Two-Step Problem Solving

I want the plan to focus on developing our understanding on how to solve 2 step problems involving addition and subtraction. Create a success criteria for this lesson Create a high engaging introduction and a range of questioning for this maths lesson Identify common misconceptions and areas of difficulty for developing our understanding on how to solve 2 step problems involving addition and subtraction.

Create use of targeted whole class questions- Questions shouldn't just ask for the correct answer they should require pupils to explain their thinking justifying their reasoning. (Use Bloom's taxonomy to help create questions beyond basic thinking and encourage deeper thinking) Create an example for children to copy into books and use to support work

Include AfL points throughout teaching and modelling stage Modelling  

Plan a task that gradually increases in complexity, e.g. by adding more elements pupils need to think about or having them apply what they have been taught to different situations.

plenary

Align with White Rose Maths Scheme

National Curriculum Links

Mathematics – Year 4

Number – Addition and Subtraction
Use addition and subtraction methods proficiently to solve problems, including two-step problems, choosing and explaining which operations and methods to use.
Problem Solving
Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Learning Objectives

By the end of this session, pupils will:

Understand what a two-step addition and subtraction problem is.
Identify the correct operations needed in a two-step problem and explain their reasoning.
Solve a range of two-step problems involving addition and subtraction accurately.
Demonstrate their thinking clearly by justifying their problem-solving process.

Success Criteria

I can:

Read and understand two-step problems.
Decide whether to add or subtract for each step.
Solve problems using addition and subtraction methods confidently.
Explain my reasoning and justify which operations I chose.
Check my answers for accuracy.

Resources

Whiteboard and pen
Printed problem cards (differing in difficulty)
Worksheets for individual tasks
Visual number lines and part-part-whole models
Mini whiteboards and pens for pupil responses

Lesson Structure (60 minutes)

1. Engaging Introduction (10 minutes)

Teacher explains:
"Today, we become brilliant problem solvers! We will tackle problems that need two operations — or two steps — to find the answer. Just like detectives, we must figure out which operations to use and in what order."

Starter Activity:
Display a simple two-step problem on the board:
"Anna has 15 apples. She gives 7 to her friend and then buys 5 more. How many apples does she have now?"

Ask the class:

What is the first thing to do?
Which operation will we use first, addition or subtraction? Why?
What is the second step?

Use questioning to encourage explanation:

Can someone explain why we subtract before we add?
How do you know when to add or subtract in a problem?

AfL: Pupils write their reasoning on mini whiteboards, showing how they would solve the problem step-by-step.

2. Modelling and Guided Practice (15 minutes)

Display an example problem on the board and model solving it aloud with clear reasoning:

Example:
"Tom has 23 marbles. He wins 14 more in a game. Later, he gives 8 marbles to a friend. How many marbles does Tom have now?"

Step 1: Identify the first operation—adding marbles won (23 + 14).
Step 2: Identify the next operation—subtracting the marbles given away (result - 8).

Write out the calculation:
23 + 14 = 37
37 - 8 = 29

Explain your thinking verbally: "I add first because Tom won marbles. Then I subtract because he gave some away."

Targeted Whole-Class Questions:

Why is it important to follow the steps in order?
What would happen if we subtracted first? Would the answer make sense?
Can you explain how to check your answer?

AfL: Use thumbs up/down or mini whiteboards to check pupils' understanding of each step.

3. Independent/Paired Task with Gradual Complexity (20 minutes)

Provide pupils with a worksheet of two-step problems. Start with numerical problems in familiar contexts, e.g.:

Lucy collects 40 stamps. She buys 15 more and then gives 18 to her cousin. How many stamps does she have now?
A bus has 50 passengers. 20 get off at the first stop and 12 get on. How many passengers are on the bus now?

After completing simpler problems, introduce challenges that require pupils to decide their own method or work with missing numbers:

Tom has some pencils. He buys 18 and then has 52. How many pencils did he start with?
A shop sells 73 chocolates. They sold some in the morning and 18 in the afternoon. 29 chocolates are left. How many were sold in the morning?

Differentiation:

Support with number lines or bar models for some pupils.
Challenge higher achievers to create their own two-step problem for a partner to solve.

Targeted Questions for Pairs:

Why did you choose those operations?
How did you work out which part comes first?
Can you explain your method to your partner?

4. Addressing Common Misconceptions (throughout)

Misconception	How to Address
Pupils mix up the order of operations	Encourage careful reading, highlighting keywords ("then," "after") and linking steps logically. Use visual timelines or flowcharts.
Adding when they should subtract (or vice versa)	Use bar models and part-part-whole diagrams to visualise the problem. Ask pupils to explain what each number represents before calculating.
Ignoring the two-step nature and answering with a one-step solution	Reinforce scanning the problem fully and summarising steps aloud before calculating. Check answers with reasoning.
Misreading quantities or remainders	Regularly ask pupils to read the problem aloud and paraphrase what it asks for. Use questioning for clarity.

5. Plenary (10 minutes)

Class discussion:
Pose a final problem and ask pupils to solve it aloud step-by-step with reasoning. For example:
"Emma has 36 stickers. She gives 9 to her brother and then buys 17 more. How many does she have now?"

Ask pupils to:

Explain the steps verbally.
Justify which calculations they did first and why.
Suggest how to check their answer.

Deeper thinking questions:

Could there be more than one way to solve this?
How might your answer help Emma if she wants to share stickers equally with her friends?

Success Criteria Check:

Invite pupils to self-assess their understanding against the success criteria.
Reflect briefly: What did they find easy or hard? What helped them?

Example for Pupil Books

Two-Step Problem Example:

Problem:
Sarah has 25 balloons. She buys 12 more and then gives 8 to her friends. How many balloons does she have now?

Step 1: 25 + 12 = 37 (Sarah’s new total after buying more)
Step 2: 37 - 8 = 29 (Balloons left after giving some away)

Answer: Sarah has 29 balloons now.

Explanation:
I add first because Sarah is getting more balloons, then subtract because she gives some away.

Assessment for Learning (AfL) Points

Use mini whiteboards during introduction and modelling for instant feedback.
Circulate during independent work to question reasoning and provide support.
Select pupils to explain answers and methods to the class to expose reasoning and misconceptions.
Use plenary to check for conceptual understanding and clarify any confusion.

Alignment with White Rose Maths Scheme

This lesson follows the White Rose Maths Year 4 Summer term focus on addition and subtraction problem solving, specifically targeting the fluency and reasoning components by applying knowledge to multi-step word problems. The structure incorporates White Rose’s emphasis on CPA (Concrete – Pictorial – Abstract) through bar models and visual aids, gradual complexity in problem tasks, and developing mathematical explanations.

This lesson plan ensures pupils deepen their understanding of multi-step addition and subtraction problems with conceptual clarity, logical ordering, and justifying answers in line with UK national curriculum expectations for Year 4.

Teaching Instructions