1. 6-1 6 th grade math Comparing and Ordering Positive and Negative Numbers

2. 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.

3. 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.

4. 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

5. How to Compare and Order Positive and Negative Numbers a)Any negative number is less than any positive number. b) Any positive number is greater than any negative number. a)-5, 30 -30 is a negative number and therefore smaller than a positive -5 b)-234, 5 -234 is a negative number and therefore smaller than a positive -234

6. c) If comparing 2 negative numbers, the number ‘farther’ away from 0 is less than the other. d) If comparing 2 positive numbers, the number closest to 0 is lesser than the other. c) -10, -15 -15 is farther away from 0 -10 > -15 or -15 < -10 d) 34, 9 ½ 9 ½ is closest to 0 34 > 9 ½ or 9 ½ < 34

7. Remember your signs! a)> means greater than. b)< means less than. c) Eat the bigger number a)-4 > -10 b)9 < 90

8. 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

9. Try It! Use, or = 1)+3 -2 2)-7 0 3)-4 -9 4)+8 -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 Why- -4 is closer to 0. 4) +8 > -2 Why- a positive is always greater than a negative.

10. 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

11. 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

12. 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.

13. Independent Practice Complete problems 12- 25 Copy original problem first. Show all work! If time, complete Mixed Review: 26-33 If still more time, work on Accelerated Math.