Rational vs. Irrational Presentation

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Rational vs. Irrational Numbers Presentation 8.NS.A.1 © IDEA GALAXY

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Teacher Directions: This presentation is designed to be a brief introduction to the concept of rational vs. irrational numbers based on the fact that rational numbers can be made into ratios. This presentation has an accompanying notes page for students to follow along with. There are 2 versions of the notes page. One version is guided notes and the other version is for students to write down what they think is the most important part. The student work page is in an accompanying file. Supports CCSS 8.NS.A.1 Tips and variations: -This presentation can be used in a flipped classroom. -Student can go through this presentation at their own pace or with partner on the computer. When students are finished you can debrief with them.

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Lesson Objective: I can identify if a number is rational or irrational. I can explain why a number is rational or irrational. 1

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What is the difference between rational and irrational numbers? 2

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What word is part of the word rational? All rational numbers have a ratio or fraction form. ______________ 3

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Can fractions be expressed as ratios? Yes. Fractions are a very common way of expressing ratios. Example: 1 to 4 becomes 1/4 4

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Therefore, if a number has a fraction form then, it has a ratio form. 5

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Can decimals be expressed as ratios? Yes. You take the digits after the decimal as the numerator and the place value as the denominator. Example: 0.13 becomes 13/100 6

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Can decimals be expressed as ratios? Example: 0.13 becomes 13/100 Convert the following decimals to ratios (fractions): 0.254 1.5 0.03 0.4081 .6 .17 254/1000 1 5/10 3/100 4081/10000 6/10 17/100 7

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Can integers be expressed as ratios? Yes. The integer is the numerator and 1 is the denominator. Example: 5 becomes 5/1 8

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Can integers be expressed as ratios? Example: 5 becomes 5/1 Convert the following integers to ratios (fractions): 7 10 300 -4 2 999 7/1 10/1 300/1 -4/1 2/1 999/1 9

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Can square roots be expressed as ratios? Sometimes. If it is a perfect square root then find the square root and it will be an integer which can be made into a ratio or fraction. Example: = 6 becomes 6/1 10

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Can square roots be expressed as ratios? Convert the following perfect square roots to ratios (fractions): Example: = 6 becomes 6/1 = 7 becomes 7/1 = 10 becomes 10/1 =2 becomes 2/1 11

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When a number can’t be expressed as a ratio we call it irrational. 12

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Non perfect square roots can’t be expressed as ratios and do not have an exact value so they are irrational. 13

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The number pi cannot be expressed as a ratio and does not have an exact value so it is irrational. (sometimes people use 22/7 to represent pi, but it is an approximation because pi is irrational.) 14

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There are other irrational numbers, but non perfect square roots and pi are the ones we are going to be working with. 15

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whole numbers positive integers negative integers fractions decimals perfect square roots non perfect square roots pi Rational Numbers Irrational Numbers 16

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Now, you can: Identify if a number is rational or irrational. Explain why a number is rational or irrational. 17

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