Two-Step Addition & Subtraction

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National Curriculum Links

Mathematics Programme of Study – Year 4 (Number – addition and subtraction):

• Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.
• Use estimation and inverse operations to check answers to calculations, and determine, in the context of a problem, levels of accuracy.

(Source: The National Curriculum for England, Department for Education)

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Learning Objectives

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

• Solve two-step addition and subtraction problems using appropriate methods.
• Use estimation strategies to check the reasonableness of answers.
• Use inverse operations to verify solutions.
• Explain their reasoning and justify method choices.

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Success Criteria

I can:

• Identify when a two-step addition or subtraction problem needs solving.
• Estimate answers before calculating to have a rough check.
• Use inverse operations (addition ↔ subtraction) to check my calculations.
• Explain my thinking clearly using maths vocabulary such as “estimate,” “inverse,” and “steps.”
• Solve progressively harder problems with confidence.

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Resources

• Whiteboard and markers
• Mini-whiteboards and pens for each pupil
• Printed problem cards (two-step addition and subtraction problems)
• Timer (for verbal reasoning tasks)
• Example notes handout (see notes section below)

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Lesson Structure (30 Minutes)

1. Introduction & Engagement (5 minutes)

Engage the class with a real-life scenario:
“Imagine you are planning a school fair. You need to buy 45 balloons and 68 sweets. You find out you already have some balloons and sweets at school, but you don't know how many. You also have a budget but need to check if you have enough money after buying some extra items. How do you work out how much you will need, and how do you check your answers to make sure they are correct?”

Targeted questions:

• “What do you notice about the problem? How many steps might this involve?”
• “How could you use estimation before working out the exact numbers?”
• “Why might it be useful to check your answer with an inverse operation?”

This hooks their attention while linking the maths to a practical context.

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2. Teaching Input and Modelling (10 minutes)

Step 1: Modelling solving a 2-step problem

Write on the board:
"Sarah had £50. She bought a book for £17 and a toy for £23. How much money does Sarah have left?"

Modelling with Active Reasoning:

• Estimate first: “£17 + £23 is about £20 + £20 = £40. So from £50, Sarah will have about £10 left.”
• Solve step 1: Calculate total spent: 17 + 23 = 40
• Solve step 2: Subtract total from £50: 50 – 40 = 10

Checking using inverse:

• Inverse check: 10 + 40 = 50, which matches Sarah’s starting amount, so our answer is correct.

Prove it / Reasoning Question:
“Why is it helpful to estimate before calculating? Can you explain how the inverse helped check the answer?”
Use sentence stems on the board:

• "I estimate by..."
• "I checked my answer by..."

Timer: Allow 1 minute for paired pupils to discuss verbally before writing one sentence each in their mini-whiteboards.

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3. Guided Practice with Layered Questioning (8 minutes)

Present three problems on mini-whiteboards or printed cards with increasing complexity:

Problem 1:
Jane has 50 stickers. She gives 18 to her friend and buys 12 more. How many stickers does she have now?

Problem 2:
A farmer has 123 apples. He sells 48 and then picks 37 more. How many apples does the farmer have altogether?

Problem 3:
A toy costs £38. You have £60. You buy the toy and then buy a book costing £15. How much money do you have left?

Whole class questioning:
For each, ask:

• “What is the first step you will do and why?” (Understanding operation choice)
• “How can you estimate to check if your answer seems reasonable?”
• “What inverse operation could you use to verify your answer?”
• "Explain how you knew which operation to use first."

Encourage full sentence responses, justifying thinking to deepen reasoning (application of Bloom's Levels: Understand, Apply, Analyse, Evaluate).

Common Misconceptions to Monitor:

• Performing operations in the wrong order (e.g., adding when they should subtract first).
• Forgetting to check answers or misusing inverse (e.g., using the wrong inverse operation).
• Confusing the two steps and mixing up numbers between steps.
• Neglecting estimation as a checking strategy.

AfL: Use mini-whiteboards during this stage to quickly scan all pupils’ working and explanations for misconceptions.

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4. Independent Practice (5 minutes)

Hand out progressive worksheets or problem cards where pupils work individually with these instructions:

• Solve each two-step problem.
• Estimate before calculating.
• Check answer by using the inverse.
• Write a sentence explaining how estimation and inverse helped check your answer.

Example for pupils to copy into books:

Example:
Problem: I have 80 sweets. I gave 27 to my friend and then bought 15 more sweets. How many sweets do I have now?

1. Estimate: 27 + 15 about 30 + 20 = 50; 80 – 50 = about 30 sweets left.
2. Calculate: 27 + 15 = 42; 80 – 42 = 38 sweets left.
3. Check using inverse: 38 + 42 = 80 (correct!)
4. Explanation: I estimated so my answer would be reasonable, and used the inverse addition to check the subtraction.

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5. Plenary (2 minutes)

Conduct a quick quiz using targeted questions:

• “Why do we use estimation before solving problems?” (Understanding)
• “How does the inverse operation help us check answers?” (Applying)
• “Explain the steps you would take to solve two-step word problems.” (Analysing)
• “If your estimate and your answer are very different, what should you do next?” (Evaluating)

Ask 3–4 pupils to share their explanations aloud, encouraging sentence starters like:

• “I estimate first because…”
• “I checked my answer by…”

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Notes for Pupils to Refer Back To

How to Solve Two-Step Addition & Subtraction Problems

1. Read the problem carefully to understand what is happening in each step.
2. Decide which operation you need to do first.
3. Estimate the answer for both steps roughly to check if the final answer is reasonable.
4. Solve step by step, writing down your working out.
5. Use the inverse operation to check your answer:
   • Addition checks subtraction (e.g., if you subtract 15, add 15 to check).
   • Subtraction checks addition (e.g., if you add 12, subtract 12 to check).
6. Explain your working and why your answer makes sense.

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Additional Teacher Notes

• Use active reasoning aloud during modelling to make thinking visible.
• Encourage all pupils to verbalise their reasoning (with sentence stems) to support language development.
• Time-probe students during reasoning questions to build fluency and confidence.
• Targeted questioning should prompt pupils to justify, analyse, and evaluate, moving beyond recall.
• Watch for students solving the problems in the wrong order or skipping the checking phase.
• Adapt complexity during independent work for lower and higher attaining pupils.
• Where possible, link estimation to mental math strategies learned earlier in Year 4 White Rose units.

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This lesson plan aligns with Year 4 expectations from the national curriculum and White Rose Maths Scheme, supporting progression in addition and subtraction problem-solving strategies by integrating estimation and inverse checking techniques with reasoning skills.