• Conversion chart posters (hours-minutes-seconds).

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This highly structured, interactive lesson carefully scaffolds understanding of converting time and applying this to problem-solving, ensuring pupils meet the requirements of the National Curriculum for England whilst engaging in meaningful mathematical communication and reasoning.