The Zero Property
Explain the Zero Property
the same integer can be represented different ways using different numbers of counters, by including several zeros. Consider the fact that −1 + 1 = 0.
Model −4 + 8 using a number line.
On the board!
Model the subtraction −5 − (−2). What is the result?
-3
This subtraction expression has a positive result: () - ( ) What values could go in the brackets?
7 (-3)
The temperature at 7 a.m. was -8 degrees Celsius. By noon, it had dropped another 5 degrees, but then it increased by 3 degrees in the afternoon. What was the temperature at the end of the day?
-10
Represent +3 using five counters.
4 Positive 1 Negative
1 Positive Cancels out 1 Negative
Model (−7) + (−3) using counters
On the board!
−5 − (+12)
-17
Which result is different from the others? A −10 − (+8) B −4 − (−2) C 6 − 8 D −1 − (+1)
A
A submarine is at a depth of -6,000 meters below sea level. If it ascends 2,851 meters and then descends another 1,268 meters, what is its new depth?
-4,417 meters below sea level.
Represent +3 using seven counters.
5 Positive 2 Negative
2 and -2
99 + (−4)
95
-8 − (−8)
0
10−(−7)+(−3)
14
Emily’s bank account has a balance of $150. She withdraws $80 for shopping, deposits $50, withdraws $30, then deposits another $40. Afterward, she withdraws $60 for groceries. What is her final account balance?
$70
What number is represented with 8 Positive and 4 Negative Counters
+4
What is the sum of −10 and +8?
-2
Which of these subtraction expressions results in −15?
A −7 − 22 B −10 − (−5) C −12 − 3 D −21 − 6
C
−45+20−(−15)
-10
Mercury boils at +357C and freezes at -39C. What is the difference between the boiling point and the freezing point of mercury?
The difference between the boiling point and the freezing point of mercury is 3960C.
What number is represented with 127 Negative Counters and 213 Positive Counters?
86
-96587 + (-2510)
−99097
How does this pattern help you see what −12 − (−1) equals? −12 – 3 −12 – 2 −12 – 1 −12 – 0 −12 − (−1)
It increases by +1 everytime
−35+25−(−20)+(−15)
-5
A mountaineer starts at 12,500 meters above sea level. He climbs 3,250 meters, descends 4,750 meters due to a steep slope, climbs another 6,400 meters, and finally descends 7,300 meters to reach a camp.
10,100 meters above sea level.