Rational vs. Irrational: Cracking the Number Code

Algebra 1 Grades High School 2:18 Video
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Lesson Description

Learn to distinguish between rational and irrational numbers. Explore examples and master the key properties that define these number types.

Video Resource

Recognizing rational and irrational numbers (examples) | Algebra I | Khan Academy

Khan Academy

Duration: 2:18
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Key Concepts

  • Rational Numbers: Numbers that can be expressed as a ratio of two integers (a/b, where b ≠ 0).
  • Irrational Numbers: Numbers that cannot be expressed as a ratio of two integers; they have non-repeating, non-terminating decimal representations.
  • Perfect Squares: Understanding perfect squares helps identify irrational square roots.

Learning Objectives

  • Students will be able to define and identify rational numbers.
  • Students will be able to define and identify irrational numbers.
  • Students will be able to classify numbers as either rational or irrational.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they know about rational and irrational numbers. Briefly review the definition of integers and fractions.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Recognizing rational and irrational numbers (examples)'. Instruct students to take notes on the examples presented.
  • Guided Practice (10 mins)
    Work through additional examples on the board, similar to those in the video. Encourage student participation by asking them to identify the numbers as rational or irrational and explain their reasoning.
  • Independent Practice (10 mins)
    Distribute a worksheet with a variety of numbers. Students will classify each number as either rational or irrational, justifying their answers. This worksheet could include fractions, decimals, square roots, and pi.
  • Wrap-up and Discussion (3 mins)
    Review the key concepts and address any remaining questions. Briefly preview the next steps, such as working with operations involving rational and irrational numbers.

Interactive Exercises

  • Number Sort
    Create a digital or physical sorting activity where students drag and drop numbers into categories labeled 'Rational' and 'Irrational'.
  • Think-Pair-Share
    Pose a question such as, 'Give an example of an irrational number you encounter in geometry.' Students think individually, discuss with a partner, and then share with the class.

Discussion Questions

  • Can a number be both rational and irrational?
  • How can you determine if a square root is rational or irrational?

Skills Developed

  • Critical Thinking
  • Number Sense
  • Classification
  • Problem Solving

Multiple Choice Questions

Question 1:

Which of the following numbers is irrational?

Correct Answer: √5

Question 2:

Which of the following is a rational number?

Correct Answer: 0.333...

Question 3:

Which statement is true about irrational numbers?

Correct Answer: They cannot be expressed as a fraction.

Question 4:

Is the number 7.252525... a rational or irrational number?

Correct Answer: Rational

Question 5:

Which of the following is an example of a rational number that is NOT an integer?

Correct Answer: 1/2

Question 6:

Which number is classified as rational?

Correct Answer: 1.6

Question 7:

Which best describes the decimal expansion of an irrational number?

Correct Answer: Non-terminating and non-repeating

Question 8:

Which number is NOT rational?

Correct Answer: √2

Question 9:

If a number can be written as a fraction, it is:

Correct Answer: Rational

Question 10:

Which of these is an irrational number?

Correct Answer: √17

Fill in the Blank Questions

Question 1:

Numbers that can be written as a fraction are called ______ numbers.

Correct Answer: rational

Question 2:

A decimal that neither terminates nor repeats represents an ______ number.

Correct Answer: irrational

Question 3:

The number π (pi) is a well-known example of an ______ number.

Correct Answer: irrational

Question 4:

√4 is a ______ number because it simplifies to 2.

Correct Answer: rational

Question 5:

The square root of a non-perfect square is always an ______ number.

Correct Answer: irrational

Question 6:

Integers are ______ numbers.

Correct Answer: rational

Question 7:

0.333... is a ______ number because it is a repeating decimal.

Correct Answer: rational

Question 8:

Numbers that *cannot* be written as a ratio of two integers are called ______.

Correct Answer: irrational

Question 9:

Terminating decimals are always ______.

Correct Answer: rational

Question 10:

5/1 is the fractional form of the rational number ______.

Correct Answer: 5

Educational Standards

A1.N.1:[Standard] Extend the understanding of exponents to include square roots and cube roots. A1.A.3.4:[Objective] Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y.

Teaching Materials

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