Mathematics · Year 6

Active learning ideas

Investigating Multiples and Factors

Active learning helps students see the difference between factors and multiples as actions rather than abstract definitions. When students build arrays or move in timed relays, they feel the difference between dividing into equal parts and counting forward in jumps. This physical and social engagement turns number theory into something they can manipulate and explain.

• ACARA Content Descriptions
• AC9M6N01

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 35 min · Pairs

Array Building: Factor Pairs

Provide square tiles or grid paper. Students build rectangles for numbers like 12 or 18, listing dimensions as factor pairs. Pairs compare arrays to identify common factors and compute GCF. Share findings on class chart.

Differentiate between a multiple and a factor of a number.

Facilitation Tip

During Array Building, have students rotate partners so each pair explains their rectangle to a new group before switching roles.

What to look for

Present students with two numbers, such as 18 and 24. Ask them to list all factors of each number, identify the GCF, list the first five multiples of each number, and identify the LCM. Review their lists to check for accuracy in identifying factors and multiples.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 25 min · Small Groups

Multiples Relay: LCM Challenges

Divide class into teams. Call out pairs of numbers; first team member runs to board, writes multiples until common ones appear, tags next for LCM. Discuss efficient strategies post-race.

Analyze how finding the least common multiple can help solve real-world problems.

Facilitation Tip

In Multiples Relay, set a visible timer and call out the next multiple so students practice listening while moving.

What to look for

Pose a problem: 'Sarah has 12 stickers and wants to share them equally among her friends. What are the possible numbers of friends she can share with?' Students write down the factors of 12. Then, ask: 'If John has 2 chores to do every 3 days and Mike has 2 chores to do every 4 days, when will they next have the same number of chores due on the same day?' Students calculate the LCM of 3 and 4.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 45 min · Small Groups

Real-World Sharing Stations

Set up stations with problems: divide 48 cookies by 6 and 8 kids (GCF), bus schedules (LCM). Groups solve with drawings or counters, rotate, and explain solutions.

Justify why every number has an infinite number of multiples but a finite number of factors.

Facilitation Tip

At Real-World Sharing Stations, station signs should include visuals like plates or baskets so students connect the math to the objects.

What to look for

Ask students to explain in their own words why a number like 7 has only two factors (1 and 7) but an infinite number of multiples. Facilitate a discussion comparing the number of factors and multiples for prime versus composite numbers.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 20 min · Whole Class

Factor Bingo Boards

Students create bingo cards with factors of 36. Call multiples; they mark factors. First to line wins, then justify choices in pairs.

Differentiate between a multiple and a factor of a number.

Facilitation Tip

With Factor Bingo Boards, require students to write the factor pair in the corner of each square before marking it to reinforce the definition.

What to look for

Present students with two numbers, such as 18 and 24. Ask them to list all factors of each number, identify the GCF, list the first five multiples of each number, and identify the LCM. Review their lists to check for accuracy in identifying factors and multiples.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teachers approach this topic by starting with concrete models before moving to abstract lists. Arrays help students visualize factor pairs as the sides of a rectangle, while multiples become the increasing rows or columns. Avoid rushing to algorithms; let students discover patterns through repeated building and counting. Research shows that students who explain their arrays to peers retain the difference between factors and multiples better than those who only complete worksheets.

Successful learning looks like students using physical tools to model factors as rectangle sides and multiples as growing chains. They discuss why some numbers have only two factors, and they apply LCM and GCF to real sharing problems without mixing up the terms. Clear explanations from students show they see the connection between arrays, lists, and real-world use.

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Watch Out for These Misconceptions

• During Array Building, watch for students labeling the total number of tiles as a factor instead of the side lengths.

  Ask them to point to the two numbers that multiply to make the total and label those sides as the factors. Have them explain to a partner why the total is not a factor.

• During Multiples Relay, watch for students assuming all multiples are even because they only use even starter numbers.

  Have them run the relay with odd starters like 3 or 5 and record the multiples. After the round, ask the group to describe the pattern and why it differs from even multiples.

• During Multiples Relay, watch for students thinking the LCM is always the larger number.

  Stop the relay at 12 for 4 and 6, then ask students to compare the timeline to both numbers. Ask them to find the next common point and explain why it is larger than both.

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Methods used in this brief

• Collaborative Problem-Solving