Understanding Integers

Objective

By the end of the lesson, students will demonstrate an understanding of integers, including ordering, adding, and subtracting them. This lesson aligns with the US Common Core State Standards for Mathematics, particularly:

• CCSS.MATH.CONTENT.6.NS.C.5: Understanding that positive and negative numbers are used together to describe quantities having opposite directions or values.
• CCSS.MATH.CONTENT.6.NS.C.6: Understanding a rational number as a point on the number line.

Materials Needed

• Whiteboard and markers
• Number line (physical or drawn on a board)
• Integer cards (index cards with different integers written on them)
• Counters for visual representation
• Student notebooks and pencils

Lesson Structure

Introduction (5 minutes)

• Begin with a quick discussion: Ask students where they might have seen or used integers in real life (e.g., temperatures above or below zero, bank account overdrafts, elevations above or below sea level).
• Introduce vocabulary: Integers, positive integers, negative integers, zero.

Direct Instruction (10 minutes)

1. Number Line Visualization

   • Draw a large number line on the whiteboard. Label it with integers from -10 to +10.
   • Discuss position: Explain that numbers to the right of zero are positive, and those to the left are negative. Zero is neutral.

2. Integer Ordering

   • Use integer cards. Randomly pick numbers and have students place them on a vertical number line from smallest (top) to largest (bottom).
   • Highlight that numbers increase in value from left to right and what this means for comparing integers.

3. Basic Operations with Integers

   • Briefly explain adding and subtracting integers using the number line.
   • Use examples:
     • Adding a positive integer (move right).
     • Adding a negative integer (move left).
     • Subtracting a positive integer (move left).
     • Subtracting a negative integer (move right).

Guided Practice (15 minutes)

• Distribute integer cards to students. Have them pair up to practice:

  • Activity 1: Integer Match-Up
    • Each student picks a card and practices placing it on an imagined number line in front of them.
    • Ask them to find the sum or difference of their two integers using counters on a drawn number line.

• Activity 2: Real-world Role Play

  • Role-play scenarios: Assign each student or pair a real-world situation (e.g., temperature change, various altitudes) and have them explain the integer representation of their scenario to the class.

Independent Practice (10 minutes)

• Hand out worksheets with integer problems, including basic addition and subtraction tasks. Ask students to solve them individually in their notebooks.
• Encourage students to label their moves on their personal number line for clarity.

Conclusion (5 minutes)

• Quick recap: Review key concepts and ask a few students to share their real-world scenarios.
• Exit Ticket: Give each student a sticky note. Ask them to write down one real-world example of integers they didn't think of before the lesson and stick it to the "Integer Ideas" board.

Assessment

• Informally assess students during activities by observing their understanding of integer operations and ordering.
• Review worksheets and exit tickets to gauge individual understanding and identify concepts that may need further clarification in the next lesson.

Differentiation

• For advanced students: Introduce simple multiplicative operations involving integers and patterns in their behavior.
• For students needing more support: Offer additional number line practice and use concrete models (such as counters) for operations. Pair these students with peers for collaborative learning.