Number Problem Solving

Overview

A lively, hands-on 25-minute maths session designed to develop Reception children’s problem-solving skills using number, aligned with the National Curriculum for England Early Years Foundation Stage (EYFS) Maths Development Matters statements.

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Learning Objectives

By the end of the lesson, children will:

• Begin to solve practical problems involving numbers up to 10. (EYFS: Early Learning Goal – Numbers)
• Develop an understanding of number relationships and patterns through active exploration.
• Use language related to addition and subtraction in everyday context.
• Communicate their mathematical thinking through discussion (speaking and listening skills).
• Engage in collaborative and independent mathematical investigations with appropriate challenge.

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Curriculum Links

This lesson closely follows the Early Years Framework for Mathematics:

• Number - Numerical Patterns: Count objects, actions and sounds.
• Number - Numerical Patterns: Subitise (recognise quantities without counting) up to 5 and beyond.
• Number - Numerical Patterns: Automatically recall number bonds for numbers 0–5.
• Problem solving & reasoning: Solve real-world mathematical problems with numbers up to 10.
• Develop spatial awareness through manipulating objects.

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Resources

• Number cards 1-10 (laminated)
• Small counting objects such as coloured counters or plastic bears (sets of 20 per group)
• “Magic Mystery Bag” (a decorated bag with objects to count/problem solve with)
• Large floor number line (1-10)
• Individual whiteboards and pens for independent talk task
• Visual problem-solving story cards (simple scenarios based on addition/subtraction)

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Timing, Activities & Differentiation

Time	Activity	Description	Differentiation
0-5	Engage & Count	Gather children & introduce “Magic Mystery Bag”. Teacher pulls out objects (e.g., 4 plastic bears). Children count aloud together. Use floor number line to place objects.	Support: Count objects with teacher assistance. Challenge: Estimate before counting.
5-10	Group Problem Solving	In small groups (6 groups of 5), children receive problem card (e.g., “I have 6 bears. 2 go home. How many are left?”). Use counters to represent problem physically and solve. Teacher circulates, supports, and questions to scaffold reasoning.	Support: Use objects and number line. Challenge: Combine two problems or create own problem.
10-20	Independent Talk Task (Active & Hands-on)	Children work independently at tables with sets of counters & problem cards. Task: “Show me how to make 5 in two different ways.” Children represent answers on whiteboards or with counters and explain to a partner.	Support: Use counters and visual aids, sentence starters provided. Challenge: Explore subtraction problems or make up story problems using numbers 1-10.
20-25	Interactive Review & Reflect	Volunteer pairs share solutions & explain their thinking. Teacher uses questioning to deepen understanding: “How do you know that?” “What happens if we add one more?” End with quick “magic number” game: children show a number with fingers and others guess the number by asking questions (e.g., “Is it more than 3?”).	All children participate orally, using hands-on resources to support answers.

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Assessment

• Continuous formative assessment through observation:
  • Ability to count accurately and confidently.
  • Use of mathematical language (more, less, add, take away).
  • Engagement and ability to explain reasoning during partner talk.
• Annotate whiteboards and observe group work to identify starting points for individual next steps.
• Use plenary questioning to check understanding and correct misconceptions.

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Teaching Tips to ‘Wow’

• Emphasise creativity in problem-solving - allow children to invent their own small problems once confident.
• Use enthusiasm and interactive questioning to create excitement.
• Encourage physical movement by having children place objects on the floor number line.
• Incorporate storytelling to contextualise problems and spark imagination.
• Vary groupings to support social maths talk and language development.

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Reflection & Next Steps

• Reflect on observed children who needed additional support or extended challenge, planning follow-up activities.
• Next lesson: Develop number recognition and bonding to 10 using games and paired counting.
• Integrate technology next time by using digital number games or interactive whiteboard problem-solving.

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This lesson plan provides a rich, inclusive, and dynamic environment fostering early problem-solving skills in number, fully aligned with the National Curriculum’s emphasis on active learning and mathematical communication.