Mathematics · Class 6

Active learning ideas

Factors and Multiples

Active learning helps students grasp factors and multiples by letting them manipulate numbers physically, which builds a strong mental model of how numbers relate. When students arrange counters or fill grids, they see patterns like pairs and skip-chains, making abstract ideas like prime numbers feel concrete and real.

• CBSE Learning Outcomes
• NCERT: Playing with Numbers - Class 6

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Pairs

Pairs: Factor Array Builder

Each pair receives 24 square tiles and builds arrays for numbers 12 to 36, recording factor pairs from each rectangle's dimensions. Pairs swap arrays with neighbours to verify and list all factors. Conclude with a class chart of patterns observed.

Explain what makes prime numbers the building blocks of all other numbers.

Facilitation Tip

During Factor Array Builder, insist students arrange counters in neat rows and columns and label each side to show the pair relationship.

What to look for

Present students with a list of numbers (e.g., 15, 17, 21, 23). Ask them to circle the prime numbers and underline the composite numbers. Then, for one composite number, ask them to list all its factors.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 40 min · Small Groups

Small Groups: Prime Sieve Grid

Groups get a 1-100 number grid and circle multiples of 2, then 3, crossing out composites to reveal primes. They justify choices and extend to predict primes up to 50. Share findings on the board.

Differentiate between a factor and a multiple of a given number.

Facilitation Tip

During Prime Sieve Grid, encourage students to use two different coloured pencils to mark multiples of 2 and 3 clearly before moving to 5.

What to look for

Give each student a card with a number (e.g., 36). Ask them to write down two multiples of this number and two factors of this number. Also, ask them to state if the number is prime or composite and why.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 35 min · Whole Class

Whole Class: Multiple Skip Chain

Divide class into teams; first student says a multiple of 6, next adds 6 more, forming a chain up to 100. Teams race while correcting errors. Discuss why chains reveal multiples.

Construct a method to find all factors of a composite number systematically.

Facilitation Tip

During Multiple Skip Chain, ask students to say the chain aloud together so the rhythm helps internalise multiples.

What to look for

Pose this question: 'If a number is a multiple of another number, does that mean the second number is always a factor of the first?' Facilitate a class discussion using examples like 10 being a multiple of 5, and 5 being a factor of 10, and then explore cases like 10 being a multiple of 2, and 2 being a factor of 10.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 25 min · Individual

Individual: Factor Rainbow Sort

Students draw rainbows for numbers 16-32, colour-coding factor pairs from both ends inward. Check with a partner, then display for peer review. Note prime rainbows have short arcs.

Explain what makes prime numbers the building blocks of all other numbers.

Facilitation Tip

During Factor Rainbow Sort, remind students to write every factor on a separate card and arrange them from smallest to largest in the rainbow shape.

What to look for

Present students with a list of numbers (e.g., 15, 17, 21, 23). Ask them to circle the prime numbers and underline the composite numbers. Then, for one composite number, ask them to list all its factors.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Experienced teachers approach this topic by letting students experience the joy of discovery first, then naming the concepts. They avoid rushing to definitions; instead, they use activities to build intuition, then formalise it. Research shows that students who physically organise numbers remember the ideas longer and can apply them to new problems.

By the end of these activities, students should confidently list factors of any number using pair methods, distinguish primes from composites through sieve patterns, and explain the difference between factors and multiples using their own examples. They should also justify their reasoning clearly during discussions.

---

Watch Out for These Misconceptions

• During Factor Array Builder, watch for students who mistakenly include 1 as a prime number.

  Ask them to count the factors of 7 using the counters; when they see 7 has only two counters in a single row, compare it with 1, which has just one counter, to clarify why 1 is not prime.

• During Factor Rainbow Sort, watch for students who swap factors and multiples cards.

  Remind them to read each card aloud: a factor divides the number, a multiple is made by multiplying the number, and have them explain their choice before placing the card.

• During Prime Sieve Grid, watch for students who assume every odd number greater than 2 is prime.

  Have them cross out multiples of 3 and 5 together, then ask them to check 9 and 15 in their sieves to see why these odd numbers are composite.

---

Methods used in this brief

• Stations Rotation