Whole Numbers to 100,000 · Semester 1

Factors and Multiples

Students will identify common factors and multiples, differentiate between prime and composite numbers, and apply these concepts to problem-solving.

About This Topic

Factors and multiples build essential number sense for Primary 4 students. They learn to list all factors of two-digit numbers through systematic pairing, identify multiples by skip-counting or repeated addition, and find common factors and the lowest common multiple (LCM) of two numbers. Students also classify numbers as prime, with exactly two distinct factors (1 and itself), or composite. These concepts connect multiplication and division, enabling problem-solving like dividing resources equally or planning repeated events.

Positioned in the Whole Numbers unit up to 100,000, this topic strengthens computational fluency and pattern recognition. It lays groundwork for fractions in later semesters by showing how factors relate to unit fractions and equivalence. Logical listing fosters perseverance, while prime identification sparks curiosity about number properties.

Active learning excels with this topic because visual arrays from counters or tiles make factor pairs concrete and verifiable. Pair games prompt students to justify choices aloud, clarifying differences between factors and multiples. Collaborative LCM challenges reveal efficient strategies through shared trials, turning rote listing into flexible problem-solving.

Learning Objectives

• Calculate all factors for any given 2-digit number by using systematic listing.
• Identify the lowest common multiple (LCM) of two numbers up to 50.
• Classify numbers up to 100 as prime or composite, justifying the classification based on the number of factors.
• Compare and contrast the definitions of factors and multiples, providing examples for each.
• Solve word problems involving common factors and multiples.

Before You Start

Multiplication and Division Facts

Why: Students need a strong understanding of multiplication and division to identify factors and multiples.

Number Patterns

Why: Recognizing patterns through skip-counting is essential for finding multiples.

Key Vocabulary

Factor	A factor is a number that divides exactly into another number without leaving a remainder. For example, 3 is a factor of 12.
Multiple	A multiple is a number that can be divided exactly by another number. Multiples are found by skip-counting or repeated addition. For example, 24 is a multiple of 6.
Common Factor	A common factor is a number that is a factor of two or more different numbers. For example, 4 is a common factor of 12 and 20.
Lowest Common Multiple (LCM)	The lowest common multiple is the smallest positive number that is a multiple of two or more given numbers. For example, the LCM of 4 and 6 is 12.
Prime Number	A prime number is a whole number greater than 1 that has only two factors: 1 and itself. For example, 7 is a prime number.
Composite Number	A composite number is a whole number greater than 1 that has more than two factors. For example, 9 is a composite number because its factors are 1, 3, and 9.

Active Learning Ideas

Pairs: Factor Pairs Race

Pairs receive a two-digit number and race to list all factor pairs using mini-whiteboards, checking by multiplying back. Teacher calls time after 3 minutes; pairs swap numbers and repeat twice. Discuss systematic order from 1 up.

⏱ 25 min·Pairs

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Small Groups: Multiples Chain Game

In groups of four, students sit in a circle and say the next multiple of two given numbers in turn, like 4 and 6. If stuck, pass a counter; first to LCM wins a point. Rotate roles and numbers for three rounds.

⏱ 35 min·Small Groups

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Whole Class: Prime Sort Relay

Divide class into two teams. Call a number; first student from each team runs to board, states if prime or composite with factors. Correct team scores; continue for 10 numbers, then review rules.

⏱ 30 min·Whole Class

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Individual: LCM Puzzle Cards

Students match pairs of numbers to their LCM cards, using factor lists as clues. Self-check with answer key, then pair to explain one match. Extend by creating own puzzles.

⏱ 20 min·Individual

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Real-World Connections

Bakers use factors to divide ingredients equally when making large batches of cookies or cakes. For instance, if a recipe needs to be multiplied by 12, they might use factors of 12 (like 3 batches of 4) to manage the process efficiently.

Event planners use multiples to schedule recurring events or deliveries. For example, if decorations are delivered every 3 days and food every 4 days, they would find the LCM to know when both deliveries coincide.

Watch Out for These Misconceptions

Common Misconception

1 is a prime number.

What to Teach Instead

Prime numbers have exactly two distinct factors: 1 and the number itself. Number 1 has only one factor. Sorting cards into prime/composite piles in small groups lets students test divisibility collaboratively, refining definitions through peer debate.

Common Misconception

Factors and multiples mean the same thing.

What to Teach Instead

Factors divide a number evenly; multiples are products of the number times integers. Array-building activities in pairs help students see factors as dimensions of rectangles and multiples as totals, bridging the concepts visually.

Common Misconception

LCM is always the product of the two numbers.

What to Teach Instead

LCM is the smallest shared multiple, found by considering common factors. Venn diagram overlaps in small groups highlight shared primes, showing why division by GCF simplifies; active sharing corrects over-multiplication.

Assessment Ideas

Exit Ticket

Give students a card with two numbers, e.g., 18 and 24. Ask them to list all factors of 18, then list all factors of 24. Finally, ask them to identify the common factors and the LCM of 18 and 24.

Quick Check

Write a list of numbers on the board (e.g., 1, 2, 13, 15, 19, 21). Ask students to hold up one finger for prime numbers and two fingers for composite numbers. Then, ask volunteers to explain their reasoning for two of the numbers.

Discussion Prompt

Pose this scenario: 'Sarah has 30 stickers and wants to share them equally among her friends. She also has 40 pencils and wants to put them into equal packs. What is the largest number of friends she can share stickers with so everyone gets the same amount? What is the largest number of pencils she can put in each pack so all packs are equal?' Guide students to identify the need for common factors.

Frequently Asked Questions

How do you teach finding factors of a two-digit number?

Start with systematic listing from 1, pairing factors that multiply to the number, like 1x36 and 2x18 for 36. Use arrays or division facts to verify. Hands-on tile rectangles confirm pairs without trial-and-error guesswork, building confidence for LCM problems later in the unit.

What activities engage students with prime and composite numbers?

Prime hunts with number charts or relay sorts classify numbers quickly. Students justify choices using factor checklists. These games reinforce that primes have no divisors other than 1 and themselves, while composites do, preparing for factorization in higher grades.

How can active learning help students understand factors and multiples?

Concrete manipulatives like counters form factor arrays, making abstract pairs visible. Collaborative games, such as multiples chains, require explaining skips to peers, deepening relational understanding. Group LCM races encourage strategy sharing, like prime factorization shortcuts, far beyond worksheets for retention and application.

Common misconceptions in LCM and common multiples?

Students think LCM equals the larger number or direct product. Correct by listing multiples side-by-side in pairs, spotting the lowest shared one first. Venn diagrams for factors clarify GCF links, with group discussions resolving errors through evidence from listings.