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Real Number System: Rational and Irrational (Mr Myers)

By Lonnie Myers
Last updated over 4 years ago
9 Questions
This Real Number System Formative should be completed throughout the week.
Feedback will be provided on a daily basis. Please email your teacher if have any questions or problems accessing the content.
CCSS.MATH.CONTENT.8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually
CCSS.MATH.CONTENT.8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Real Number System:

Rational vs. Irrational Number System

Objective: Students will be able to describe the differences between rational and irrational numbers and classify them accordingly.

Connecting Square Roots to Rational Numbers

Complete the Square Dance-Square Roots Desmos
1.

Did you complete the Square Dance-Square Roots Desmos.

The Real Number System video below explains how we categorize numbers into groups that define them.

Link to above video https://www.youtube.com/watch?v=0OwvN-957aE

If you would like a more advanced, explanation you can find it by clicking here.

Please review this information


KEY VOCABULARY

Terminating decimal: a decimal that ends or stops

Repeating Decimal: A decimal with a continuous pattern that goes on forever, often symbolized with a bar over the portion that repeats

Irrational Number: A number that cannot be written as a fraction, or ration made up of two integers. (examples include square roots of non-perfect squares and symbols such as pi.)

Rational Number: A number that can be written in the form a/b (a fraction) where a and b are both integers.


Watch Paul categorize numbers below as being rational or irrational.

Give it a try Self-checking Desmos Rational vs Irrational


Don't worry if you make mistakes: You're just starting out


2.

Choose the best response. I completed the Self-checking Rational vs irrational activity

Please review the Frayer Models below to help expand your knowledge of Rational and Irrational numbers

3.

Rational vs Irrational Self check 2. Categorize each example as rational or irrational

  • 4.589
  • .66666666......
  • 1.732.....
  • .022022022....

  • Rational
  • Irrational
4.

Choose the best response. I completed the 2nd Rational vs irrational self check

Typically at this point students get confused identifying and classifying these types of real numbers: nonterminating, Terminating decimals, non-terminating recurring decimals and terminating non-recurring decimals

Watch the video below
https://youtu.be/3YwrcJxEbZw

Still not confident?

Here's a song which former MAMS students claim, "REALLY helps"

https://youtu.be/aZxkbJYguWQ

Do you think that you can decide by looking at it whether a number is rational or irrational? Complete the activity below to see how you did

5.

Self- check 3. Rational vs Irrational challenge. (you

  • 22/99
  • 1.1234567.....
  • .5555555......
  • -2.5
  • Rational
  • Irrational

Teachers note.

A majority of people even adults will make mistakes classify square roots of factions so it's best to use a calculator to determine if the square roots of fractions are rational or irrational. (I do)

FYI.

How do you find the square root of a fraction?

To find the square root of a fraction, you first find the square root of the numerator and the denominator. For example: 4/9 the square root would be 2/3. If the denominator has a square root that is irrational, for example the square root of two, then multiply the numerator and denominator by the irrational number.

The square root of a fraction is the square root of the top divided by the square root of the bottom.
So, √(1/4) = √(1)/√(4)=1/2

The only thing that gets tricky is that you shouldn't leave a fraction under a square root. So, if you have √(1/3) you should first convert the fraction to something that is a perfect square. In this example, multiply top and bottom of the fraction by 3 to get √(3/9), which is √(3)/√(9), which simplifies to √(3)/3
Answer key for 5 Use this link https://1ce.org/1#S10lYNw5U

More Practice

Complete IXL D5. Identify rational and irrational numbers
6.

I scored a smartscore of 80 or more on IXL D5

Complete the activity below if you struggled or would like more practice


https://quizlet.com/_4o6uiv?x=1jqt&i=17q5ds

Closure activity.

Complete the Rational and Irrational Numbers Padlet. Please post your name. Anonymous post will be removed

You 'll want to know how to enter the square root symbol √ from your keyboard

Ipad Select ''Option'' v

PC Keyboard press "Alt" and, at the same time, type in the number 251 on the number keypad.

8.

I completed the Rational and irrational Padlet. The post lists my name.

9.

Select all that apply
How I feel about graphing square roots on a number line...