Solving Addition and Subtraction

Overview

This 60-minute intervention session is designed for a Year 4 student who is struggling with word problems involving addition and subtraction. The session uses visual aids, concrete resources, and step-by-step scaffolding tailored towards the National Curriculum for England’s Number - addition and subtraction objectives. It incorporates Functional Skills principles, promoting practical and applicable mathematical understanding.

Curriculum Links

Mathematics Programme of Study: Key Stage 2, Year 4

Use formal written methods of addition and subtraction.
Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.
Interpret and construct pictorial representations to support problem solving.

Learning Objectives (WALT)

We are learning to use pictorial and concrete methods to solve word problems involving addition and subtraction.
We are learning to understand the problem, select appropriate methods, and explain our reasoning.

Success Criteria

I can identify key information in a word problem.
I can represent the problem using pictures or objects.
I can solve addition or subtraction problems using these representations.
I can explain how I found the answer.

Resources

Counters, cubes, or small objects (e.g. snap cubes or counters)
Printed or drawn number lines
Whiteboard and markers
Word problem cards tailored to the student’s interests
Visual number sentences cards (+, – signs)
Blank storyboard templates for pictorial representation

Lesson Structure

1. Introduction (10 minutes)

Use simple, engaging word problems to introduce the task.
Model how to read a problem carefully and pick out the numbers and the question.
Explain the use of physical counters to represent numbers concretely.
Show how to use a number line to support addition and subtraction visually.
Use the WALT and success criteria sheets to establish clear expectations.

2. Guided Practice (20 minutes)

Present a word problem slowly: for example, "Sara has 15 apples. She gives 7 to her friend. How many apples does Sara have left?"
Student uses counters to represent 15 apples. Physically remove 7 counters to show subtraction.
Transfer understanding by using a number line, starting at 15 and moving backwards 7 steps.
Draw a simple pictorial story to represent the problem: e.g., pictures of apples leaving the basket.
Repeat for an addition problem: e.g., "Tom has 8 marbles. He finds 6 more. How many does he have now?" Use counters and number line adding forward.
Encourage the student to verbalise their process and reasoning.

3. Independent Practice (15 minutes)

Provide three varied word problems with increasing complexity and ask the student to:

Identify and underline key numbers and operation keywords.
Use counters or cubes to model the problem physically.
Draw pictorial representations (using the storyboard template).
Write the number sentence that matches the problem.
Solve using the number line or counters.

Offer support as needed but encourage independent thinking.

4. Review and Reflect (10 minutes)

Discuss the answers together, asking the student to explain their reasoning using pictures and counters.
Check each success criterion.
Identify any stumbling blocks and praise successful strategies.
Recap the WALT and praise progress.

5. Extension Activity for Advanced Learners (Optional)

Introduce two-step word problems requiring both addition and subtraction, e.g., "Anna has 20 sweets. She gives 5 to her brother and then buys 8 more. How many sweets does she have now?"
Guide the student to break down the problem into parts, model each with counters and pictorial methods, then combine answers.
Introduce estimation techniques to check answers (e.g., rounding numbers).

Differentiation Strategies

Learner Type	Strategy
Student struggling with language	Use simplified vocabulary, visuals, and repeat instructions. Encourage drawing before abstract solving.
Student with fine motor difficulties	Focus more on pictorial and number line methods if handling small counters is difficult.
Student with strong visual memory	Encourage more detailed pictorial stories and prediction of answers before calculation.
Student with English as an Additional Language (EAL)	Use clear, visual word problem cards, speak slowly, and allow extra time.

Assessment

Formative assessment during guided and independent tasks: observe student’s ability to identify operations, use models, and explain reasoning.
Use a simple checklist mapped to success criteria.
Summative assessment: final two or three word problems answered independently, demonstrating understanding of both addition and subtraction through concrete and pictorial methods.

Teacher Reflection and Next Steps

Review how well the student transfers concrete and pictorial understanding into abstract number sentences.
Plan further sessions including addition and subtraction with larger numbers or incorporating multiplication/division if appropriate.
Incorporate more real-life contexts based on student interests to deepen engagement and functional skills relevance.