Classifying Real Numbers

Name _____________________________________ Unit: Real Number System Student Handout 5 Date ______________________________Pd______ Classifying Real Numbers INTRODUCTION: Over the summer, Ethan spent a week at an overnight camp. He ended up meeting tons of friends, and some ended up being people that he goes to school with this year. On the first day of school, he recognized one of his camp friends in his math class. Other friends that he met at camp live in different states, but they still keep in touch throughout the year. TASK 1: In no particular order, the headings below describe the different types of friends that Ethan met at camp. Using the graphic organizer below, see if you can place each of the headings in the box where they belong. {Same State} {Same Class} {Out of State} {Same City} {Same School} Friends from Camp DISCUSS: • • • Is it possible for a friend in the same class to go to a different school? Is it possible for a friend in the same state to go to a different school? Ryan is one of Ethan’s camp friends who is also in his first period class. Write Ryan’s name in all of the boxes where he would be included. Is it necessary to write Ryan’s name in more than one box? ©Maneuvering the Middle LLC, 2015 TASK 2: Read through the types of real numbers in the table below. Give a few examples of each. REAL NUMBERS DEFINITION EXAMPLES Natural • The set of all positive counting numbers 1 (numbers on a number line); starting with ____ 1,2,3... • The set of all positive counting numbers 0 starting with ________ 0,1,2,3..... Integers • The set of whole numbers and their opposite _______________ ...-3,-2,-1,0,1,2,3... Rational • Numbers that can be written as fractions • Terminating decimals, repeating decimals and perfect _______________ squares Whole Irrational • Numbers that cannot be written as ____________ fractions • Non-terminating decimals, non-repeating decimals and ____________ non perfect squares .29, 4/7, √ 25  √ 31 , 2π  TASK 3: Place the headings for each type of real number in the graphic organizer below. Then, see if you can correctly place each of the following values into the box where they belong: {2 64, -15, 16 75 , 0, -12.2} 4, rational -12.2 integers -15 whole numbers irrational 0 √ 75  2 √ 64  natural 16/4 = 4 Summarize today’s lesson: ©Maneuvering the Middle LLC, 2015 Name _____________________________________ Unit: Real Number System Homework 5 Date ______________________________Pd______ Classifying Real Numbers Classify the numbers in the table by checking all that apply. Natural Whole Integer Rational Irrational Real 1. -6.75 2. 175 3. 5π 30 4. 3 5. − 9 6. Rachel states that -5.5 is an integer because it is negative. Is she correct? Why or why not? 7. Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern. Is he correct? Why or why not? She's not correct because integers can't be decimal __________________________________________ He's not correct because Rational number's are Rational if they __________________________________________ __________________________________________ can turn into a fraction. __________________________________________ __________________________________________ __________________________________________ __________________________________________ __________________________________________ The graphic organizer represents the sets of all real numbers. 8. Which could be the value of D? A) -10 B) 0 C) ¾ D) 2.5 B C D E A 9. Which could not be the value of B? A) 5 C) -12.5 B) ½ D) 32 1π 10. Give an example of a value that could be represented by A. _______ ©Maneuvering the Middle LLC, 2015