| start (℉) | change (℉) | final (℉) | addition equation |
1 | +40 | 10 degrees warmer | +50 | 40 + 10 = 50 |
2 | +40 | 5 degrees colder | | |
3 | +40 | 30 degrees colder | | |
4 | +40 | 40 degrees colder | | |
5 | +40 | 50 degrees colder | | |
1A
| start (℉) | change (℉) | final (℉) | addition equation |
a | 15 | 30 degrees warmer | | |
b | 15 | 5 degrees colder | | |
c | 15 | 15 degrees colder | | |
d | 15 | 20 degrees colder | | |
e | 15 | 40 degrees colder | | |
1B
| start (℉) | change (℉) | final (℉) | addition equation |
a | -20 | 30 degrees warmer | | |
b | -20 | 35 degrees warmer | | |
c | -20 | 15 degrees warmer | | |
d | -20 | 15 degrees colder | | |
2A
What do you notice about the last two problems?
We notice...
| start (℉) | change (℉) | final (℉) | addition equation |
a | -30 | 40 degrees warmer | | |
b | -30 | 30 degrees warmer | | |
c | -30 | 10 degrees warmer | | |
d | -30 | 10 degrees colder | | |
e | -30 | 15 degrees colder | | |
2B
Did you notice anything interesting about adding with negative numbers?
We notice….
A mountaineer is climbing on a cliff. She is 200 feet above the ground. If she climbs up, this will be a positive change. If she climbs down, this will be a negative change.
starting elevation (feet) | change (feet) | final elevation (feet) |
+200 | +70 | |
+200 | -120 | |
+200 | | +300 |
+200 | | +110 |
+200 | | +35.2 |
3A
A spelunker is down in a cave next to the cliff. If she climbs down deeper into the cave, this will be a negative change. If she climbs up, whether inside the cave or out of the cave and up the cliff, this will be a positive change.
starting elevation (meters) | change (meters) | final elevation (meters) |
-20 | -15 | |
-20 | +130 | |
-20 | | +61 |
-20 | | -5 |
-20 | | -50 |
-20 | +27.5 | |
-20 | | +73.5 |
4A
5A
#1 -3 + 8 = | #6 -9 + 2 = |
#2 -4 + 7 = | #7 -8 + 3 = |
#3 -6 + 10 = | #8 -14 + 5 = |
#4 -7 + 12 = | #9 -12 + 5 = |
#5 -5 + 14 = | #10 -15 + 10 = |
Discuss: What do you notice about the solutions in the pink column compared to the solutions in the blue column? Why is that happening?
5B
#1 -3 + 2 = | #6 -7 + 8 = |
#2 -4 + 1 = | #7 -8 + 10 = |
#3 -10 + 4 = | #8 -5 + 9 = |
#4 -12 + 3 = | #9 -9 + 12 = |
#5 -13 + 5 = | #10 -11 + 20= |
Discuss: What do you notice about the solutions in the pink column compared to the solutions in the blue column? Why is that happening?
6A
#1 -7 + (-1) = |
#2 -9 + (-3) = |
#3 -8 + (-6) = |
#4 -6 + (-9) = |
#5 -7 + (-13) = |
#6 -8 + (-17) = |
In this problem set, you were always asked to add two negative numbers together. What do you notice about adding two negative numbers?
We notice….
6B
#1 -5 + (-3) = |
#2 -4 + (-6) = |
#3 -2 + (-7) = |
#4 -5 + (-9) = |
#5 -7 + (-10) = |
#6 -9 + (-13) = |
In this problem set, you were always asked to add two negative numbers together. What do you notice about adding two negative numbers?
We notice….
#1. 3 + = -2 | #6 -10 + = -60 |
#2. 8 + = -2 | #7. -10 + = 20 |
#3. 8 + = 2 | #8 -100 + = 100 |
#4 1 + = -5 | #9 -100 + = 0 |
#5 -10 + = -5 | #10 -100 + = -300 |
7A: Fill in the blanks.
#1. -6 + = -8 | #6 -10 + = -40 |
#2. -6 + = -3 | #7. -10 + = 40 |
#3. -6 + = -1 | #8 300 + = 200 |
#4 -6 + = -11 | #9 300 + = 0 |
#5 -10 + = 0 | #10 300 + = -500 |
7B: Fill in the blanks.
8A
-25 + (-37) = |
-85 + (37) = |
55 + (-62) = |
-350 + (14) = |
These numbers have larger magnitudes (they are farther from zero) which makes them more challenging. Choose one problem and explain why you think your answer makes sense.
We think….
8B
-29 + (-81) = |
-120 + 37 = |
50 + (-62) = |
-125 + 29= |
These numbers have larger magnitudes (they are farther from zero) which makes them more challenging. Choose one problem and explain why you think your answer makes sense.
We think….
9A
#1 is _____ because….
#2 is ______ because…
#3 is ______ because….