Multiplication Word Problems

Overview

This 60-minute lesson for Year 4, aligned with the National Curriculum for England and White Rose Maths, focuses on solving two-step multiplication word problems with addition, supported by the grid method. The lesson aims to deepen pupils’ conceptual understanding and problem-solving skills using concrete representation and metacognitive questioning.

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National Curriculum Links

Mathematics Programmes of Study: Year 4 (Number - Multiplication and Division)

• Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; multiplying together three numbers.
• Multiply two-digit and three-digit numbers by a one-digit number using formal written layout (grid method).
• Solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by one-digit numbers.
• Reasoning and Problem Solving: Solve addition and multiplication two-step problems in contexts, deciding which operations and methods to use and why.

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Learning Objectives

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

• Use the grid method to multiply two-digit numbers by one-digit numbers accurately.
• Solve two-step word problems involving multiplication and addition.
• Explain and justify the choice of methods used to solve word problems.
• Reflect on strategies and identify errors in their reasoning or calculations.

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Success Criteria

I can:

• Read and understand two-step word problems involving multiplication and addition.
• Use the grid method to set out and calculate multiplication accurately.
• Identify in which order to use multiplication and addition to solve problems.
• Explain my thinking clearly and justify my answers.
• Check my answers and correct any mistakes.

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Resources

• Whiteboards and pens for pupil responses
• Printable or projected word problems
• Grid method multiplication templates
• Example problem and worked solution on the board/visualiser
• Counters or place value charts (optional for modelling)

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Lesson Structure

1. Introduction (10 mins) – Engaging Starter and Questioning

Objective: Activate prior knowledge of multiplication and build curiosity about solving multi-step problems.

• Begin with a quick recap of the grid method: present a simple 2-digit by 1-digit multiplication (e.g., 23 × 4).
• Use a visualiser or board to model the grid layout step-by-step while explaining.
• Pose an open-ended question:
  • “If Jamie buys 23 packets of pencils, each with 4 pencils inside, how many pencils does he have?” – quick mental check.
• Introduce a two-step word problem involving multiplication and addition. Example:
  “Jamie bought 23 packets of pencils (4 pencils in each). Then, he bought 17 more pencils separately. How many pencils does Jamie have in total?”
• Ask pupils to discuss in pairs what steps they would take.
• Targeted questions:
  • “Which maths operation should we use first and why?”
  • “How will we organise our working out to avoid mistakes?”
  • “What does the grid method help us with here?”

AfL Check #1: Use mini whiteboards for pupils to write down the first step’s expression (either multiplication or addition). This allows quick assessment of their understanding of order of operations and problem decomposition.

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2. Modelling and Guided Practice (20 mins)

Objective: Model solving two-step multiplication word problems using the grid method; scaffold pupils in applying this independently.

• Display the example problem:
  “Jamie bought 23 packets of pencils with 4 pencils in each packet, then 17 single pencils. How many pencils does Jamie have in total?”
• Model setting out the multiplication step using the grid method:
  • Partition 23 into 20 and 3, and multiply each by 4.
  • Set out the grid with multiplication facts:
    | | 20 | 3 |
    |---|----|---|
    | 4 | 80 | 12|
  • Add the two products: 80 + 12 = 92 pencils from packets.
• Explain finding the total by adding the 17 extra pencils:
  • 92 + 17 = 109 pencils altogether.
• Emphasise writing clear, organised working out and labelling steps.
• Targeted questions (Bloom’s Taxonomy):
  • _“Why did we partition 23 as 20 and 3?” (Understanding)
  • _“Could we solve this problem another way? Why or why not?” (Evaluating)
  • _“What would happen if we added before multiplying?” (Analysing and Predicting)
  • _“How do we know 109 pencils is a reasonable answer?” (Evaluating, Checking)
• Ask selected pupils to explain the reasoning behind each step and justify the method aloud.

AfL Check #2: Observe pupil explanations and responses to questions to assess reasoning skills and identify any emerging misconceptions, e.g., adding before multiplication or errors in grid method layout.

• Hand out similar scaffolded problems for pairs or small groups to solve collaboratively using the grid method and explain their solutions to a partner.

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3. Independent Application (20 mins)

Objective: Pupils practise solving a range of two-step multiplication and addition word problems independently or in pairs.

• Provide a worksheet with 3-4 word problems of increasing complexity, each requiring two steps: multiplication using the grid method and then addition.
• Encourage pupils to:
  • Read the problem carefully.
  • Underline key numbers and operations required.
  • Set out the multiplication using the grid method clearly.
  • Write the addition step separately and find the final answer.
  • Write one or two sentences explaining their approach and checking their answer.
• Teachers circulate to prompt with higher-order questions and provide targeted support:
  • “How did you decide which part to multiply first?”
  • “Explain why you arranged your grid like this.”
  • “Can you check if your answer makes sense?”

AfL Check #3: Use marking, observation, and questioning to check pupil’s method, calculation accuracy, and ability to explain their approach.

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4. Plenary (10 mins)

Objective: Consolidate learning, address misconceptions, and encourage reasoning reflection.

• Invite a few pupils to share their solutions and explain their thinking step-by-step, using the grid method and addition clearly.
• Use a “spot the mistake” approach: present an incorrect example on the board where, for instance, addition was done before multiplication or grid method has missing parts.
• Ask the class:
  • “Can you find the mistake?”
  • “What would you do differently?”
• Summarise the success criteria, reinforcing the importance of using the grid method for multiplication and then adding.
• Finish with a reflective question:
  • “Why might solving two-step problems be harder than one-step? How does the grid method help?”

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Common Misconceptions and Difficulties

• Mixing order of operations: Pupils may add before multiplying because addition seems simpler. Emphasise the logic of solving multiplication first in multi-step problems.
• Grid method errors: Forgetting to partition numbers correctly, missing cells in grids, or adding part products incorrectly.
• Misunderstanding problem context: Pupils may fail to identify that two steps involve different operations or confuse quantities to be multiplied or added.
• Over-reliance on one method: Difficulty in justifying or explaining other strategies; encourage flexible thinking.

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Example for Pupils to Copy

Problem:
A school orders 46 packs of crayons, each containing 5 crayons. Later, they receive an extra 29 crayons as a gift. How many crayons does the school have in total?

Working:

• Multiply 46 × 5 using the grid method:

	40	6
5	200	30

• Add: 200 + 30 = 230
• Now add the extra crayons: 230 + 29 = 259
• Answer: The school has 259 crayons in total.

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This lesson plan enables pupils to build fluency, reason mathematically, and solve multi-step problems confidently, fully aligned with the National Curriculum standards and the White Rose Maths approach.