Transcript Lesson 6-1a

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.