Mathematics · Year 4

Active learning ideas

Factors of Whole Numbers

Active learning works well for factors because students need to see and touch the idea of pairing numbers. When they build arrays or group objects, they move from abstract symbols to concrete evidence of how factors multiply to form a whole. This hands-on approach builds confidence and accuracy, especially for learners who struggle with rote recall.

• ACARA Content Descriptions
• AC9M4N03

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Hexagonal Thinking
• 35 min · Small Groups

Array Builder: Factor Grids

Provide counters and grid paper. Students select a number like 24 and build rectangular arrays, recording factor pairs such as 3x8 or 4x6. They test if arrays fit perfectly and discuss why some dimensions fail. Extend by finding all pairs systematically.

Differentiate between a factor and a multiple of a number.

Facilitation Tip

During Array Builder, circulate and ask students to explain how their grid shows both factors of the number and not multiples.

What to look for

Provide students with the number 36. Ask them to: 1. List all factor pairs of 36. 2. Draw an array representing 36. 3. State one divisibility rule they used to find factors.

• Analyze
• Evaluate
• Create
• Self-Awareness
• Relationship Skills

Activity 02

• Hexagonal Thinking
• 25 min · Small Groups

Divisibility Dash: Rule Relay

Divide class into teams. Place number cards around the room. Students run to a card, apply one divisibility rule to identify a factor, and tag the next teammate. Teams compare lists at the end and verify with multiplication.

Construct a method to find all factors of a given number.

Facilitation Tip

For Divisibility Dash, stand near the rule cards so you can gently correct misapplied rules in real time.

What to look for

Write the numbers 7, 15, and 25 on the board. Ask students to hold up fingers to indicate the number of factors each number has. Then, ask them to write down the factors for one of the numbers and explain why it is prime or composite.

• Analyze
• Evaluate
• Create
• Self-Awareness
• Relationship Skills

Activity 03

• Hexagonal Thinking
• 20 min · Pairs

Factor Pair Match-Up: Card Game

Create cards with numbers and possible pairs. In pairs, students match factor pairs to products, then justify using arrays or rules. Shuffle for multiple rounds, timing for speed and accuracy.

Explain how factors are used in real-world situations like grouping.

Facilitation Tip

In Factor Pair Match-Up, listen for students using divisibility rules to justify their matches before confirming correctness.

What to look for

Pose the question: 'How are factors and multiples related?' Guide students to explain that multiples are built from factors. Ask: 'If a number is a multiple of 6, what do you know about its factors?'

• Analyze
• Evaluate
• Create
• Self-Awareness
• Relationship Skills

Activity 04

• Hexagonal Thinking
• 30 min · Pairs

Grouping Challenge: Real-World Scenarios

Present problems like dividing 36 cookies among friends. Students draw arrays or list factors to find sharing options. Groups present solutions and vote on the fairest method.

Differentiate between a factor and a multiple of a number.

Facilitation Tip

During Grouping Challenge, ask guiding questions like 'How many ways can you divide 24 cookies fairly?' to prompt systematic thinking.

What to look for

Provide students with the number 36. Ask them to: 1. List all factor pairs of 36. 2. Draw an array representing 36. 3. State one divisibility rule they used to find factors.

• Analyze
• Evaluate
• Create
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teachers approach this topic by starting with concrete manipulatives before moving to abstract symbols, aligning with research showing that visual and tactile experiences strengthen number sense. Avoid rushing to formulas; instead, guide students to discover patterns through repeated exposure to arrays and grouping. Emphasise that factors are not just about listing but about understanding the structure of numbers, which prepares them for later work with prime factorisation and greatest common factors.

Successful learning looks like students confidently listing factor pairs without missing numbers and explaining why a number is prime or composite. They should use divisibility rules to speed up their work and describe the relationship between factors and multiples clearly.

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Watch Out for These Misconceptions

• During Array Builder, watch for students confusing factors with multiples by counting rows as multiples and columns as factors.

  Prompt students to label their arrays clearly: write the total number of counters at the top and the factor pairs along the sides to reinforce the difference.

• During Factor Pair Match-Up, watch for students assuming all numbers have exactly two factors.

  Have students count the number of cards in each match and discuss why some numbers (like 7) have only one pair while others (like 12) have multiple.

• During Grouping Challenge, watch for students excluding 1 as a factor because it feels too simple.

  Ask groups to start with 1xN arrays and discuss why 1 is always a factor, using examples like 1x5=5 to normalise its inclusion.

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Methods used in this brief

• Hexagonal Thinking