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Numbers: Stepping onto the Line

Lesson Plan

Stepping onto the Line

Students will be able to define integers, identify positive and negative integers, and compare integers using a number line.

Understanding integers is fundamental for advanced math, including algebra. It helps students describe quantities like temperature, altitude, and financial transactions.

Audience

7th Grade

Time

60 minutes

Approach

Interactive lecture, guided practice, and independent worksheet.

Materials

Prep

Review Materials

15 minutes

Step 1

Warm-Up: What's the Temperature?

5 minutes

Begin by having students complete the What's the Temperature? Warm-Up.
- Discuss student responses as a class.
- "Think about how we describe temperatures. Sometimes it's above zero, sometimes it's below zero. How do we show that difference in math?"

Step 2

Introduction to Integers

15 minutes

Display the Integers on a Number Line Slide Deck and go through the first few slides.
- Introduce the concept of integers as whole numbers and their opposites.
- Emphasize the role of zero as neither positive nor negative.
- Use real-world examples (temperature, sea level, money).
- "Look at our first slide. What do you notice about these numbers? How are they different from the numbers you usually work with?"

Step 3

The Number Line: Visualizing Integers

15 minutes

Continue with the Integers on a Number Line Slide Deck focusing on the number line.
- Explain how a number line visually represents integers, with positive numbers to the right of zero and negative numbers to the left.
- Guide students through plotting various integers on a number line.
- "Now, let's see how a number line helps us understand integers. If I say '-3', where would that go on our number line? Why?"

Step 4

Comparing Integers

10 minutes

Using the Integers on a Number Line Slide Deck, teach students how to compare integers.
- Explain that numbers further to the right are greater, and numbers further to the left are smaller.
- Provide examples and ask students to compare pairs of integers.
- "Which is greater, -5 or -1? How does the number line help you decide?"

Step 5

Guided Practice: Number Line Worksheet

10 minutes

Distribute the Number Line Worksheet.
- Guide students through the first few problems, ensuring they understand how to plot and compare integers.
- Circulate around the room to provide individual support.
- "Work on the first two problems together. Don't worry if you're not sure, we'll discuss them!"

Step 6

Independent Practice & Wrap-Up

5 minutes

Students continue working independently on the Number Line Worksheet.
- Collect worksheets for assessment.
- Briefly review key concepts: definition of integers, positive/negative, and comparison on a number line.
- Have students complete the Integers Exit Ticket as a cool-down.

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Slide Deck

Welcome: Hot or Cold?

How do we talk about temperatures above zero and below zero? Think about a really cold day or a scorching hot day!

Greet students and start with the warm-up question about temperature. Encourage discussion about how we represent values above and below zero.

What Are Integers?

Integers are whole numbers and their opposites.

  • Positive Integers: 1, 2, 3... (numbers greater than zero)
  • Negative Integers: -1, -2, -3... (numbers less than zero)
  • Zero: Neither positive nor negative.

Examples:

  • Temperature: 10 degrees below zero (-10°)
  • Elevation: 200 feet above sea level (+200 feet)
  • Money: A debt of $5 (-$5)

Introduce the term 'integers'. Define them as whole numbers and their opposites. Emphasize that zero is neither positive nor negative. Provide relatable examples.

Mapping Integers: The Number Line

A number line helps us visualize integers.

  • Zero (0) is in the middle.
  • Positive Integers are to the right of zero.
  • Negative Integers are to the left of zero.

Let's try placing some integers: -4, 2, 0, -1, 3

Explain how a number line is constructed. Point out zero as the origin, positive numbers to the right, and negative numbers to the left. Guide students in placing a few simple integers.

Plotting Points: Where Do They Go?

To plot an integer, find its position on the number line.

  • For positive integers, move right from zero.
  • For negative integers, move left from zero.

Practice:
Plot -5, 1, -2, 4, -3

Demonstrate how to plot integers on the number line. Ask students to come up and plot integers or verbally guide you. Reinforce the concept of distance from zero.

Who's Bigger? Comparing Integers

On a number line, numbers increase in value as you move to the right.
Numbers decrease in value as you move to the left.

Which is greater?

  • -2 or 3?
  • -5 or -1?
  • 0 or -4?

Activity: Use <, >, or = to compare:

  • -7 ___ 2
  • -3 ___ -8
  • 5 ___ -5

Explain the concept of comparing integers. The further to the right a number is, the greater its value. The further to the left, the smaller its value. Use examples that include both positive and negative comparisons.

Practice Time: Your Turn!

Now it's time to practice!

You'll be using a number line to:

  • Plot integers.
  • Compare integers.
  • Solve real-world problems involving integers.

