Transcript Comparing and Ordering Integers

Problem Solving Strategy:
Working Backwards
7.13C: Selecting the appropriate problem solving strategy.
Mr. Brewer’s 7th Grade Math
September 9, 2009
Alto, Texas has a population of 1407 people. New
Summerfield, Texas has a population of 1388
people. What is the difference between the two
towns’ populations?
A. 21
B. 24
C. 19
D. 2795
The Texas Rangers had an incredible start to the
year. They scored 387 runs during the first 43
games. If they scored the same amount of runs
every game, how many points did they score per
game?
A. 7
B. 9
C. 6
D. 2
The zoo uses a total of 268 pounds of food every
day for the 67 animals they keep. If each animal
ate the same amount of food, how many pounds of
food does each animal eat?
A. 5
B. 3
C. 17
D. 4
The Liberty Middle School 7th grade football team
scored 63 points in each of their first four football
games. How many total points did they score in
their first four games?
A. 378
B. 252
C. 48
D. 53
Warm-Up
Copy these numbers in your ‘Warm Up’ section and
order them from least to greatest. There are four sets
of numbers to order: Set A, Set B, Set C, and Set D.
A. 567
356
0
B. 1.2
1.55
1.58
C. 5.65
56.5
0
D. -7
5
0
-5
867
1.9
565
7
24
-23
0
-565
-24
Comparing and
Ordering Integers
7.1A: Compare and order integers and positive rational numbers.
Mr. Brewer’s 7th Grade Math
September 9, 2009
Reviewing Vocabulary
• Integers – The set of all whole numbers, their
opposite numbers, and zero (what’s on the
number line (-8, 0, 4, -8 etc…))
• Negative numbers – The set of all real
numbers less than zero (-8, -4, -2, etc…)
• Rational numbers – Any number that can be
written as a fraction (3/4, 8, -8, .40)
Reviewing Vocabulary
• Integers
– Give an example of an integer?
– Give an example of something that is not an integer?
• Negative numbers
– Give an example of a negative number?
– Give an example of something that is not a negative?
• Rational numbers –
– Give two examples of a rational number?
– Give an example of something that is not a rational
number?
What’s an Opposite?
The opposite of a number is the same
distance from 0 on a number line as the
original number, just in the opposite direction.
–4 and 4 are opposites
–4
4
•
•
–5–4–3–2–1 0 1 2 3 4 5
Negative integers
Positive integers
0 is neither positive
nor negative
Graph the integer -7 and its opposite on a
number line.
7 units
7 units
–7–6–5–4–3–2–1 0 1 2 3 4 5 6 7
The opposite of –7 is 7.
Graph the integer -5 and its opposite on a
number line.
5 units
5 units
–7–6–5–4–3–2–1 0 1 2 3 4 5 6 7
The opposite of –5 is 5.
The Number Line – Key Understandings
• Negative integers closer to zero have a greater
value than those numbers further from zero.
• From any point on a number line, an integer’s
value increases as you move right and
decreases as you move left.
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4
5 6
7
The Number Line
Order the following numbers using the number line.
6 -7 8 3 0 -2 -3 6
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4
5 6
7
The Number Line
1. What two whole numbers fall between 4 & 7 on the number line?
2. Negative 3 lies the right or left of zero?
3. Tell me three numbers less than -2 on the number line?
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4
5 6
7
Signs of Comparison
• Less Than
‹ 4‹8
‹
• “Four is less than eight”
• Greater Than
› 8›4
• “Eight is greater than eight”
• Equal To
= 8=8
• “Eight is equal to eight”
›
=
Which Sign?
< > =
Which Sign?
< > =
Which Sign?
< > =
Which Sign?
4
5
< > =
Which Sign?
-8
-5
< > =
Which Sign?
Copy these numbers into your notes section and
determine the appropriate sign.
10
2
-6
6
-2
-8
Where do we see
negative integers
in the real world?
Do we see
negative integers
in sports?
What about in
geography?
Highest and Lowest, USA
Mt. McKinley
Death Valley
20,320 Ft.
- 282 Ft.
Credit Cards
Temperature?
Altitude
There are four people out on the
ocean.
1. Floating on a raft
2. Scuba diving at -32 ft
3. In a boat 5 feet above the
water.
4. Snorkeling at -1 ft
Who is the highest, who is the
lowest?
Comparison: Altitude
<
>
=
Sports
Which is the better play?
A.
B.
C.
D.
E.
Sack for 9 yards
Run for 5 yards
Incomplete for 0 yards
Run, lose 1 yard
Pass for 35 yards
Comparison: Sports
<
>
=
Business
Which business would you be least likely to buy? Most
likely?
A.
B.
C.
D.
A car wash that makes $500 per week.
A restaurant that loses $200 per week.
A diner that makes $200 per week.
A CD store that loses $450 per week.
Order these stores from best to worst (greatest to
least).
Credit Cards
Who has less money?
A.
B.
C.
D.
E.
Bob owes $30
Mary owes $40
Mark owes $0
Marty owes $100
Dom owes $85
Order Least to Greatest
Temperature
Temperatures
– All in degrees F
•
•
•
•
•
•
McAllen, TX
Mexico City
Fairbanks, AK
Athol, MA
The Forks, ME
Whitefish, MT
75
85
-10
28
-5
-15
Order these temperatures
from least to greatest.
• Put the following lists of numbers in order
from greatest to least:
-19, -20, 20, 19, -23, 34, -1
130, -25, 87, -125, 52, -94, 2
• Put the following lists of numbers in order
from least to greatest:
-9, -11, -15, -13, -7, -17, 0
-13, 12, -11, 10, -9, 8, -7, 6, -5
Integer Exercise
• Instructions: Give 5 examples of positive and
negative integers found in the real world.
• For each example, describe in full sentences
which integer is least in value and which is
greatest in value and why?