Problem Solving Maths

Overview

A 25-minute lesson on addition and grouping designed for Reception students (aged 4-5). The lesson builds number sense through problem solving using practical resources such as tens frames, counters, and cubes. It aligns specifically with the Early Years Foundation Stage (EYFS) Development Matters and the National Curriculum for Mathematics (Reception content) for England, focusing on early number skills, addition, and grouping.

---

National Curriculum Links

• EYFS Framework (Early Learning Goal: Numbers)

  • Children count reliably with numbers from 1 to 20.
  • Use quantities and objects to add and subtract two single-digit numbers.
  • Solve problems including simple addition.

• Development Matters – Mathematics:

  • Children recognise numbers to 10 and beyond.
  • Everyday language to talk about size, quantity, compare quantities.
  • Explore counting and cardinality through practical activities.

---

Learning Objectives

By the end of the lesson, all children will be able to:

• Understand grouping of objects in small sets (up to 10).
• Solve simple addition problems using practical resources.
• Explain their mathematical thinking during a talk task.

Stretch and challenge:

• Attempt addition problems with numbers beyond 10.
• Use own strategies for solving problems.
• Work with varying group sizes and recording their reasoning.

Support for lower ability pupils:

• Use smaller numbers (1-5).
• Extra adult support to scaffold counting and addition.
• Step-by-step modelling and visual aids.

---

Resources Needed

• Tens frames (large enough for class use, laminated if possible)
• Counters (two colours)
• Interlocking cubes
• Whiteboards and pens (optional for recording)
• Picture cards showing groups of objects for modelling
• Number sentence or problem cards

---

Lesson Structure

1. Introduction (5 minutes)

• Sit children in a circle and use a large tens frame with counters.
• Model counting out a small number of counters (e.g. 3 counters red, then 2 counters blue).
• Verbally describe the addition problem: "We have 3 red counters and 2 blue counters. How many counters do we have altogether?"
• Demonstrate grouping and counting all counters together.
• Write or show a simple number sentence on a board: 3 + 2 = ?

2. Modelled Activity (7 minutes)

• Present 3-4 addition problems using picture cards and tens frames.
• Examples:
  • "4 apples in one basket and 3 apples in another. How many apples altogether?"
  • "5 cubes and 2 cubes. How many?"
• Use counters and cubes to physically add groups.
• Encourage children to use their fingers to count.
• Highlight counting all objects rather than counting only one group.
• Verbalise the addition number sentence each time.

3. Independent Talk Task with Concrete Manipulatives (10 minutes)

• Divide children into pairs or small groups with a mix of abilities.
• Provide each group with tens frames, counters, and cubes.
• Give problem cards with simple addition problems (e.g., "You have 2 red counters and 3 blue cubes. How many altogether?")
• Children solve problems independently or with peer discussion.
• Encourage children to say their answer aloud and explain their thinking ("I put 2 counters here and 3 cubes here, then I counted all to get 5.").
• Adults circulate to support lower ability children by prompting counting and grouping, and challenge higher ability children to create their own problems or add numbers beyond 10 using two tens frames.

4. Plenary / Review (3 minutes)

• Regroup and invite 3-4 children to share how they solved a problem.
• Ask: "How did you find your answer? How did your counters help?"
• Reinforce the vocabulary: addition, group, altogether, count, more.
• Praise attempts to explain reasoning and use manipulatives effectively.

---

Assessment Opportunities

• Observe children's ability to group and count sets correctly during the modelled and independent phases.
• Listen to explanations during independent talk task for correct use of addition vocabulary and logical thought.
• Use notes on individual children who needed additional support or showed stretch in problem complexity.

---

Differentiation

Level	Support Strategies	Stretch & Challenge
Lower Ability	Use numbers 1-5 only; adult scaffolding; step-by-step counting with manipulatives	N/A
Expected Year Reception	Use numbers up to 10; independent grouping and counting; explain reasoning	N/A
Higher Ability / GD	Use addition problems >10 with two tens frames; create own problems; use cubes & counters to explore 'more than' and 'less than'	Record number sentences or draw pictures to represent addition.

---

Teacher Tips (WOW ideas)

• Use storytelling: create mini-stories for each problem, e.g., "3 ducks on the pond, 2 ducks join. How many ducks now?" to engage imaginations.
• Use magnetic tens frames on the whiteboard for whole class interactive counting.
• Incorporate time challenges for higher achievers to solve and explain problems quickly.
• Utilize peer teaching: encourage confident children to explain ideas to peers, deepening understanding.

---

Summary

This lesson engages Reception pupils in early addition and grouping through practical problem solving, using manipulatives aligned with the National Curriculum and EYFS framework. It encourages active learning, language development, and mathematical reasoning suited to a diverse range of abilities.