Introduce the worksheet and explain that students will practice plotting and comparing integers. Reiterate that they should use the number line as a tool.

Quick Check: What did we learn?

Write down one new thing you learned about integers or number lines today!

Wrap up the lesson with a quick reflection. Ask students to share one thing they learned. This helps solidify understanding and provides quick feedback.

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Worksheet

Number Line Worksheet

Name: _________________________ Date: _________________________

Part 1: Defining and Identifying Integers

  1. What is an integer? Give two examples of integers and two examples of numbers that are NOT integers.






  2. Circle the integers in the list below:
    3.5, -7, 0, 1/2, 100, -2.3, -25, 4

  3. For each real-world situation, write the integer that represents it:

    • A debt of $50: ____________
    • 3,000 feet above sea level: ____________
    • 15 degrees below zero: ____________
    • A gain of 7 yards in football: ____________

Part 2: Plotting Integers on a Number Line

Plot each integer on the number line provided. Label each point with its corresponding letter.

A. 4
B. -2
C. 0
D. -5
E. 1

<---|---|---|---|---|---|---|---|---|---|--->
   -5  -4  -3  -2  -1   0   1   2   3   4   5




Plot each integer on the number line provided. Label each point with its corresponding letter.

F. -3
G. 2
H. -1
I. 5
J. -4

<---|---|---|---|---|---|---|---|---|---|--->
   -5  -4  -3  -2  -1   0   1   2   3   4   5




Part 3: Comparing Integers

Compare each pair of integers using <, >, or =.

  1. -5 ____ 3
  2. 0 ____ -8
  3. -2 ____ -6
  4. 10 ____ -10
  5. -7 ____ -1
  6. -4 ____ 4
  7. -9 ____ 0
  8. -12 ____ -15
  9. 3 ____ -3
  10. 6 ____ 6

Challenge!

Order the following integers from least to greatest:

7, -2, 0, -5, 3, -8, 1




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Answer Key

Number Line Worksheet Answer Key

Part 1: Defining and Identifying Integers

  1. What is an integer? Give two examples of integers and two examples of numbers that are NOT integers.

    • An integer is a whole number (not a fraction or decimal) that can be positive, negative, or zero.
    • Examples of Integers: -10, 0, 5, -200, 15
    • Examples of Non-Integers: 3.5, 1/2, -2.3, 0.75

  2. Circle the integers in the list below:
    3.5, **-7**, **0**, 1/2, **100**, -2.3, **-25**, **4**

  3. For each real-world situation, write the integer that represents it:

    • A debt of $50: -50
    • 3,000 feet above sea level: +3000 (or 3000)
    • 15 degrees below zero: -15
    • A gain of 7 yards in football: +7 (or 7)

Part 2: Plotting Integers on a Number Line

Plot each integer on the number line provided. Label each point with its corresponding letter.

A. 4
B. -2
C. 0
D. -5
E. 1

<--D----B---C---E---------A--->
   -5  -4  -3  -2  -1   0   1   2   3   4   5

Plot each integer on the number line provided. Label each point with its corresponding letter.

F. -3
G. 2
H. -1
I. 5
J. -4

<-----J--F--H---G-------I--->
   -5  -4  -3  -2  -1   0   1   2   3   4   5

Part 3: Comparing Integers

Compare each pair of integers using <, >, or =.

  1. -5 < 3
  2. 0 > -8
  3. -2 > -6
  4. 10 > -10
  5. -7 < -1
  6. -4 < 4
  7. -9 < 0
  8. -12 > -15
  9. 3 > -3
  10. 6 = 6

Challenge!

Order the following integers from least to greatest:

7, -2, 0, -5, 3, -8, 1

Answer: -8, -5, -2, 0, 1, 3, 7

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Warm Up

What's the Temperature? Warm-Up

Instructions: Think about temperatures you've experienced recently. Write down a temperature for a very hot day and a very cold day.

  1. Hot Day Temperature: ____________________

  2. Cold Day Temperature: ____________________

  3. How do we usually describe temperatures that are really, really cold, especially when they go below zero? What kind of numbers do we use?



  4. On a simple number line, where would you place the temperature 0 degrees? And where would you put a very cold temperature like -5 degrees?



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Cool Down

Integers Exit Ticket

Instructions: On this exit ticket, answer the following questions to show what you learned today.

  1. In your own words, what is an integer?



  2. Plot the integers -3 and 2 on the number line below:

    <---|---|---|---|---|---|---|---|---|---|--->
   -5  -4  -3  -2  -1   0   1   2   3   4   5




  3. Which is greater, -4 or 1? How do you know, based on the number line?



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