Mathematics · Grade 4

Active learning ideas

Introduction to Factors and Multiples

Active learning builds concrete understanding of factors and multiples because these concepts rely on spatial and numerical patterns. Students need to see how numbers break apart into equal groups and extend outward through repeated addition, which hands-on activities make visible in ways worksheets cannot.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.4.OA.B.4

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

Activity 01

• Stations Rotation
• 30 min · Small Groups

Tile Arrays: Factor Pairs

Give each small group interlocking cubes and number cards from 16 to 48. Students build all possible rectangular arrays for a number, record side lengths as factor pairs, then test completeness by multiplying pairs. Groups share one unique array with the class.

Explain the relationship between factors and multiples.

Facilitation Tip

During Tile Arrays, encourage students to physically rearrange tiles to find all possible rectangles, ensuring they include the 1 x n shape.

What to look for

Present students with a number, such as 24. Ask them to write down all the factor pairs for 24 and list the first five multiples of 4. Review responses to gauge understanding of both concepts.

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

Activity 02

• Stations Rotation
• 25 min · Pairs

Skip-Count Number Lines: Multiples

Pairs draw number lines from 1 to 100. One partner calls a number like 7; the other marks multiples by skipping equal intervals. They compare with another pair's line for 7 and discuss patterns like every seventh number.

Construct a list of all factor pairs for a given number.

Facilitation Tip

During Skip-Count Number Lines, have students mark multiples with colored dots and then trace backward to identify corresponding factors.

What to look for

Give each student a card with a number (e.g., 17, 20, 30). Ask them to write: 1) two factor pairs for the number, 2) three multiples of the number, and 3) whether the number is prime or composite, explaining why. Collect and review.

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

Activity 03

• Stations Rotation
• 35 min · Small Groups

Prime-Composite Sort: Card Challenges

Prepare cards numbered 1-50. Small groups sort into prime, composite, and neither piles, listing factors for each. Rotate cards among groups for verification, then hold a class vote on tricky numbers like 1 or 25.

Differentiate between prime and composite numbers based on their factors.

Facilitation Tip

During Prime-Composite Sort, ask partners to justify each placement using factor lists before gluing cards to prevent hasty sorting.

What to look for

Pose the question: 'If 5 is a factor of a number, what do you know about that number?' Guide students to explain that the number must be a multiple of 5 and therefore end in a 0 or 5. Discuss how this connects to divisibility rules.

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

Activity 04

• Stations Rotation
• 20 min · Whole Class

Factor Bingo Boards: Whole Class Game

Students create 4x4 bingo cards with numbers 20-60. Call factor pairs like '3 and 8'; students mark multiples of 3 or 8, or numbers with those factors. First to connect four wins and explains their marks.

Explain the relationship between factors and multiples.

Facilitation Tip

During Factor Bingo, circulate to listen for students verbalizing factor pairs aloud as they cover squares, reinforcing spoken reasoning.

What to look for

Present students with a number, such as 24. Ask them to write down all the factor pairs for 24 and list the first five multiples of 4. Review responses to gauge understanding of both concepts.

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

A few notes on teaching this unit

Start with visual models like arrays to ground abstract definitions in tangible experiences. Avoid rushing to symbolic notation before students can explain why 12 has six factors. Use partner talk to surface misconceptions early, and correct them immediately with materials rather than explanations. Research shows that students grasp inverse relationships best when they physically perform both operations on the same set of numbers, so alternate between finding factors and generating multiples in each lesson.

Students will confidently identify all factor pairs for numbers up to 100 and generate accurate lists of multiples. They will distinguish prime and composite numbers by explaining the count of their factors, showing clear reasoning in both written and verbal explanations.

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Watch Out for These Misconceptions

• During Prime-Composite Sort, watch for students placing 1 in the prime category.

  Have students create two columns on their desk labeled Prime and Composite, then use their factor pair lists from Tile Arrays to test 1: ask them to find another factor besides 1 and itself, which does not exist, to confirm 1 is neither prime nor composite.

• During Tile Arrays, watch for students excluding 1 and the number itself from their factor pair lists.

  Prompt students to build a 1 x n rectangle first, then rotate tiles to find other arrangements, explicitly naming these as valid factor pairs and recording them in a T-chart.

• During Skip-Count Number Lines, watch for students confusing factors and multiples as the same concept.

  After marking multiples on the number line, have students divide the last multiple by the starting number to recover the original factor, reinforcing the inverse relationship through repeated practice.

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Methods used in this brief

• Stations Rotation