Decoding the Negative Sign: More Than Just Minus!

Mathematics Grades 7th Grade 5:01 Video
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Lesson Description

Explore the meaning of the negative symbol as 'opposite' and how it applies to numbers on the number line. Learn to interpret and simplify expressions with multiple negative signs.

Video Resource

Negative symbol as opposite | Negative numbers | 6th grade | Khan Academy

Khan Academy

Duration: 5:01
Watch on YouTube

Key Concepts

  • Opposite of a number
  • Negative symbol as 'opposite'
  • Simplifying expressions with multiple negative signs

Learning Objectives

  • Students will be able to define the term 'opposite' of a number and represent it on a number line.
  • Students will be able to interpret the negative symbol as meaning 'the opposite of'.
  • Students will be able to simplify expressions involving multiple negative signs to find the resulting value.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of positive and negative numbers and their placement on the number line. Briefly discuss real-world examples of negative numbers (e.g., temperature below zero, debt).
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Negative symbol as opposite'. Encourage students to take notes on key definitions and examples.
  • Guided Practice (10 mins)
    Work through examples similar to those in the video as a class. Start with simple examples like 'the opposite of 5' and 'the opposite of -2'. Gradually progress to examples with multiple negative signs, such as '-(-4)' and '-(-(-3))'.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing problems of varying difficulty related to identifying opposites and simplifying expressions with multiple negative signs. Circulate to provide assistance as needed.
  • Wrap-up (3 mins)
    Summarize the key concepts learned in the lesson. Preview how these concepts will be used in future lessons involving operations with negative numbers.

Interactive Exercises

  • Number Line Game
    Draw a number line on the board. Call out a number (e.g., 3). Ask a student to point to its opposite on the number line. Increase difficulty by calling out expressions like '-(-2)'.
  • Opposite Card Sort
    Prepare a set of cards with numbers and expressions. Have students sort the cards into pairs of numbers and their opposites.

Discussion Questions

  • How does the number line help us understand the concept of opposites?
  • Can a number and its opposite ever be the same? If so, when?
  • What real-world situations can be represented using negative numbers and their opposites?

Skills Developed

  • Number sense
  • Abstract reasoning
  • Problem-solving

Multiple Choice Questions

Question 1:

What is the opposite of 7?

Correct Answer: -7

Question 2:

The negative sign in front of a number means:

Correct Answer: The opposite of the number

Question 3:

What is -(-5) equal to?

Correct Answer: 5

Question 4:

Which of the following is the opposite of -3?

Correct Answer: 3

Question 5:

On a number line, a number and its opposite are:

Correct Answer: Equidistant from zero

Question 6:

What is -(-(-1)) equal to?

Correct Answer: -1

Question 7:

If 'A' represents a number, then '-A' represents:

Correct Answer: Both B and C

Question 8:

The opposite of a positive number is always:

Correct Answer: Negative

Question 9:

What does the expression '-(-(-(-2)))' simplify to?

Correct Answer: 2

Question 10:

The distance between a number and its opposite on the number line is:

Correct Answer: Twice the distance from zero

Fill in the Blank Questions

Question 1:

The opposite of a number is the same distance from zero on the number line, but on the ________ side.

Correct Answer: opposite

Question 2:

The negative symbol can be read as 'the ________ of'.

Correct Answer: opposite

Question 3:

-(-8) is equal to ________.

Correct Answer: 8

Question 4:

If a number is 6 units to the right of zero, its opposite is 6 units to the ________ of zero.

Correct Answer: left

Question 5:

The opposite of zero is ________.

Correct Answer: zero

Question 6:

-(-(-4)) is equal to ________.

Correct Answer: -4

Question 7:

The negative symbol indicates the ________ of a number.

Correct Answer: opposite

Question 8:

Every time you add a negative symbol, you ________ the side of the number line you are on.

Correct Answer: flip

Question 9:

The opposite of -9 is ________.

Correct Answer: 9

Question 10:

When simplifying -(-(-(-5))), the answer will be a ________ number.

Correct Answer: positive

Educational Standards

7.N.1:Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals. Explain and apply the concept of absolute value. 7.N.1.3:Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value. Apply the concept of absolute value to model and solve problems. 7.A.4.1:Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.

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