Factors and HCF

Overview

This 40-minute lesson supports first-year students (12-13 years) to deepen their understanding of number sets and introduce factors and the Highest Common Factor (HCF). It aligns with the Irish Junior Cycle Mathematics specification, focusing on Number Strand learning outcomes, addressing mathematical reasoning, problem-solving, and communication skills.

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Curriculum Links

Junior Cycle Mathematics Specification (Specifically Number Strand):

• Recognise, generate and describe number patterns and sequences
• Understand and use factors, multiples, prime numbers, and highest common factors in problem-solving contexts
• Use appropriate mathematical language and notation confidently
• Develop competence in mental and written procedures
• Reason and communicate confidently using mathematical language

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Learning Objectives

By the end of the lesson students will be able to:

1. Recall and classify number sets (Natural numbers, Whole numbers, Integers, etc.) accurately (Reflecting Junior Cycle Number Objective N1).
2. Define and identify factors of whole numbers.
3. Calculate the factors of given numbers using practical methods.
4. Determine the Highest Common Factor (HCF) of two given numbers with understanding.

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Success Criteria

• Explain key number sets with examples on the board confidently.
• Identify all factors of at least two numbers correctly.
• Use the list of factors to find the HCF of two numbers and explain the reasoning clearly.
• Show clear step-by-step working for factor and HCF calculations.

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Lesson Structure

1. Recap and Learning Check on Number Sets (10 minutes)

Activities:

• Begin with a quick whole-class quiz: name examples or properties of Natural numbers, Whole numbers, Integers, and Rational numbers.
• Use mini whiteboards to show answers for engagement and instant feedback; circulate to support learners.
• Display number set Venn diagrams with some missing types for students to fill in (dyslexia-friendly design: use clear fonts, colour-coded sets).
• Ask targeted questions: “Is -3 a natural number? Why? What sets does it belong to?”

Differentiation:

• Provide visual number line aids to help with negative numbers (supports EAL and dyslexic students).
• Use sentence starters like “A natural number is…” to support those needing language scaffolding.

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2. Introducing Factors (12 minutes)

Activities:

• Concrete example: Use small counters or cubes. Model finding factors of 12 by making rectangles (groups) and recording the pairs that neatly arrange (eg. 1x12, 2x6, 3x4).
• Students work in pairs using mini cubes to find factors of 18 or 20, writing the pairs on mini whiteboards.
• Highlight that factors come in pairs that multiply to the original number.
• Discuss prime vs composite numbers briefly to consolidate understanding.

Success Check:

• Students show factors of their number pairs visibly, correctly identifying all factors.

Differentiation:

• Visual learners: factor pairs chart displayed.
• Students requiring challenge: explore factors of a 3-digit number or discuss prime factorisation briefly.

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3. Finding the Highest Common Factor (HCF) (12 minutes)

Activities:

• Define HCF clearly: largest common factor two numbers share.
• Demonstrate: Choose 12 and 18. List factors (on board or projected), then identify the highest one common to both.
• Practice: split class into small groups for a HCF “treasure hunt” with numbers around the room (e.g., 24 & 30, 36 & 48). Groups write down factors and circle the HCF.
• Challenge: Students explain how to find the HCF to a peer, improving mathematical communication and reasoning.

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4. Plenary and Assessment (6 minutes)

Activities:

• Quick quiz: On mini whiteboards, write factors and HCFs of 15 & 25, 20 & 28.
• Exit ticket: One sentence describing what the HCF is and why it might be useful.

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Extension Activities

• Investigate the HCF using prime factorisation method with larger numbers.
• Word problem solving involving HCF contexts (e.g. packaging items, dividing into groups).
• Explore Lowest Common Multiple (LCM) as a complementary concept.

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Differentiation Strategies

• Provide worked examples and step-by-step guides.
• Use practical materials to support hands-on learners.
• Pre-teach key vocabulary with dyslexia-friendly fonts (such as OpenDyslexic).
• Allow extra processing time and verbal explanations for students with processing difficulties.
• Pair stronger and weaker students for peer support.

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Resources Required

• Mini whiteboards and pens
• Counters or cubes for factor grouping
• Number set Venn diagram posters (colour-coded)
• Factor and HCF worksheets (clear print, dyslexia-friendly fonts)
• Projector or board for factor lists
• Exit tickets for plenary

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This lesson plan balances conceptual understanding, practical activity, peer collaboration, and assessment, fully aligned with the Irish Junior Cycle Mathematics Curriculum, while being accessible and engaging for a diverse classroom of 12-13 year olds.