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Making Sense of Rational and Irrational Numbers

Making Sense of Rational and Irrational Numbers. Objectives: Identify number sets. Write decimals as fractions. Write fractions as decimals. MONDAY. STARTER http://vimeo.com/5793093 LESSON: MAKING SENSE OF RATIONAL AND IRRATIONAL NUMBERS

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Making Sense of Rational and Irrational Numbers

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  1. Making Sense of Rational and Irrational Numbers Objectives: Identify number sets. Write decimals as fractions. Write fractions as decimals.

  2. MONDAY • STARTER http://vimeo.com/5793093 • LESSON: MAKING SENSE OF RATIONAL AND IRRATIONAL NUMBERS • ACTIVITY: USE GRAPHIC ORGANIZER TO RELATE CATEGORIZING REAL NUMBER SUBSETS TO STAUTON’S LOCATION IN RELATION TO THE REST OF THE WORLD • HW: WORKSHEET

  3. TUESDAY • STARTER • HOMEWORK HUDDLE • LESSON: RATIONAL AND IRRATIONAL NUMBERS CONTINUED • ACTIVITY: CREATE VISUAL OF GRAPHIC ORGANIZER USED TO SORT REAL NUMBERS INTO SUBSETS • HW: WORKSHEET / QUIZ-KNOW GRAPHIC ORGANIZER • EXTRA: CARD PERCENTS

  4. WEDNESDAY • STARTER • CHECK HOMEWORK • QUIZ ON GRAPIC ORGANIZER • ACTIVITY: SORT REAL AND IRRATIONAL NUMBERS INTO PROPER SUBSETS ON GRAPHIC ORGANIZER • PRACTICE SHEET • HW: TEST: STUDY PPT NOTES, GRAPHIC ORGANIZER, HOMEWORK SHEETS, AND PPT ON MY WEBSITE

  5. THURSDAY • STARTER • TEST • READ SCHOLASTIC MATH AND COMPLETE ACTIVITIES • PUZZLE CHANNEL • HW: NONE

  6. FRIDAY • STARTER • LESSON: PROPERTIES • ACTIVITY: PROPERTIES CUBES INTRO AND PRACTICE IDENTIFYING PROPERTIES • FINISH PUZZLE CHANNEL • NO HOMEWORK • NEXT WEEK: PROPERTIES, HANDS ON EQUATIONS INTRO LEADING INTO TWO STEP EQUATIONS

  7. Real Numbers Rational numbers Irrational numbers Integers Whole numbers The set of real numbers is all numbers that can be written on a number line. It consists of the set of rational numbers and the set of irrational numbers.

  8. Recall that rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals. 4 5 23 3 = 3.8 = 0.6 1.44 = 1.2

  9. Rational Numbers Natural counting numbers. Natural Numbers - 1, 2, 3, 4 … Whole Numbers - Natural counting numbers and zero. 0, 1, 2, 3 … Integers - Whole numbers and their opposites. … -3, -2, -1, 0, 1, 2, 3 … Rational Numbers - Integers, fractions, and decimals. -0.76, -6/13, 0.08, 2/3 Ex:

  10. Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko. Rational Numbers are classified this way as well! You already know that some numbers can be classified as whole numbers, integers, or rational numbers. The number 2 is a whole number, an integer, and a rational number. It is also a real number. Animal Reptile Lizard Gecko

  11. Venn Diagram: Naturals, Wholes, Integers, Rationals Real Numbers Rationals Integers Wholes Naturals

  12. Name all the sets of numbers to which the given number belongs. Circle the most specific set. , Rationals Integers Rationals Naturals , Integers , Rationals , Wholes Wholes , Integers , Rationals Rationals

  13. Irrational numberscan be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so 2 is irrational. Caution! A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.

  14. Real numbers are all the positive, negative, fraction, and decimal numbers you have heard of. They are also called Rational Numbers. IRRATIONAL NUMBERS are usually decimals that do not terminate or repeat. They go on forever. Examples: π Reminder

  15. Identify each root as rational or irrational.

  16. Decimal to Fraction: A skill you will need for this unit! • To change a decimal to a fraction, take the place value and reduce! • 0.5 means 5 tenths, so 5/10. • Now reduce 5/10 = ½ • 0.5 = 1/2

  17. Converting Fractions and Decimals Fraction Decimal To change a fraction to a decimal, take the top divided by the bottom, or numerator divided by the denominator.

  18. Complete the table. Fraction Decimal

  19. Repeating Decimals Fraction Decimal Every rational number (fraction) either terminates or repeats when written as a decimal.

  20. Repeating Decimals Fraction Decimal

  21. Repeating Decimals Fraction Decimal

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