Factors and Multiples

Overview

This 60-minute lesson is designed for Year 7 students and focuses on developing a deep understanding of factors and multiples. The lesson aligns with the Australian Curriculum: Mathematics, specifically addressing the content description ACMNA122: "Investigate and use square roots of perfect squares, and apply knowledges of factors and multiples".

Students will explore factors and multiples through engaging and interactive activities, building their numeracy skills and confidence with fundamental number concepts.

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Lesson Plan

Learning Intentions

By the end of the lesson, students will:

1. Know what factors and multiples are.
2. Understand that each number has infinitely many multiples.
3. Be able to find factors of a number.
4. Be able to find multiples of a number.

Success Criteria

Students will demonstrate success when they can:

• Explain the difference between factors and multiples.
• Identify all factors of a given number.
• Generate a list of multiples for a given number.
• Solve factors and multiples problems confidently in class activities.

Resources Required

• 30 small whiteboards and marker pens (one per student).
• Printouts of a "Factors and Multiples Table Challenge" worksheet (1 per student).
• A class set of counters or tokens (for hands-on exploration).
• A projector and PowerPoint slides displaying visual prompts.
• A timer or stopwatch.
• (Optional) Mathematics mini whiteboard grid cards for group challenges.

Classroom Setup

Arrange desks in small table groups of 4-5 students for collaborative learning. Provide individual resources (whiteboards, pens) at the start of the lesson. Allocate space at the front for collective discussions with the projector for visual display.

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Lesson Sequence

1. Tuning In (10 minutes)

Warm-up Exercise: "Number Clouds"

• Begin by displaying a visual "number cloud" of integers on the whiteboard (e.g., 12, 18, 24, 30, 36, 48).
• Ask students to write down as many "factors" as they can for one of the displayed numbers (e.g., Factors of 12: 1, 2, 3, 4, 6, 12) on their individual whiteboards.
• Ask students to compare their answers with their group. Encourage discussion for errors or differences.
• Follow up by reviewing the answers as a class, emphasising how factors divide a number exactly.

Teacher Questioning:

• What does it mean for a number to be a "factor"?
• How do we know if one number is a factor of another?

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2. Explicit Teaching: Factors and Multiples (10 minutes)

Key Teacher Explanation:

• Introduce factors: Explain that a factor is a number that divides another number exactly, leaving no remainder. Use a multiplication array (e.g., for 12: rows 1x12, 2x6, and 3x4).
• Introduce multiples: Explicitly explain that multiples involve repeated addition of a number (e.g., multiples of 5: 5, 10, 15, 20, …). Highlight the concept of infinite multiples.

PowerPoint Visuals:

• Side-by-side comparison chart showcasing examples of factors vs multiples. Use numbers like 6 or 12 to show the differences (Factors: 1, 2, 3, 6. Multiples: 12, 24, 36…).

Interactive Quick Questions:

• As a class, brainstorm multiples of 4 and factors of 20 with student contributions aloud. Display the answers as a shared list.

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3. Guided Practice: Hands-On Activities (15 minutes)

Activity 1: Factor Hunt Game (Individual Work, Small Whiteboards)

1. Give each student a random number between 1 and 50 (e.g., through projector spin or worksheet).
2. Challenge students to list all factors of their given number on their whiteboards.
3. Once complete, project the answers for each number, and let students check their own work.

Activity 2: Collaborative Multiples Game (Group Work)

1. Provide each group with tokens or counters and give them a group starting number (e.g., 7 or 9).
2. Ask them to create a visual number line on the table with the first 10 multiples of their group number using counters. Monitor speed and accuracy.
3. Discuss patterns observed by the groups when lining up multiples (e.g., are all the multiples odd/even? Do multiples grow larger or smaller?).

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4. Independent Practice and Extension (15 minutes)

Worksheet: Factors and Multiples Table Challenge

• Hand out the "Factors and Multiples Table Challenge" worksheet, with a mix of age-appropriate problems:
  • Fill in missing multiples (e.g., multiples of 8: 8, __, 24, 32, __).
  • Identify factor pairs for specific numbers.
  • Circle all prime numbers in a pre-defined list.

Optional Extension Activity for High Achievers:
Pose an investigative question such as: "Can a number be both a factor and a multiple of another at the same time? Find examples and explain why."

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5. Plenary: Class Reflection (10 minutes)

Quickfire Quiz with Peer Scoring

• Display a series of quickfire questions on the board:
  • “What is a factor of 18?”
  • “Find the first four multiples of 6.”
  • “List two numbers that are factors of 24.”
• Students write answers on their whiteboards, hold them up, and self-check answers as the teacher reviews.

Final Discussion Prompts

• “What is one new thing you learned today?”
• “Why do you think factors and multiples are important in real-life applications?”

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Assessment

Formative Assessment:

• Monitor responses during the warm-up and discussions to gauge baseline understanding.
• Observe group activity involvement to assess teamwork and application of concepts.
• Collect and review the completed worksheet to evaluate individual progress.

Summative Assessment:

• Provide a short written assessment in the following class covering similar problems from the independent practice activity.

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Reflection for Teacher

At the end of the lesson, note key observations: Which students grasped factors/multiples concepts quickly? Were there any common misconceptions? Use these reflections to plan follow-up lessons or interventions.

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Differentiation

1. Support Students: Offer visual aids, multiplication charts, or paired help for students who require additional scaffolding.
2. Extend Students: Pose challenging number theory problems like identifying Lowest Common Multiples (LCM) or Highest Common Factors (HCF).
3. Engagement Strategy: Use relatable, real-life applications of factors and multiples (e.g., sharing/dividing objects fairly or skip counting in sports scoring).

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This detailed lesson plan equips Year 7 teachers in Australia with a dynamic approach to teaching factors and multiples, fostering curiosity, collaboration, and deeper mathematical understanding.