Problem Solving Steps

Overview

This one-to-one intervention session is designed for a Year 4 student who struggles with two-step word problems involving addition and subtraction. The lesson focuses on building confidence and skills in-solving multi-step problems that form part of the statutory requirements of the National Curriculum for England, Key Stage 2 Mathematics.

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National Curriculum Alignment

Domain: Number - Addition and Subtraction Programme of Study Reference: Pupils should be taught to solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction (Year 4 Programme of Study Number - Addition and subtraction).

Key Learning Objective:

• Solve two-step addition and subtraction problems in contexts, deciding which operations and methods to use and why.

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Learning Objectives (WALT)

• We Are Learning To solve two-step word problems involving addition and subtraction independently.
• We Are Learning To identify relevant information clearly from the problems.
• We Are Learning To explain how we choose which operations to use in a problem.

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Success Criteria

• I can read and understand each part of the problem carefully.
• I can identify the two operations needed to solve the problem (addition and subtraction).
• I can work through the problem step-by-step, organising my working clearly.
• I can check my answers and explain my reasoning.
• I can attempt an extension problem independently.

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Resources Needed

• Whiteboard and pen
• Visual problem cards (large print, with pictures) including stepwise hints
• Number line (0-100) for support
• Recording sheet with problem and space for working
• Counters or cubes for practical modelling
• Mini whiteboard and marker for student

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Lesson Sequence (60 minutes)

1. Introduction and Engagement (10 mins)

• Begin with a brief chat about what two-step problems are and why they can be tricky.
• Use a simple practical example with counters: For example, "You have 15 counters. You give 7 to your friend and then find 5 more in your pocket. How many do you have now?"
• Use a number line to model addition and subtraction practically.
• Explain the learning objectives and success criteria in student-friendly language.

Teaching Tip: Use ‘think aloud’ modelling to demonstrate your thought process when approaching the problem.

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2. Guided Practice (20 mins)

• Present two-step word problems one at a time using visual cards with pictures to support understanding.
• For each problem:
• Read the problem aloud together, underlining or highlighting key information.
• Ask the student what operations they think will be needed — addition, subtraction, or both.
• Use counters and the number line to model each step.
• Write down the steps and solutions on the recording sheet.

Example problem: "Sarah has 24 apples. She gives 9 apples to her neighbour. Then she buys 12 more apples. How many apples does she have now?"

• Check the answer together and talk about the method used.

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3. Independent Practice and Support (15 mins)

• Provide a similar problem on the mini whiteboard for the student to solve independently: "For example, 'Tom has 18 marbles. He loses 7 marbles at the park. Then he finds 4 more. How many marbles does Tom have now?'"
• Encourage the student to:
• Read the problem carefully twice.
• Identify the two steps needed.
• Use drawings, counters or number line as they prefer.
• Write down each step of working clearly.
• Explain their answer aloud or in writing, depending on preference.

Differentiation: For learners who need extra help, offer guiding questions or hints. For example, "What happened first? What do we do next?"

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4. Extension Activity (10 mins)

• Challenge the student to create their own two-step word problem involving addition and subtraction.
• They can use objects in the classroom or pictures to write their problem, with two steps clearly identified.
• Encourage them to solve their own problem, explaining each step aloud.
• This supports metacognition and helps deepen understanding.

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5. Assessment and Reflection (5 mins)

• Review the work completed during the session together.
• Ask the student to verbally explain how they decided which operations to use.
• Identify areas still needing support to inform next steps in teaching.
• Provide positive feedback focusing on what they did well, such as breaking down the problem or checking their answer.

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Differentiation Strategies

• For Students Needing Extra Support:

• Use concrete manipulatives throughout.

• Provide sentence starters to guide explanations: e.g., "First I…", "Next I…".

• Allow extra time and frequent breaks.

• Use simpler numbers or fewer steps initially.

• For Advanced Learners:

• Increase complexity of problems by including larger numbers or introducing simple multiplication or division as a third step.

• Challenge them to solve without using concrete manipulatives or number lines.

• Introduce problems that require choosing the order of operations independently.

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Functional Skills Maths Connections

• Supports working with everyday numerical problems of increasing complexity.
• Builds skills in interpreting information, making reasoned decisions, and checking accuracy—key for Level 1 Functional Skills.
• Focuses on clarity in recording working and explanations, boosting communication of mathematical reasoning.

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This highly personalised, scaffolded approach not only supports the development of arithmetic skills but also builds the student's problem-solving confidence, essential for progressing in both KS2 Maths and Functional Skills maths contexts.