Subtraction with Borrowing

Overview

This intervention lesson is designed to support a Year 4 student who struggles with subtraction involving borrowing (regrouping). Using visual and tactile approaches like bar modelling and Cuisenaire rods aligns with the National Curriculum for England’s emphasis on concrete, pictorial, and abstract representations in maths. This session is tailored for a 1:1 setting to allow for personalised pacing and immediate feedback.

---

National Curriculum Links

Mathematics Programmes of Study (Year 4 Number - Addition and Subtraction):

• Solve subtraction problems using formal written methods (columnar subtraction) with increasingly large numbers.
• Develop fluency in calculating differences by relating to concrete and pictorial representations.
• Understand place value and regrouping (borrowing) through manipulatives and diagrams.

---

Learning Objectives (WALT)

• WALT understand subtraction with borrowing using visual models and concrete materials.
• WALT apply bar modelling and Cuisenaire rods to represent and solve subtraction problems.
• WALT demonstrate improved confidence and accuracy in performing subtraction with borrowing.

---

Success Criteria

• I can explain what borrowing means in subtraction.
• I can use bar models to represent subtraction problems visually.
• I can use Cuisenaire rods to model and solve subtraction with borrowing.
• I can solve subtraction calculations with borrowing more independently and accurately.

---

Resources

• Cuisenaire rods set (particularly rods marked for tens and ones)
• Whiteboard or paper for bar modelling diagrams
• Subtraction problem cards tailored for borrowing
• Pencil, rubber
• Visual place value charts

---

Lesson Structure (60 minutes)

1. Introduction and Diagnostic Check (10 minutes)

• Discuss pupil’s current understanding: Ask the student to attempt a few 2-digit subtraction problems without support to identify precise areas of difficulty.
• Define subtraction with borrowing: Use very simple language and symbolic notation, e.g., “When you don’t have enough in the ones place, you take one ten away from the tens.”
• Introduce the session’s WALT and success criteria clearly.

2. Concrete Experience Using Cuisenaire Rods (15 minutes)

• Present a subtraction problem with borrowing (e.g., 43 - 27).
• Ask the student to model 43 using rods: 4 tens rods and 3 ones rods.
• Show the problem of subtracting 7 ones, which is more than 3 ones available.
• Demonstrate borrowing: exchange one ten rod (a 10 rod) for ten one rods.
• Let the pupil physically make the exchange and subtract.
• Repeat with one or two more examples, encouraging explanation of each step aloud.

3. Pictorial Representation Through Bar Modelling (15 minutes)

• Draw a long bar representing the total number (e.g. 43).
• Partition the bar into tens and ones visually.
• Show subtracting the smaller number bar under the bigger one, highlighting the need to “borrow” when the ones bar is too short.
• Guide the pupil to draw their own bar models for set problems involving borrowing, showing the regrouping explicitly.
• Discuss how the pictorial bar model relates to the Cuisenaire rod activity.

4. Guided Practice with Varied Problems (15 minutes)

• Provide a series of subtraction problems that specifically require borrowing (e.g., 43 - 27, 62 - 38).
• Instruct pupils to first use Cuisenaire rods to model the problem physically.
• Next, have pupils draw bar models to represent the subtraction and the borrowing process.
• Finally, guide pupils to complete the written subtraction method, emphasizing the borrowing step.
• Use prompts such as, “Can you see where you need to borrow? How does your model help you?”
• Offer additional support for pupils who struggle by breaking down the borrowing step further.
• Celebrate successes to build confidence and encourage persistence.

5. Assessment and Reflection (5 minutes)

• Present a couple of mixed subtraction problems without using rods or bar models to gauge independent understanding.
• Encourage the pupil to visualise the borrowing process as they solve.
• Review the success criteria with the pupil, asking which steps feel easy or difficult now.
• Set a positive goal for next steps.

---

Differentiation Strategies

• For learners needing extra support: Use step-by-step physical modelling with rods and bar models; break down borrowing into smaller, manageable steps; provide one-on-one verbal prompts and visual cues.
• For learners with language difficulties: Use clear, simple language and visual aids; reinforce key vocabulary like "borrow", "exchange", "tens", and "ones"; encourage peer support and use of first language where helpful.
• For confident learners: Challenge with multi-digit subtraction problems involving borrowing; encourage mental subtraction strategies; reduce use of concrete materials earlier to promote abstract thinking.

Extension Activities

• Encourage pupils to create their own subtraction problems involving borrowing and illustrate them using rods and bar models.
• Have pupils write a simple explanation or 'how-to' guide on the borrowing process to reinforce understanding.
• Introduce addition with carrying using similar visual tools to deepen number sense.
• Suggest use of interactive digital tools or apps that simulate rods and bar models for further practice at home or school.

Teacher Reflection Notes

• Monitor the pupil’s ability to transfer understanding from concrete (rods) to pictorial (bar models) to abstract (numerical algorithms).
• Assess vocabulary understanding: does the pupil use terms like “borrow”, “exchange”, “tens”, and “ones” with confidence?
• Adjust pace and repetition as needed; encourage frequent self-explanation to embed conceptual understanding.

This intervention harnesses tactile and visual strategies highly recommended in the National Curriculum for Maths mastery, promoting deep, durable learning and confidence in tricky subtraction skills.