The Number System: 1. Know that numbers that are not rational are irrational. Understand informally that every number has a decimal expansion, for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into rational number. 2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximate on a number line diagram, and estimate the value of expressions (e.g., pi squared). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Artifact 1: Irrational Numbers
Goal: Know that there are numbers that are not rational, and approximate them by rational numbers.
Objectives:
TSW complete the worksheet, "Kuta Software: Decimals and Fractions"
- TSW complete exercises found at the end of this lesson: Classifying Rational and Irrational numbers.
- TSW complete worksheet Ordering for Rational Numbers - Independent Practice Worksheet.
- TSW complete IXL modules: D.1 through D.8.
- TSW earn energy points on Khan academy by watching: Converting repeating decimals to fractions 1&2; and complete exercises:"Converting 1 digit repeating decimals to fractions and Converting multi-digit repeating decimals to fractions.
- TSW take a quiz in which they order Rational Numbers and identify Irrational numbers using Study Island.
- TSW create a PowerPoint using Google Drive using their notes, worksheets, practice problems from IXL, and the quiz.
Set: Here is Spock using pi as a weapon. Here a nine interesting facts about pi that can be used to start class
Instructional Procedure: Day 1 Classroom
SET: Ask why the computer was destroyed by having to calculate the last digit of pi?
- Pass out calculators.
- Demonstrate how to find the square roots of numbers with a calculator.
- I will show them and then they can spend a minute explaining it to one another.
- Explain the fact that if you multiply, divide, add, or subtract any number from an irrational number that result is irrational as well.
- Have students complete the exercises found at the end of this document. This will be printed out before class. (This is also a great resource for getting a substitute teacher up to speed on what is being taught on a sick day.)
- Check for understanding.
- Close.
Instructional Procedure: Day 2 Lab
Set: Ask students what they think of using Google Drive after explaining that Google Drive is basically a watered down version of Microsoft Tools. Lead a class discussion extolling the merits of learning how to use these tools at an early age.
- Students will be issued an email address through Google that is controlled by the school.
- Students will record username and password in a paper file that will be kept in the classroom.
- Using a digital camera, have students take pictures of the previous day's classwork and send them to my work email, matthewquinn@k12tn.net. (Now we have our first digital record!)
- Short class discussion regarding digital records.
- Students will be directed to Blogger.com to create their own blog using the email given to them by the school. Here is an example of what that could look like.
- Have students create a page in Blogger titled, "Irrational Numbers."
- Students will save their picture of the previous day's class work under this page.
- Close
Instructional Procedure: Day 3 Classroom
- Recall why the computer was destroyed by having to calculate the last digit of pi?
- Why do we have multiple number systems?
- Are there are any limits on these number systems? On the number system we use in class?
- What are the characteristics of a rational number? An irrational number?
- What is the definition of real numbers?
- Are all square roots irrational?
No comments:
Post a Comment