The Number System · Grade 7 · 7.NS.A.1.b | 7.NS.A.1.c
Roots of Reason
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Adding and Subtracting on the Number Line
Name
Date
Correct / 10
1
Draw the Jump
- start at the first number. The sign gives the direction, the number gives the distance. Draw your arrow above the line.
1. −3 + 7 =
2. −2 + (−5) =
3. 4 + (−9) =
4. −6 + 0 =
The Number System · Grade 7 · 7.NS.A.1.b | 7.NS.A.1.c
Roots of Reason
rootsofreason.org
2
Rewrite the Subtraction
- subtracting a number is adding its opposite: p − q = p + (−q). Rewrite first, then jump in the space below.
5. 3 − 8
3 + ( ) =
6. −4 − (−6)
−4 + ( ) =
7. −5 − 2
−5 + ( ) =
3
Change or Distance?
- change carries a sign. Distance never does.
A diver hangs at −8 m. A gull flies at 5 m.
8. The gull dives straight down to the diver. What is the signed change in its height?
change = m
9. How far apart are they? Write it with absolute value bars first.
= m
10. At dawn the temperature was −4°F. By noon it read 9°F. What was the change in temperature, with its sign?
change = °F
The Number System · Grade 7 · 7.NS.A.1.b | 7.NS.A.1.c
Roots of Reason
rootsofreason.org
Adding and Subtracting on the Number Line
1Draw the Jump
1. −3 + 7 = 4
2. −2 + (−5) = −7
3. 4 + (−9) = −5 not +5: the bigger size wins the sign
4. −6 + 0 = −6 a jump of zero goes nowhere
The Number System · Grade 7 · 7.NS.A.1.b | 7.NS.A.1.c
Roots of Reason
rootsofreason.org
2Rewrite the Subtraction
5. 3 − 8
start at 3, jump 8 left,
past zero to −5
past zero to −5
3 + ( −8 ) = −5
6. −4 − (−6)
the opposite of −6 is +6:
jump 6 right, land at 2
jump 6 right, land at 2
−4 + ( +6 ) = 2
7. −5 − 2
start at −5,
jump 2 more to the left
jump 2 more to the left
−5 + ( −2 ) = −7
3Change or Distance?
A diver hangs at −8 m. A gull flies at 5 m.
8. change = −13 m
from 5 down to −8 is −8 − 5 = −13. Down means negative.
from 5 down to −8 is −8 − 5 = −13. Down means negative.
9. |−8 − 5| = |−13| = 13 m
same 13, but distance drops the sign. A gap is never negative.
same 13, but distance drops the sign. A gap is never negative.
10. Dawn −4°F, noon 9°F.
9 − (−4) = 9 + 4 = +13.
It crossed zero, so both pieces count: 4 up to zero, then 9 more.
It crossed zero, so both pieces count: 4 up to zero, then 9 more.
change = +13 °F