Mixed Addition and Subtraction

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National Curriculum Links

Year 4 Maths:

• Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.
• Add and subtract numbers with up to 4 digits using formal written methods of columnar addition and subtraction where appropriate.
• Recall and use addition and subtraction facts to 100 fluently, and derive and use related facts up to 1000.

(Reference: Mathematics Programme of Study - Number - Addition and Subtraction)

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Learning Objectives

By the end of the lesson, pupils will be able to:

• Solve mixed addition and subtraction problems involving up to 4-digit numbers confidently and accurately.
• Decide and explain which operation is needed for solving contextual problems.
• Use formal written methods where appropriate to calculate answers.
• Justify their reasoning and explain the steps taken to solve mixed problems.

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Success Criteria

• I can read the problem carefully and identify whether to add or subtract.
• I can choose the correct operation and method to solve mixed problems.
• I can use written methods for addition and subtraction confidently.
• I can check my answers by estimating or using inverse operations.
• I can explain how I solved the problem and why I chose my method.

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Resources

• Whiteboards and pens
• Exercise books and pencils
• Counting cubes or place value charts for demonstrations
• Example problem sheet (printed, with guided steps)
• Visual aids (number lines, formal column methods posters)

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Lesson Structure (60 Minutes)

1. Introduction & Engagement (10 minutes)

Hook: Show a real-life scenario involving money and shopping (e.g., Sara had £125, bought a toy for £78, then found £40. How much money does she have now?).

• Ask: "What should we do first? Add or subtract? Why?"
• Use a numberline visual to model moving forwards and backwards.
• Emphasise key vocabulary: difference, total, more than, less than, altogether.

Whole-class questioning (targeted with Bloom’s Taxonomy):

• Remembering: What do addition and subtraction mean?
• Understanding: How do you know which operation to choose for this problem?
• Applying: Can you show on a number line where we start and where we end?
• Analysing: Why might someone get the wrong answer if they don’t read the question carefully?
• Evaluating: Which method is more efficient for this question – mental or written? Why?
• Creating: Can you make up your own problem using addition and subtraction?

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2. Modelling & Demonstration (15 minutes)

• Model solving a mixed problem on the board step-by-step.

Example for the board:

"Liam has 2,345 stickers. He gives away 1,287 to his friends. Later, his uncle gifts him 1,150 more. How many stickers does Liam have now?"

Steps:

1. Identify the operations (subtract first, then add).
2. Write the subtraction in column form.
3. Complete subtraction, emphasising place value.
4. Write the addition in column form below.
5. Complete addition carefully, explaining carrying over numbers.
6. Check answer by rounding and estimating.

AfL Point:

• Ask pupils to annotate their own version in books with their thinking process.
• Check verbal explanations: "Why did I subtract first?"
• Identify common misconceptions (see below).

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3. Guided Practice (20 minutes)

Task:

• Pupils work on mixed addition and subtraction problems in pairs.
• Problems increase in difficulty: starting with 3-digit numbers and progressing to 4-digit numbers, some requiring 2-step operations with both addition and subtraction.

Examples:
a) 864 + 157 − 432 = ?
b) 3,450 − 1,298 + 600 = ?
c) Tina had 4,000 points on a game. She lost 1,245 points but earned 1,600 points later. What’s her new total?

Scaffold:

• Provide place value charts for those who need support.
• Encourage use of estimation before calculating.

Targeted questioning during task:

• "Can you explain aloud how you decided which operation to do first?"
• "Show me how you are checking your working out."
• "What could be a good strategy if you get stuck?"

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4. Addressing Common Misconceptions (5 minutes)

• Confusing which operation to use (e.g., adding when the problem requires subtraction first).
• Errors in column subtraction, especially when borrowing or regrouping.
• Forgetting to carry over in addition or subtracting digits incorrectly.
• Losing track of order in two-step problems.
• Not estimating or checking answers to catch errors.

Strategy:

• Explicitly highlight these and how to avoid them during modelling and practice.
• Use mini whiteboards for quick checks and corrections.

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5. Independent Application Task (7 minutes)

• Pupils solve 3 mixed problems independently in their books.
• One problem must be contextual (real-life scenario).

Example:
"A library had 2,356 books. They removed 575 damaged books and then received 1,210 new books. How many books does the library have now?"

Success criteria checklist for pupils:

• Write the calculation sequence clearly.
• Use formal methods correctly.
• Explain reasoning in full sentences.

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6. Plenary & Reflection (3 minutes)

• Ask pupils to share how they decided which operations to use for their problems.

• Use a few targeted questions encouraging reasoning and justification:

  • "How did you decide which part to subtract first?"
  • "What did you check to be confident your answer is correct?"
  • "If you were to explain your method to a friend, what would you say?"

• Highlight excellent explanations and reasoning from pupils (verbal AfL).

• Summarise key learning points: understanding operation choice, formal written methods, and checking work.

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Differentiation

• Support: Scaffolded problems with visual aids and place value resources, and working in pairs.
• Challenge: Problems including 4-step operations with reasoning, e.g., combining multiplication or division estimates to check answers, or explaining alternative solving strategies.

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Assessment for Learning (AfL) Opportunities

• Continuous questioning during modelling and guided practice.
• Pupils annotate working steps in books with thought-process notes.
• Use of mini whiteboards for instant feedback.
• Peer discussion to explain reasoning.
• Plenary Q&A to gauge understanding and reasoning ability.

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Example for Pupils’ Books (Copy this)

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Mixed Addition and Subtraction Problem

Jeena has 3,645 beads. She uses 1,872 beads for a necklace. Later, she buys 1,450 more beads. How many beads does Jeena have now?

Step 1: Identify operations

• Subtract beads used: 3,645 − 1,872
• Then add beads she bought: + 1,450

Step 2: Calculate subtraction
3,645
− 1,872
= 1,773

Step 3: Calculate addition
1,773

• 1,450
  = 3,223

Answer: Jeena has 3,223 beads now.

Explain:
I subtracted first because Jeena used some beads, so I needed to take away that number. Then, I added the beads she bought later. I checked my answer by estimating (about 3,600 − 1,800 = 1,800, plus about 1,400 = 3,200), so my answer makes sense.

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This example supports learners to model clear, logical steps, and encourages reasoning alongside calculation, fully aligned with National Curriculum expectations and White Rose Maths progression.