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In this lesson students will explore the fascinating world of real numbers, focusing on both rational and irrational numbers, and where these numbers are located on a number line.

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Ordering real numbers  from least to greatest

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8.NR.1

Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.

8.NR.1.1

Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.

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Students will be able to:
• compare and order rational and irrational numbers.

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Describe ways to compare and order rational and irrational numbers.

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Students can accurately compare a set of rational and irrational numbers, identifying which numbers are greater, lesser, or equal.

Students can correctly order a mixed set of rational and irrational numbers on a number line or in a list format.

Students demonstrate the ability to explain their reasoning using appropriate mathematical language and terminology.

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Students can describe at least two methods for comparing and ordering rational and irrational numbers, such as using number lines or decimal approximations.

Students effectively communicate their thought process during discussions, using vocabulary related to rational and irrational numbers.

Students can write a brief explanation or summary that outlines the key concepts of comparing and ordering real numbers, demonstrating an understanding of the topic.

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A type of real number that cannot be expressed as a simple fraction, meaning it cannot be written in the form abba​, where aa and bb are integers and b≠0b=0. Irrational numbers have decimal expansions that are non-repeating and non-terminating, which means they go on forever without repeating a specific pattern.

Some common examples of irrational numbers include:

2 (the square root of 2)

π (approximately 3.14, the ratio of the circumference of a circle to its diameter)

e (approximately 2.718, the base of the natural logarithm)

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A number that can be expressed as the square of an integer. In other words when you multiply a whole number by itself, the result is a perfect square.

Examples:

The perfect square of 16 is 4. 4x4 = 16

The perfect square of 9 is 3. 3x3 = 9

The perfect square of 25 is 5. 5x5 = 25

The square root of a perfect square is always a whole number.

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A square root of a number is a value that, when multiplied by itself, gives that original number.

For example:

The square root of 9 is 3 because 3×3=9.

The square root of 16 is 4 because 4×4=16.

The square root of 25 is 5 because 5×5=25.

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Calculator

Workbook

Chromebook

Pencil

Ready to learn mindset

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Ordering Real Numbers Lesson 14.3 Guided Practice

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1. With your group: complete workbook page 24 #1-6.

2. On your own: complete pages 25-26 #7-10,13,15,17.

3. Enrichment: Using Canva create an infographic explaining how to compare and order real numbers on a number line. Detailed instructions are located in your google classroom.

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When there is 7:00 minutes left on the work session timer, complete this exit ticket.

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Ordering Numbers from least to greatest. 

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Ordering Numbers from least to greatest. 

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Order the numbers - least to greatest (Compare Real Numbers)

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How do you estimate the square root of a non-perfect square?

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How do you estimate the square root of a non-perfect square?