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6-1 6th grade math Comparing and Ordering Positive and Negative Numbers Objective • To compare and order positive and negative numbers. • Why? To understand all types numbers. Negatives are to the left of the number line. Zero is in the middle. Positives are to the right. California State Standards NS 1.1 : Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line. MR 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information … sequencing and prioritizing information, and observing patterns. Vocabulary • Integers – A set of numbers either positive or negative. The term: integer is now used instead of the term: number. • …, -3, -2, -1, 0, +1, +2, +3, … • Negative Numbers – Integers whose value is less than zero • -5, -10 , -23 9/11, -456, etc. • Positive Numbers – Integers whose value is more than zero. At times a positive number may NOT have the + sign. • +2, +63, +77 2/3, etc. • Absolute Value | | – The distance an integer is from zero on a number line. It is neither positive nor negative. • |2| = 2 • |-5|= 5 • Opposites – A pair of integers that are the same distance from zero • -2 and +2 How to Compare and Order Positive and Negative Numbers a) -5 , 30 a) Any negative number is less than any positive number. b) Any positive number is greater than any negative number. -30 is a negative number and therefore smaller than a positive -5 < -30 or -30 > -5 b) -234, 5 -234 is a negative number and therefore smaller than a positive -234 < 5 or 5 > -234 c) If comparing 2 negative numbers, the number ‘farther’ away from 0 is less than the other. c) -10, -15 -15 is farther away from 0 -10 > -15 or -15 < -10 d) If comparing 2 positive numbers, the number closest to 0 is lesser than the other. d) 34, 9 ½ 9 ½ is closest to 0 34 > 9 ½ or 9 ½ < 34 Remember your signs! a) > means greater than. a) -4 > -10 b) < means less than. b) 9 < 90 c) Eat the bigger number Placing Integers on a Number Line +2, -0.5, +1 ¾, 0, -2 ¼, -3 1) Separate the negative integers from the positives 2) Remember: larger negative integers are farther away from 0 and are placed farthest away from 0. Count backwards. 3) Count forward when placing positive integers. 4) Place on a number line, starting with the negative integers. 1) -0.5, -2 ¼, -3 2) 0 3) +2, +1 ¾ 4) -3, -2 ¼, -0.5, 0, +1 ¾, +2 Try It! Use < , > , or = 1) +3 -2 1) +3 > -2 Why- a positive is always greater than a negative. 2) -7 < 0 Why- zero is always greater than a negative. 3) -4 > -9 2) -7 0 Why- -4 is closer to 0 . 4) +8 > -2 3) -4 -9 4) +8 -2 Why- a positive is always greater than a negative. Try Some More! Arrange in order: least to greatest. 5) 0, +5, -12, +15 6) -5, +2 ½, -3 ½,-2.25, +1 ¾ 5) -12 0 +5, +15 -12, 0, +5, +15 6) -5, -3 ½, -2.25 +2 ½, +1 ¾ -5, -3 ½, -2.25, +1 ¾, +2 ½ Here’s Even More! Find the absolute value AND the opposite. 7) -11 8) -43 9) +18 10) -25 7) -11 |-11| = 11 11 8) -43 |-43| = 43 +43 9) +18 |18| = 18 -18 10) -25 |-25| = 25 +25 Objective Review • To compare and order positive and negative numbers. • Why? Now you can understand all types numbers. Negatives are to the left of the number line. Zero is in the middle. Positives are to the right. Independent Practice • Complete problems 1225 • Copy original problem first. • Show all work! • If time, complete Mixed Review: 26-33 • If still more time, work on Accelerated Math.