Solving Number Problems

I want the plan to focus on understanding how to solve number problems (NFER assessment style questions by using strategies)

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 understanding how to solve number problems (NFER assessment style questions by using strategies)

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)

Use of Layered questioning which requires pupils to think deeper to give an explanation of their reasoning. Use of Active reasoning.

Create an example for children to copy into books and use to support work

Include AfL points throughout teaching and modelling stage ( tell me What AfL to use, where to use it?) Modelling

use model for a reasoning question - use sentence stems and timer so that children can explain the answer verbally before they write them.

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 Key Stage 2 (Year 4)
- Number - number and place value:
  Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
- Number - addition and subtraction:
  Add and subtract numbers with up to 4 digits using formal written methods of columnar addition and subtraction where appropriate
- Mathematical reasoning:
  Solve number and practical problems that involve increasingly large numbers, including using efficient written and mental methods

Aligned with White Rose Maths Scheme, Year 4 – Number: Addition and Subtraction Unit

Learning Objectives

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

Use a range of strategies to solve number problems involving 4-digit numbers confidently.
Explain and justify their reasoning clearly when solving number problems.
Demonstrate resilience when approaching multi-step problems with increasing complexity.

Success Criteria

I can:

Identify the key information in a number problem.
Choose and use a strategy to solve a number problem (e.g., column addition/subtraction, related facts, breaking numbers apart).
Explain my reasoning using sentence stems, e.g., "I know this because...", "I solved it by...".
Tackle problems with more than one step by working systematically.
Check my answers for accuracy.

Lesson Structure (30 minutes)

1. Engaging Introduction (5 minutes)

Start with a quick challenge: Display a problem on the board:
“There are 1,245 apples in a store. 379 apples are sold. How many apples are left?”
Ask pupils to discuss with a partner how they might solve it and then share their ideas.
Emphasise there is more than one way to solve, and today they will learn to choose strategies and explain their thinking clearly.
Questioning:
- "What information is important in this problem?" (Recall/Understanding)
- "Can someone explain how to solve this without calculating yet?" (Applying)
- "Why might it help to use column subtraction here?" (Analysing)

2. Modelling and Teacher Demonstration (7 minutes)

Display the above problem and model solving it step-by-step using column subtraction.
Use a visual number line or place value chart as needed to support understanding.
Active Reasoning: Ask pupils to explain aloud each step before proceeding, using sentence stems:
- “I am subtracting the ones first because…”
- “I regrouped the tens because…”
Set a 1-minute timer for a partner talk: "Explain why we can't subtract 9 from 5 in the ones column."
AfL: Use mini-whiteboards for pupils to write the subtraction steps and highlight errors immediately. Ask targeted questions to spot misconceptions (e.g., subtract 9 from 5 without regrouping).
Emphasise and discuss common misconceptions:
- Pupils subtract digits incorrectly when borrowing/regrouping is required.
- Difficulty understanding place value when decomposing numbers.
- Skipping steps or performing operations out of order in multi-step problems.

3. Guided Practice with Layered Questioning (10 minutes)

Present two problems on the board with increasing complexity:
1. “A library has 2,634 books. They buy 1,179 more. How many books do they have now?”
2. “A theatre has 3,450 seats. 1,285 tickets are sold for the morning show and 1,020 for the afternoon show. How many seats are left unsold?”
Pupils work in pairs to solve the first problem, then discuss how to approach the second one (multi-step).
Targeted questions for pupils:
- “What strategy will you use to add (or subtract) these numbers? Why?” (Evaluating)
- “Can you explain the steps for solving the second problem?” (Analysing)
- “How do you know your answer is reasonable?” (Evaluating)
- “What do you find tricky in this problem?” (Reflecting)
Provide sentence stems to support reasoning write-ups:
- “I started by...”
- “I checked my work by...”
AfL: Circulate and listen for verbal explanations, prompt pupils who struggle with questions, and note misconceptions. Use quick quiz questioning to check understanding of place value concepts involved.

4. Independent Task: Applying Strategies (5 minutes)

Pupils receive a worksheet with 3 number problems (NFER-style) increasing in complexity:

Example problems:
a) Subtract 1,587 from 3,204.
b) There are 4,392 marbles in a jar. 1,768 are red, the rest are blue. How many blue marbles are there?
c) A school has 5,630 pencils. They give 1,275 to Year 3 and 2,430 to Year 4. How many pencils are left?
Encourage pupils to:
- Identify the key facts,
- Choose the strategy,
- Solve,
- Write their reasoning for one question using sentence stems.
Set a timer to build focus and pace.

5. Plenary (3 minutes)

Select 3 pupils to share their reasoning for one of the problems verbally using the sentence stems and modelled approach.
Whole-class discussion on:
- “Which strategies were most effective?”
- “What was challenging, and how did you overcome it?”
- “How does explaining your thinking help your understanding?”
Recap learning objectives and success criteria, praise efforts demonstrating reasoning.

Example for Pupils to Copy in Books

Problem:
There are 3,218 tickets for a concert. 1,479 tickets have been sold. How many tickets are left?

Solution (modelling):

Step 1: Subtract hundreds and thousands starting from ones column.
Step 2: 8 − 9 (not possible, so regroup 1 ten as 10 ones)
Step 3: 18 − 9 = 9 (ones)
Step 4: 0 − 7 (regroup 1 hundred as 10 tens)
Step 5: 10 − 7 = 3 (tens)
Step 6: 1 − 4 (regroup 1 thousand as 10 hundreds)
Step 7: 11 − 4 = 7 (hundreds)
Step 8: 2 − 1 = 1 (thousands)

Answer: 1,739 tickets are left.

Reasoning Sentence:
"I regrouped when I could not subtract the ones because eight is smaller than nine. I worked from right to left, subtracting each digit carefully, which helped me get the correct answer."

Common Misconceptions & Difficulties

Confusing place values during subtraction or addition (e.g., subtracting tens from ones).
Forgetting to regroup (borrow) when needed.
Not reading the whole problem carefully—missing multi-step elements.
Rushing through without checking answers for reasonableness.
Difficulty explaining and justifying their reasoning clearly.

Assessment for Learning (AfL) Opportunities

Use mini whiteboards during modelling to check pupils' grasp of regrouping.
Partner talk after explaining subtraction steps to verbalise understanding.
Targeted questioning and listening during guided practice.
Observing independent work and providing instant verbal feedback.
Plenary oral feedback to assess reasoning and articulation.

This lesson plan incorporates rich questioning, scaffolded support, reasoning opportunities, and assesses understanding dynamically, fulfilling the National Curriculum requirements for Year 4 number problem solving with a focus on reasoning and strategy use.

Teaching Instructions