Factors and MultiplesActivities & Teaching Strategies
Active learning shifts the abstract ideas of factors and multiples into hands-on experiences where students can see, touch, and manipulate numbers. When students work in pairs, small groups, or individually with visual tools like cards and arrays, they build mental models that last beyond the lesson.
Learning Objectives
- 1Identify all factors for a given number up to 100.
- 2List the first five multiples for any given number up to 12.
- 3Compare and contrast the definitions of a factor and a multiple.
- 4Explain the inverse relationship between multiplication and finding factors.
- 5Construct a list of common multiples for two given numbers.
Want a complete lesson plan with these objectives? Generate a Mission →
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.
Prepare & details
Differentiate between a factor and a multiple of a number.
Facilitation Tip: During Factor Pair Cards, listen for students to articulate why 1 and the number itself belong in every pair, reinforcing the definition through conversation.
Setup: Tables/desks arranged in 4-6 distinct stations around room
Materials: Station instruction cards, Different materials per station, Rotation timer
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.
Prepare & details
Construct a list of all factors for a given number like 24.
Facilitation Tip: While Array Builders, circulate to ask groups how changing one dimension of the array affects the other, guiding them to see factors as dimensions.
Setup: Tables/desks arranged in 4-6 distinct stations around room
Materials: Station instruction cards, Different materials per station, Rotation timer
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.
Prepare & details
Explain the relationship between multiplication and finding factors and multiples.
Facilitation Tip: For Multiples Skip Count, stand back during the opening round to let students self-correct rhythm errors, then model the correct skip pattern on the board.
Setup: Tables/desks arranged in 4-6 distinct stations around room
Materials: Station instruction cards, Different materials per station, Rotation timer
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.
Prepare & details
Differentiate between a factor and a multiple of a number.
Facilitation Tip: During Factor Lists Challenge, provide blank grids for students who rush to slow down and list systematically from smallest to largest.
Setup: Tables/desks arranged in 4-6 distinct stations around room
Materials: Station instruction cards, Different materials per station, Rotation timer
Teaching This Topic
Teachers introduce factors and multiples through concrete materials before moving to symbolic notation. Use arrays and skip counting to bridge multiplication facts to new concepts, avoiding premature abstract rules. Research shows that students who physically arrange objects develop stronger number sense than those who only see written lists.
What to Expect
By the end of these activities, students should confidently list factors and multiples without prompting, explain how they are related to multiplication tables, and identify common factors and multiples with minimal support. Their explanations should include precise language such as 'divides evenly' and 'whole number multiples.'
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Factor Pair Cards, watch for students to claim factors must be larger than 1 and smaller than the number.
What to Teach Instead
Prompt pairs to include the card with 1 and the card with the target number, modeling the pair (1, number) and (number, 1) to show these are always valid factors.
Common MisconceptionDuring Array Builders, watch for students to exclude 1 as a factor when building arrays.
What to Teach Instead
Challenge groups to build a 1-by-n array for any n, then ask them to identify the corresponding factor pair, reinforcing that 1 is always a factor.
Common MisconceptionDuring Multiples Skip Count, watch for students to skip even multiples when counting odd numbers.
What to Teach Instead
Have the class count aloud while you write multiples on the board, pausing to ask, 'How do we know 15 is a multiple of 5?' to redirect any errors in rhythm or pattern.
Assessment Ideas
After Factor Pair Cards, write the number 36 on the board and ask students to write down: 1) Three factors of 36. 2) Two multiples of 36. 3) One factor pair for 36.
During Array Builders, 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 before continuing.
After Factor Lists Challenge, 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.
Extensions & Scaffolding
- Challenge: Ask students to find all common multiples of 6 and 8 up to 100 and explain why these appear in both skip-counting sequences.
- Scaffolding: Provide partially completed factor pair lists with blanks for missing numbers to reduce cognitive load during Factor Pair Cards.
- Deeper exploration: Have students investigate prime numbers by building arrays with only one row or one column, then classifying numbers as prime or composite based on their array shapes.
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. |
Suggested Methodologies
Planning templates for Mastering Mathematical Thinking: 4th Class
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Number Systems and Place Value
Place Value and Number Systems (Integers)
Extending understanding of place value to larger integers, including millions and billions, and exploring different number systems.
2 methodologies
Properties of Integers: Factors, Multiples, Primes
Investigating properties of integers including factors, multiples, prime numbers, composite numbers, and prime factorisation.
2 methodologies
Comparing and Ordering Rational and Irrational Numbers
Comparing and ordering integers, fractions, decimals, and introducing irrational numbers on a number line.
2 methodologies
Rounding and Significant Figures
Applying rounding to decimal places and significant figures in various contexts, including scientific notation.
2 methodologies
Estimating and Approximating Calculations
Developing strategies for estimating and approximating calculations involving various number types and operations.
2 methodologies
Ready to teach Factors and Multiples?
Generate a full mission with everything you need
Generate a Mission