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( 7.1 ) Number, operation, and quantitative reasoning.

7.1A Comparing and Ordering Integers. ( 7.1 ) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: ( A ) compare and order integers and positive rational numbers. Comparing Integers.

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( 7.1 ) Number, operation, and quantitative reasoning.

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  1. 7.1A Comparing and Ordering Integers (7.1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: (A) compare and order integers and positive rational numbers.

  2. Comparing Integers Integers are the set of all counting numbers and their opposites and zero. Positive integers are greater than zero and negative integers are less than zero. Integers can be represented on a number line that extends in both directions from 0. 0 You can use a number line to compare any two integers, x and y. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 • If the integer x is to the leftof the integer y on the number line, then x < y . • If the integer x is to the rightof the integer y on the number line, then x > y .

  3. Ordering Integers A number line can be used to order 3, -7 and -4 from greatest to least. 3 › -4 Since 3 is to the right of -4 on the number line, 3 > -4. 0 -4 › -7 Since -4 is to the right of -7 on the number line -4 > -7. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 3 > -4 > -7 The numbers in order from greatest to least are 3 , -4 , and -7.

  4. 7.1A STUDENT ACTIVITY #1 Part I: Use a number line to order -5, -2 and 1 from least to greatest. 0 1 -2 ‹ 1 • Since -2 is to the left of ____ on the number line, ____ ___ ____. -5 -5 ‹ -2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 • Since ____ is to the left of -2 on the number line, ____ ___ ____. -5 1 -2 The integers in order from least to greatest are ____, ____, and ____.

  5. 7.1A STUDENT ACTIVITY #1 Part II: Circle the larger integer in each pair. -3 -2 5 -5 -10 -1 -9 7 4 -6 -8 8 0 -3 left -2 -10 4 -9 -8 5 -3 -5 -1 -2 -6 7 8 • For the first pair of integers, since ____ is to the ________ of _____ , _____ <_____. • For the second pair of integers, since ____ is to the ________ of _____ , _____ >_____. • For the third pair of integers, since ____ is to the ________ of _____ , _____ < _____. • For the fourth pair of integers, since ____ is to the ________ of _____ , _____ < _____. • For the fifth pair of integers, since ____ is to the ________ of _____ , _____ >_____. • For the sixth pair of integers, since ____ is to the ________ of _____ , _____ < _____. 5 right -5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -10 left -1 -9 left 7 4 right -6 -8 left 8

  6. 7.1A STUDENT ACTIVITY #1 Part III: • Order these temperatures from coldest to warmest: 10°, -15°, 12°, and -3°. • ______ < ______ < ______ < ______ • The temperatures in order from coldest to warmest are: • ______ , ______ , ______ , ______ • Order these altitudes from highest to lowest: 14, -6, 1, and -3. • ______ > ______ > ______ >______ • The altitudes in order from highest to lowest are: • ______ , ______ , ______ , ______ -15 -3 10 12 -15° -3° 10° 12° 14 1 -3 -6 14 1 -3 -6 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

  7. 7.1A STUDENT ACTIVITY #2-PART 2 PART I: Work with a partner to complete the following integer statements. Use the number line to justify the integer you choose to complete the statements. -1 • The integer __________ is four spaces to the left of 3. • The integer __________ is three spaces to the right of 0. • The integer __________ is three spaces to the right of -2. • The integer __________ is ten spaces to the right of -5. • The integer __________ is five spaces to the right of 2. • The integer __________ is seven spaces to the left of 0. • The integer __________ is two spaces to the left of 1. • The integer __________ is five spaces to the right of 3. • The integer __________ is two spaces to the left of -1. • The integer __________ is thirteen spaces to the right of 0. 3 0 1 5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 7 -7 -1 8 -3 13

  8. 7.1A STUDENT ACTIVITY #2-PART 2 PART II: Continue to work with your partner to answer the following questions. If 0 feet represents sea level, what does -300 represent? _______________________________ If -9 represents 9 kilometers south, what does +18 represent? ___________________________ If +17 represents gaining 17 yards in football, what does -8 represent? ____________________________ If -4 represents going down 4 floors in an elevator, what integer represents going up 7 floors? ____________________________ If -25 represents 25 yards west, what integer represents 12 yards east? ____________________________ 300 feet below sea level 18 kilometers north losing 8 yards +7 +12

  9. Comparing Rational Numbers To place a group of rational numbers in order, first convert them to the same form, such as fractions or decimals, and then place them in order. The form used will depend on the numbers being ordered. Following are guidelines for comparing rational numbers and placing them in order: • To compare whole numbers, compare the digits in each place value, starting at the left. • To compare fractions with the same denominator, compare the numerators. • To compare fractions with different denominators, rewrite the fractions as equivalent fractions with the same denominator. Next, compare the numerators. • To compare mixed numbers, first compare the whole number parts. If the whole number parts are equal, then compare the fractional parts.

  10. Comparing Rational Numbers • To compare decimal numbers, compare the digits in each place value, starting at the left. When comparing decimals, the numbers should all have the same number of places to the right of the decimal point. Place zeros to the right of the last digit if necessary.

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