Download File - Mrs. Heidesch

Bell Work
Tuesday, April 1, 2014
Number Systems
“Natural Numbers” (a.k.a. “Counting Numbers”) are
numbers used to count things that occur in nature.
Example: 1, 2, 3, 4, …
“Whole Numbers” are natural numbers and 0.
Example: 0, 1, 2, 3, ...
“Integers” are whole numbers and their opposites.
6. Name the set or sets that each of the numbers below belongs to.
counting numbers
1
7
2
integers
–3 ,
, 2 ,
, 0 and – 3.6
4
8
rational numbers
7. Copy the statements below and determine which is true and which
is false.
The set of rational numbers includes the set of integers.
All counting numbers are rational numbers.
A mixed number is a rational number.
Zero is not a rational number.
3
8. What is the opposite of 4 ? Explain why.
9. On the same winter morning, the temperature is -28° F in
Anchorage, Alaska and 65° F in Miami, Florida. How many degrees
warmer was it in Miami than in Anchorage on that morning?
4
2
3
10. Find and label the numbers
, 5 ,  , and  on the
3
3
4
4
number line.
-1
0
1
6. Name the set or sets that each of the numbers below belongs to.
counting numbers
1
7
2
integers
–3 ,
, 2 ,
and – 3.6
4
8
rational numbers
3
–3=
1
integers
rational numbers
7
8
2= 2
rational numbers
1
counting numbers
integers
rational numbers
6
3
18
 3.6  3  3  
10
5
5
0
0
1
1 9
2 
4 4
rational numbers
integers
rational numbers
rational numbers
7. Which statement(s) is true and which is false?
The set of rational numbers includes the set of integers.
True; -3 = -3/1
All counting numbers are rational numbers.
True; 3 = 3/1
A mixed number is a rational number.
True; 2 1/3 = 7/3
Zero is not a rational number.
False; 0/4 = 0
8.
3
What is the opposite of 4 ? Explain why.
The opposite of ¾ is – ¾ because they both have the same
absolute value, distance from zero.
9. On the same winter morning, the temperature is -28° F in
Anchorage, Alaska and 65° F in Miami, Florida. How many
degrees warmer was it in Miami than in Anchorage on that
morning?
The temperature in Anchorage is 28 below zero and in
Miami it is 65 above zero, so the difference in temperatures
is 28+65=93 degrees.
9. On the same winter morning, the temperature is -28° F in
Anchorage, Alaska and 65° F in Miami, Florida. How many
degrees warmer was it in Miami than in Anchorage on that
28
65
morning?
Miami, Florida
Anchorage, Alaska
We can count from -28 up to 65. If Anchorage, Alaska was 28 degrees
warmer than it is on this winter morning, the temperature would be zero
degrees. If Anchorage, Alaska was 65 degrees warmer still, the
temperature would be 65 degrees, the same temperature as Miami,
Florida. In order for Anchorage, Alaska to be the same temperature as
Miami, Florida, Anchorage would have to be 28+65=93 degrees warmer
than it is.
Thus, Miami, Florida is 93 degrees warmer than Anchorage, Alaska.
9. On the same winter morning, the temperature is -28° F in
Anchorage, Alaska and 65° F in Miami, Florida. How many
degrees warmer was it in Miami than in Anchorage on that
morning?
Because 65−(−28)=93, we know it is 93 degrees warmer
in Miami, Florida than it is in Anchorage, Alaska.
4
2
3
5


10. Find and label the numbers
,
,
, and
on the
3
3
4
4
number line.

-1
3

4
2
3
4
1
1
3
3
0
1
5
1
1
4
4