1/12/17 Week 1 Thursday daily sheet:
Word problems with negative numbers
Daily aims:
 1. I can solve word problems with negative numbers.
We’ll do these together, and then you’ll have the chance to work in pairs on some
additional problems.
1) Jonah went scuba diving. First he descended 12 feet below sea level to the top of
the kelp. Then he went down another 13 feet, and a sea otter played with Jonah’s
flippers. Finally, Jonah descended until he was 38 feet below the surface, and he
watched a school of fish. What’s the distance between where Jonah met the otter and
where he saw the fish?
2) The temperature at 3 PM was 8F. By 8 PM it had fallen 5 degrees. By midnight it
had fallen another 7 degrees. By 7 AM the temperature was 9F. What was the
change in temperature from midnight to 7AM?
3) A submarine starts at 103.4 feet below sea level. It then drops 8.2 times its original
depth. How many feet below the surface is it now?
D. Stark 1/7/2017
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1/12/17 Week 1 Thursday daily sheet:
Word problems with negative numbers
KEY
1) Jonah went scuba diving. First he descended 12 feet below sea level to the top of
the kelp. Then he went down another 13 feet, and a sea otter played with Jonah’s
flippers. Finally, Jonah descended until he was 38 feet below the surface, and he
watched a school of fish. What’s the distance between where Jonah met the otter and
where he saw the fish?
The question is about distance. Remember that distance is always positive.
You could use a picture and forget about negative numbers or you could use
straight math with negative numbers.
picture method:
straight math method:
 The otter is at 12 + 13 = 25 ft.
 The fish are at 38 ft.
 Distance is the difference, but it’s got to be positive, so you use the
absolute value bars: | 38  (25) | = | 13 | = 13 ft.
D. Stark 1/7/2017
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2) The temperature at 3 PM was 8F. By 8 PM it had fallen 5 degrees. By midnight it
had fallen another 7 degrees. By 7 AM the temperature was 9F. What was the
change in temperature from midnight to 7AM?
The question is about change. Change can be positive (going up) or negative
(going down).
You could use a picture and forget about negative numbers or you could use
straight math with negative numbers.
picture method:
straight math method:




At 3 PM it was 8F. By 8 PM was 8  5 = 3.
By midnight it was 3  7 = 4.
The change from midnight to 7 AM is the change from 4 to 9 .
To calculate the change from A to B, always use B  A. The order here is
important. The answer could end up negative, and that’s OK for change.
 9  (4) = 9 + 4 = 5 change
D. Stark 1/7/2017
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3) A submarine starts at 103.4 feet below sea level. It then drops 8.2 times its original
depth. How many feet below the surface is it now?
You don’t necessarily need a picture, but it might help.
Also, you might want to experiment with the “substitute nice numbers for messy
ones” approach discussed on the pink NOTES sheet. I’ll use that here.
Let’s pretend the messy decimals aren’t there. We can then make intuitive sense
of what’s happening and what operations to use. Afterwards, we can substitute
the messy numbers to get the actual answer.
D. Stark 1/7/2017
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