Number Operations Challenge

Overview

This 45-minute lesson is designed for a small group of 2 Year 3 students, focusing on the interpretation and application of addition (+), subtraction (−), multiplication (×), division (÷), and equals (=) in practical contexts. The lesson aligns directly with the key learning objectives from the National Curriculum for England for Mathematics, specifically targeting Year 3 Number – Multiplication and Division, and Number – Addition and Subtraction.

Key National Curriculum Links:

• Year 3 Mathematics - Number - Addition and Subtraction
  Pupils should be able to:

  • Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

• Year 3 Mathematics – Number – Multiplication and Division
  Pupils should be able to:

  • Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.
  • Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods.
  • Solve problems, including missing number problems, involving multiplication and division.

• Mathematical reasoning and problem solving

  • Solve two-step problems in contexts, deciding which operations and methods to use and why.

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Learning Objectives

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

1. Interpret mathematical symbols (+, −, ×, ÷, =) accurately in practical situations (National Curriculum references: Number - Addition, Subtraction, Multiplication, and Division).
2. Solve problems involving whole numbers and decimals, recognising contexts such as money and measurements (Number and Measurement strands).
3. Apply the standard order of operations (BODMAS) in multi-step calculations to solve problems practically.
4. Solve two-step word problems, articulating reasoning and methods used.

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Resources Needed

• Whiteboard and markers
• Mini-whiteboards and pens for each student
• Counters or small cubes (for practical modelling)
• Printed word problem cards (with practical scenarios) including decimals
• Place value charts
• Visual BODMAS poster (simple and kid-friendly)
• Timer or stopwatch

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Lesson Breakdown (45 minutes)

1. Introduction and Warm-Up (5 minutes)

• Objective: Activate prior knowledge of mathematical symbols and terminology (+, −, ×, ÷, =).
• Teacher writes or draws a practical scenario on the board, e.g., "There are 7 apples. We buy 3 more apples. How many apples are there now?"
• Ask students to identify the mathematical operation from the context (+ for adding apples).
• Discuss the meaning of each symbol with concrete examples (using counters).
• Quick-fire questions on symbols: “What does × mean? When do we use ÷?”

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2. Practical Symbol Interpretation Activity (10 minutes)

• Present 4 mini word problems involving addition, subtraction, multiplication, and division in practical contexts:

  1. Adding money amounts (£2.50 + £3.70)
  2. Subtracting lengths (5m − 2.3m)
  3. Multiplying number of items (4 packets × 6 biscuits)
  4. Sharing sweets between friends (12 sweets ÷ 4 friends)

• Pupils work with counters and mini-whiteboards to write and solve corresponding equations that include decimals where realistic (money/measurement).

• Emphasise interpreting each symbol as they work through solutions.

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3. Teaching Multi-Step Calculations & BODMAS (10 minutes)

• Introduce the standard order of operations with the BODMAS acronym, using a colourful poster.
• Use a practical model problem:
  “I have £5. I buy 2 chocolate bars costing £1.20 each, then get £1.50 pocket money. How much money do I have now?”
• Write the equation as: £5 − (2 × £1.20) + £1.50 = ?
• Demonstrate how to tackle the brackets first (multiplication), then subtraction, then addition.
• Let students try a similar calculation on their mini-whiteboards with support.

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4. Problem Solving: Two-Step Word Problems (15 minutes)

• Present 3 two-step problems involving decimals and whole numbers, aligned to real-life contexts relevant to Year 3 (money, measurement, quantities). Examples:

  1. Sarah buys 3 notebooks at £1.80 each and pays with £10. How much change does she get?
  2. Tom runs 2.5km and then another 3.1km. How far does he run in total?
  3. There are 24 apples split into boxes of 6. Then 2 boxes are eaten. How many apples remain?

• Pupils read problems aloud, underline key numbers, and decide the operations needed.

• Encourage students to use mini-whiteboards, counters, or drawings to visualise.

• Support explanation of reasoning and method during and after working on problems.

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5. Assessment and Review (5 minutes)

• Each pupil writes and solves their own two-step word problem involving +, −, ×, ÷, and decimals.

• Share answers and reasoning one at a time, with teacher feedback focusing on correct interpretation and order of operations.

• Teacher uses mini-whiteboards to formatively assess understanding.

• Conclude with a quick verbal quiz: “What does the ÷ symbol mean?” “When do you use multiplication?” “What comes first in 5 + 3 × 2?”

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Differentiation

• For the pupil who needs more support: Use more concrete objects and stem sentences for word problems. Focus first on recognising symbols clearly.
• For the pupil who needs challenge: Increase problem complexity with three-step problems or including multiplication and division of decimals (e.g., money times quantity).

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Plenary and Next Steps

• Reinforce the importance of reading problem contexts carefully to decide operations.
• Set a short “real-world maths detective” task for homework: Find a practical situation at home involving two-step calculations and write the problem with the calculations.
• Preview next lesson: Formal written methods for multiplication and division.

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Teacher Notes

• Keep all explanations simple and practical using real, familiar contexts.
• Encourage verbalising thought processes to strengthen reasoning skills.
• Praise perseverance and accuracy in interpreting symbols.
• Use the small group size to allow personalised attention and direct questioning.

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This lesson plan delivers a rich learning experience grounded in the National Curriculum expectations for Year 3 maths, using practical activities and problem-solving strategies to build solid understanding and fluency in interpreting operations and solving multi-step calculations with whole numbers and decimals.