Exploring Multiples and Factors

National Curriculum Reference

Mathematics - Year 5
Number - Multiplication and Division:

• “Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.”
  (Department for Education, National Curriculum for England)

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Learning Objectives

By the end of the 25-minute lesson, pupils will be able to:

• LO1: Define multiples and factors.
• LO2: Identify all factor pairs of a given number up to 100.
• LO3: Recognise common factors between two numbers.
• LO4: Demonstrate quick recall of times tables to support these skills.

These objectives address developing fluency in multiplication facts alongside reasoning about factors and multiples within the Year 5 curriculum expectations.

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Resources

• Whiteboard and markers
• Individual mini-whiteboards and pens for all students
• Pre-prepared factor pair cards (numbers 1–100)
• Set of number cards (multiples)
• Times tables chant/reminder sheet
• “Multiple and Factors Bingo” sheets for quick assessment
• Stopwatch or timer

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Lesson Structure

Starter (5 minutes)

Engage and Recall Times Tables

• Begin with a 2-minute rapid-fire times tables chant (focus on 2, 3, 4, 5, 6, 8, 10).
• Use a quick-fire game where each pupil shouts out the next multiple when you say a base number (e.g., teacher says 3, progressing 3, 6, 9, 12...).
• This primes fluency needed for the main task.

Teaching Input (5 minutes)

Introduce Factors and Multiples with Visuals

• Define multiple as a number you get when you multiply a number by any whole number (e.g., multiples of 4 are 4, 8, 12…).
• Define factor as a number that divides exactly into another number (e.g., 1, 2, 4, 8, 16 are factors of 16).
• Use the whiteboard to write a number (e.g., 24) and demonstrate:
  • Find multiples until 100 (using cards or counting)
  • Find all factor pairs (1 & 24, 2 & 12, 3 & 8, 4 & 6) by checking divisibility and listing pairs.
• Explain common factors with two numbers (e.g., 24 and 36: common factors 1, 2, 3, 4, 6, 12).

Main Activity (10 minutes)

Factor Pairs Challenge - Differentiated by Ability

• Divide the class into three groups using mixed ability seating arrangements.
• Deploy Teaching Assistant (TA) to support the lowest ability group and individuals needing help by:
  • Scaffolding the factor-finding process, modelling divisibility rules, and guiding with prompts.

Group Tasks:

• Group 1 (Higher Ability):
  • Receive a set of numbers (up to 100) and must list all factor pairs for these numbers independently on mini-whiteboards.
  • Then find common factors between two larger numbers (e.g., 48 and 60).
• Group 2 (Mid Ability):
  • Work with fewer or smaller numbers; write factor pairs with some help from TA or teacher prompts.
  • Identify common factors between two smaller numbers.
• Group 3 (Developing):
  • TA supports with a guided worksheet identifying factors using times tables recall; physical resources like counters or blocks to visualise factors.

Circulate to provide on-the-spot feedback and to prompt reasoning:

• Ask “How do you know this is a factor?”
• “Can you find the matching factor pair?”
• Encourage the use of multiplication facts to validate answers.

Plenary (5 minutes)

Multiple and Factors Bingo (Quick Assessment)

• Distribute Bingo sheets showing a mixture of numbers. Call out a number and its multiples or factors (e.g., “Multiples of 7” or “Factors of 18”).
• Pupils mark numbers that match the clue.
• First few pupils to get a line shout “Bingo!”
• Quickly review key answers, consolidating learning and correcting misconceptions.

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Assessment for Learning

• Formative assessment via mini-whiteboard responses during main activities.
• Observations of group discussions and questions posed.
• Plenary Bingo provides instant feedback on children's understanding of multiples and factors.
• TA notes to support individual progress and inform next steps.

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Differentiation

• Challenge higher-ability pupils with larger numbers and common factors of three numbers.
• Scaffold with visual aids and manipulatives for those who need support.
• Use peer support by pairing stronger pupils with developing pupils during group work.
• TA actively supports learners needing additional guidance.

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Extension Ideas (If time permits)

• Challenge pupils to find prime factors of smaller numbers through factor pairs.
• Explore factor trees collaboratively.
• Create their own factor pair puzzles for peers to solve.

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Reflection for Teacher

• Were pupils able to recall times tables fluently to support factor identification?
• Did all groups engage and demonstrate progress with factor pairs?
• Note any misconceptions about factors/multiples to revisit.
• Consider adapting the number range to maximise challenge without overwhelming.

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This lesson plan maximises engagement using active recall, hands-on interaction, and peer collaboration while meeting the statutory Year 5 national curriculum requirements. It optimises TA support for inclusive learning, promoting confidence with multiples and factors.