6-16th 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) 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 < -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.

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 034 > 9 ½ or 9 ½ < 34

Remember your signs!

a) > means greater than.

b) < means less than.

c) Eat the bigger number

a) -4 > -10

b) 9 < 90

Placing Integers on a Number Line+2, -0.5, +1 ¾, 0, -2 ¼, -31) Separate the negative

integers from the positives2) 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

2) -7 0

3) -4 -9

4) +8 -2

1) +3 > -2Why- a positive is always greater than a negative.

2) -7 < 0Why- zero is always greater than a negative.

3) -4 > -9Why- -4 is closer to 0 .

4) +8 > -2Why- 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) -120+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| = 1111

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 12-25

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 26-33

• If still more time, work on Accelerated Math.