Mastering Mathematical Thinking: 4th Class · 4th Class · Number Systems and Place Value · Autumn Term

Factors and Multiples

Introducing the concepts of factors and multiples and identifying them for given numbers.

• NCCA Curriculum Specifications
• NCCA: Primary - Number

About This Topic

Factors divide a number evenly with no remainder, while multiples result from multiplying a number by whole numbers. In 4th Class under the NCCA Primary Number strand, students identify factors and multiples for numbers up to 100, such as listing 1, 2, 3, 4, 6, 12 for 24 or multiples of 5 like 5, 10, 15. They practice constructing complete lists and explain links to multiplication tables, addressing key questions on differentiation and relationships.

This topic strengthens number sense within the Number Systems and Place Value unit, revealing patterns like factor pairs summing to square numbers or common multiples in problem-solving. Students develop reasoning skills essential for divisibility, primes, and fractions later in the curriculum. Concrete examples, such as grouping 24 counters into equal sets, make these abstract ideas accessible.

Active learning benefits this topic greatly because manipulatives and games turn rote listing into pattern discovery. When students pair counters into arrays or play multiples hopscotch, they visualize relationships firsthand, correct errors through peer talk, and build fluency with joy, leading to deeper retention and confident application.

Key Questions

1. Differentiate between a factor and a multiple of a number.
2. Construct a list of all factors for a given number like 24.
3. Explain the relationship between multiplication and finding factors and multiples.

Learning Objectives

• Identify all factors for a given number up to 100.
• List the first five multiples for any given number up to 12.
• Compare and contrast the definitions of a factor and a multiple.
• Explain the inverse relationship between multiplication and finding factors.
• Construct a list of common multiples for two given numbers.

Before You Start

Multiplication Facts

Why: Students need fluency with multiplication tables to identify factors and generate multiples efficiently.

Division Concepts

Why: Understanding division as 'how many groups' or 'how much in each group' is foundational for grasping the concept of factors dividing a number evenly.

Key Vocabulary

Factor	A factor is a number that divides another number exactly, with no remainder. For example, 3 and 4 are factors of 12.
Multiple	A multiple is the result of multiplying a number by any whole number. For example, 10 and 15 are multiples of 5.
Factor Pair	Two factors that multiply together to equal a specific number. For example, (2, 6) is a factor pair for 12.
Common Multiple	A number that is a multiple of two or more different numbers. For example, 12 is a common multiple of 3 and 4.

Watch Out for These Misconceptions

Common Misconception

Factors and multiples are the same thing.

What to Teach Instead

Factors divide into the number; multiples extend from it via multiplication. Array activities help students see factors as array dimensions and multiples as repeated additions, clarifying the distinction through hands-on building and peer explanation.

Common Misconception

1 and the number itself do not count as factors.

What to Teach Instead

Every number has 1 and itself as factors. Factor pair matching games reveal these endpoints naturally, as students include them to complete pairs, reducing exclusion errors via visual confirmation.

Common Misconception

Only even numbers have factors other than 1.

What to Teach Instead

Odd numbers like 15 have factors 3 and 5. Skip-counting chains and array models demonstrate this, as groups explore odd multiples and factors, fostering inclusive listing through collaborative discovery.

Active Learning Ideas

Pairs: Factor Pair Cards

Prepare cards with numbers from 1 to 50 and their potential factors. Pairs match factor pairs that multiply to the target number, like 3 and 8 for 24. After matching, pairs justify choices to the class.

25 min·Pairs

Small Groups: Array Builders

Provide counters and grid paper. Groups build rectangular arrays for given numbers, such as 24 as 4x6 or 3x8, then list all dimensions as factors. Groups share arrays on the board.

35 min·Small Groups

Whole Class: Multiples Skip Count

Students stand in a circle. Teacher calls a number like 7; class counts multiples aloud while passing a beanbag. Speed up rounds to practice fluency, noting patterns.

20 min·Whole Class

Individual: Factor Lists Challenge

Give numbers 12 to 36. Students list all factors systematically, checking with multiplication. Collect sheets for feedback and class discussion of complete lists.

15 min·Individual

Real-World Connections

• Bakers often divide dough into equal portions to make rolls or cookies. If a baker has 24 cookies to make, they might consider factors like 2, 3, 4, 6, 8, or 12 to determine how many rows or columns to arrange them in.
• When planning a party, you might need to buy supplies in bulk. If you need 30 party favors, you would look for multiples of the number of favors per pack, such as packs of 5 or 6, to ensure you have exactly enough.

Assessment Ideas

Quick Check

Write the number 36 on the board. Ask students to write down: 1) Three factors of 36. 2) Two multiples of 36. 3) One factor pair for 36.

Discussion Prompt

Pose this question to small groups: 'If 5 is a factor of a number, what do you know about that number? If 20 is a multiple of a number, what do you know about that number?' Have groups share their reasoning.

Exit Ticket

Give each student a card with two numbers, for example, 8 and 12. Ask them to write: 1) Three factors of 8. 2) Three multiples of 12. 3) One common multiple of 8 and 12.

Frequently Asked Questions

How do I introduce factors and multiples in 4th Class?

Start with concrete examples using counters: group 24 into equal sets to find factors like 3 groups of 8. Transition to listing multiples via skip counting on a hundred chart. Use anchor charts showing pairs for 24. This builds from manipulatives to abstract lists, aligning with NCCA progression and ensuring all students grasp basics before independent practice.

What are the most common errors with factors and multiples?

Students often swap the terms, exclude 1 or the number as factors, or list incomplete sets. Address through daily number talks reviewing lists for 12 or 18. Visuals like factor rainbows, pairing smallest to largest, help spot gaps. Regular low-stakes quizzes reinforce accuracy without pressure.

How can active learning help students master factors and multiples?

Active approaches like array building with counters or factor bingo make abstract concepts tangible. Students discover patterns through movement in multiples relays or collaboration in pair matching, correcting misconceptions on the spot via discussion. This boosts engagement, retention, and number fluency far beyond worksheets, as peer teaching solidifies understanding.

How do factors and multiples connect to other maths topics?

They underpin primes, divisibility for efficient calculation, lowest common multiples for fractions, and problem-solving with groupings. In NCCA, links appear in operations and data strands. Teaching via real contexts, like sharing sweets evenly, shows relevance, preparing students for 5th Class ratio and proportion work.