Multiplying and Dividing Integers

Overview

This 30-minute lesson, designed for a class of 30 ninth grade students, is the third lesson in the unit "Mastering Integers Together." Students will learn and practice the rules for multiplying and dividing integers, focusing on the critical role of signs (positive and negative). The lesson incorporates direct instruction, guided practice, and collaborative activities to reinforce understanding and ensure skill mastery in line with Common Core State Standards.

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Common Core Alignment

Grade: 9th Grade
Domain: Number and Quantity
Cluster: The Real Number System
Standard: CCSS.MATH.CONTENT.HSN.RN.B.3

• Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Also aligns with:

• CCSS.MATH.CONTENT.7.NS.A.2 (from earlier grades, but foundational for understanding integer operations)
• Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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Learning Objectives

By the end of this lesson, students will be able to:

1. Explain the rules for multiplying and dividing integers, emphasizing the role of signs.
2. Multiply and divide integers accurately using these rules in numeric problems.
3. Apply these operations in real-world and mathematical contextual problems collaboratively.
4. Demonstrate mathematical reasoning by explaining the sign rule in their own words.

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Materials Needed

• Whiteboard & markers
• Individual mini whiteboards & dry-erase markers for students
• Integer operation task cards (with problems for multiplication/division of integers)
• Sign rule anchor charts (pre-made posters or handouts)
• Exit ticket worksheets
• Timer or stopwatch

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Lesson Breakdown (30 minutes)

1. Warm-up and Activation (5 minutes)

• Objective: Activate prior knowledge about integers and their operations.
• Begin with a quick 3-question quiz on addition and subtraction of integers on mini whiteboards (e.g., -3 + 5, 7 - (-2), -4 + (-6)).
• Review answers immediately and connect the idea that integers include positive and negative numbers, leading into multiplication and division.

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2. Direct Instruction: Rules for Multiplying and Dividing Integers (8 minutes)

• Use the whiteboard or projector to display the Sign Rules Anchor Chart:

Operation	Same Signs Result	Different Signs Result
Multiplication	Positive	Negative
Division	Positive	Negative

• Demonstrate with numerical examples, e.g.:
  • Multiplication: (-3) × (-4) = 12, 5 × (-2) = -10
  • Division: (-12) ÷ (-3) = 4, 15 ÷ (-5) = -3
• Emphasize language: “Multiplying or dividing two numbers with the same sign gives a positive result; with different signs gives a negative result.”
• Ask students to verbalize the rationale in their own words: Why does a negative × negative equal a positive?

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3. Guided Practice (7 minutes)

• Distribute integer multiplication and division problems on task cards in pairs.
• Pairs will take turns solving and explaining each problem aloud. For example:
  • Find the product: (-6) × 7
  • Find the quotient: (-56) ÷ 8
• Circulate and provide immediate feedback.
• Encourage students to write full sentences explaining the sign and numerical result as part of their practice.

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4. Collaborative Group Activity: Integer Operations Challenge (7 minutes)

• Split students into 6 groups of 5.
• Each group receives a set of 5 mixed operations problems including word problems that require multiplying or dividing integers.
• Examples:
  • A submarine descends 30 feet every minute. How far does it descend in 4 minutes? (Multiplying negative integer)
  • If a temperature drops 3 degrees every hour, what is the temperature change after 5 hours?
• Groups discuss and solve problems collaboratively.
• Ask one member from each group to summarize the group’s reasoning briefly to the class.

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5. Closure and Assessment (3 minutes)

• Distribute a brief exit ticket with 3 problems:
  1. (-8) × (-5) = ?
  2. 45 ÷ (-9) = ?
  3. Explain why a negative times a negative makes a positive in one or two sentences.
• Collect exit tickets to assess individual understanding.

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Differentiation and Supports

• For students needing support:
  • Use color-coded sign charts and hand manipulatives (like integer tiles).
  • Provide step-by-step guided worksheets.
• For advanced students:
  • Challenge with integer expressions involving multiple steps or three or more factors.
  • Introduce basic problems involving rational numbers extending from the integer rules.

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Reflection Prompts for Teacher

• Did students successfully verbalize the sign rules?
• Were most students able to solve multiplication/division of integers independently?
• Which problems or concepts might require additional review or extension?
• How well did group collaboration reinforce understanding?

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This concise but dynamic lesson plan ensures engagement, comprehension, and practical application, all while aligning exactly with Common Core standards and ninth grade cognitive levels.