Evidence-Based Reasoning

Overview

This 16-minute lesson is designed for Year 5 students (aged 9-10) and focuses on developing their ability to select appropriate evidence from a mathematical text or problem. The lesson aligns with the National Curriculum for England, supporting the development of reasoning skills in mathematics, specifically within Number and Place Value, and Reasoning and Problem-Solving strands.

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National Curriculum Links

• Mathematics — Number:
  • Pupils should be taught to:
    • Solve problems involving number up to 1,000,000 by identifying appropriate information in a problem (Programme of Study - Number and Place Value)
    • Develop fluency and confidence in counting and recognising place value (Years 5)
• Mathematical Reasoning:
  • Pupils should be taught to:
    • Develop mathematical reasoning to explain and justify answers, making use of appropriate mathematical language and evidence
    • Choose appropriate methods and strategies to solve problems, identifying necessary information from given texts and data

References:
National Curriculum in England: Mathematics Programmes of Study, Key Stage 2 (years 3-6), 2014

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Learning Objectives

By the end of this lesson, pupils will be able to:

• Identify and highlight key pieces of numerical information from a mathematical problem text to support problem-solving.
• Explain the choice of evidence from texts in solving problems using appropriate mathematical vocabulary.
• Begin to make connections between the selected evidence and an efficient problem-solving strategy.

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Success Criteria

• Pupils successfully underline or highlight relevant numbers or facts from the text.
• Pupils justify their choice of evidence orally or in writing with simple reasoning statements.
• Pupils verbalise or write a brief explanation linking evidence to their solving strategy.

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Resources

• Whiteboard and markers
• Projector or printed copies of problem texts (one problem per pupil or displayed for whole class)
• Coloured highlighters or pencils (different colours for highlighting)
• Mini whiteboards and pens for pupils
• Sticky notes for evidence justification sentences (optional)

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Lesson Structure

1. Starter (3 minutes)

• Engage pupils with a quick "spot the information" challenge:
  Show a short, worded problem on the board, for example:

"A bus has 45 seats. 27 passengers got on at the first stop, and at the second stop, 12 more passengers waited to get on. How many seats are left empty on the bus?"

• Ask: Which numbers or pieces of information are important here? Invite quick responses.

• Note different pupil highlights, emphasising the skill of selecting evidence rather than solving yet.

2. Main Activity (10 minutes)

• Step 1: Provide each pupil with a short, mathematical problem text relevant to Year 5 level (e.g., money, measurement, or multi-step problems involving numbers under 1,000,000).

• Step 2: Pupils use coloured highlighters to underline/select key evidence (numbers, units, relationships).

• Step 3: Pupils write or verbalise a short explanation on a sticky note or mini whiteboard about why they have chosen that evidence (e.g., "I chose 45 seats because it tells me the total number of available seats").

• Step 4: Invite a few volunteers to share their evidence and explanations; write exemplary examples on the board.

• Emphasise phrases like "This is important because…", “We need this number to…”, modelling mathematical language for reasoning.

3. Plenary (3 minutes)

• Recap key learning: How picking the right evidence helps us solve problems efficiently.
• Quick class reflection: Ask pupils to orally summarise one piece of evidence they would always look for in word problems and why.

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Differentiation

• Support: Provide a problem with fewer numerical details and example sentence starters ("I chose this number because...").
• Challenge: Provide a two-step word problem requiring selection of multiple pieces of evidence and justification for each.

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Assessment

• Observe pupils during main activity for correct identification of key evidence.
• Collect or review pupils’ written justifications or listen to verbal explanations for alignment with reasoning criteria.
• Use mini whiteboards or sticky notes for quick formative assessment with immediate feedback.

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Extension Idea

• For homework or a follow-up lesson, pupils could create their own word problems including at least three key pieces of evidence and explain why those pieces are important for solving their problem. This encourages metacognition and deeper engagement with mathematical texts.

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Teacher’s Tip: Make it Visual and Interactive!

Using coloured highlighters and physical sticky notes turns abstract reasoning skills into a tactile experience. Encouraging pupils to justify their choices out loud builds confidence in mathematical communication and supports writing development—a cross-curricular benefit.

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This lesson plan empowers pupils not only to solve problems but also to become mathematically discerning readers, precisely what the National Curriculum aims to develop in confident, competent young mathematicians.