Math 310 - Dr. Miller - Homework #28: Other Models for Integer Arithmetic
1. Write a number sentence for each temperature story below:
(a) The temperature is rising at 2 degrees per hour. How much warmer/colder will it
be in 10 hours?
(b) The temperature is rising at 2 degrees per hour. How much warmer/colder was it
5 hours ago?
(c) The temperature is falling at 2 degrees per hour. How much warmer/colder will it
be in 4 hours?
(d) The temperature is falling at 2 degrees per hour. How much warmer/colder was it
6 hours ago?
2. Make up temperature stories for the following expressions:
(a) 3 · (−2)
(b) 5 · (−1)
(c) 4 · 3
(d) (−4) · (−2)
(e) (−5) · (−2)
(f) (−1) · (−6)
3. Write an unsimplified number sentence for each mail-time story below, then state the
final answer.
(a) The mail carrier brings me a bill for $5 and a check for $10 and takes away a bill
for $4. What’s my net worth?
(b) The mail carrier brings me a bill for $5 and a bill for $10 and takes away a check
for $4. What’s my net worth?
(c) The mail carrier brings me two bills for $5 each and a check for $10 and takes away
a check for $4 and a bill for $9. What’s my net worth?
4. Make up mail-time stories for the following expressions:
(a) 5 + (−6) − 7
(b) (−5) − (−6)
(c) 2 · (−7) + 10 − 5 − (−8)
(d) (−7) + 2 · 10 − 2 · 5 − (−8)
(e) (−9) + (−8) − (−7) − 6
(continued on next page)
111
5. Make up meaningful Fact Patterns leading to the following computations:
(a) 4 − (−2)
(b) 5 − 7
(c) (−2) − 1
(d) 6 − (−2)
(e) 4 × (−3)
(f) (−2) × 3
(g) (−1) × (−5)
(h) (−2) × (−3)
6. Write the precise integer arithmetic problem - with answer - acted out by the ”Clown
on a Tightrope” in following the steps below; also state the answer:
(a) He starts on positive 3, faces left and walks forwards two steps, faces right and
walks backwards 6 steps, then faces left again to walk backward 1 step.
(b) He starts on negative 4, faces right and walks backwards 3 steps, faces left and
walks backwards 2 steps, and then faces right and walks forward 5 steps.
(c) He starts on negative 1, faces left and walks backwards 3 steps, faces right and
walks forwards 2 steps, and then faces left and walks forward 5 steps.
(d) He starts on negative 1, faces right and walks backwards 3 steps, faces left and
walks forwards 2 steps, and then faces right and walks backwards 5 steps.
7. Write the sequence of movements the Clown-on-a-Tightrope must make in acting out
the following computations and state the final answer as well.
(a) 5 − 9 + (−2)
(b) (−3) − (−4) − 1
(c) 2 + (−5) + 6 − 4
(d) (−1) − 3 + (−2) − (−6)
112
Math 310 - Dr. Miller - Solutions to HW #28: Other Models for Integer Arithmetic
1. (a)
(b)
(c)
(d)
(2)(10) = 20 or (+2)(+10) = +20
(2)(−5) = −10
(−2)(4) = −8
(−2)(−6) = 12
2. (a) The temperature is rising 3 degrees per hour. How much warmer/colder was it 2
hours ago?
(b) The temperature is rising 5 degrees per hour. How much warmer/colder was it 1
hour s ago?
(c) The temperature is rising 4 degrees per hour. How much warmer/colder will it be
in 3 hours?
(d) The temperature is falling 4 degrees per hour. How much warmer/colder was it 2
hours ago?
(e) The temperature is falling 5 degrees per hour. How much warmer/colder was it 2
hours ago?
(f) The temperature is falling 1 degree per hour. How much warmer/colder was it 6
hours ago?
3. (a) (−5) + 10 − (−4) = 9
(b) (−5) + (−10) − 4 = −19
(c) 2(−5)) + 10 − 4 − (−9) = 5
4. (a) The mail carrier brings me a check for $5 and a bill for $6 and takes away a check
for $7. Am I richer or poorer, and by how much?
(b) The mail carrier brings me a bill for $5 and takes away a bill for $6. Am I richer
or poorer, and by how much?
(c) The mail carrier brings me two bills for $7 apiece and a check for $10 and takes
away a check for $5 and a bill for $8. Am I richer or poorer, and by how much?
(d) The mail carrier brings me a a bill for $7 and two checks for $10 each and takes
away two checks for $5 each and a bill for $8. Am I richer or poorer, and by how
much?
(e) The mail carrier brings me one bill for $9 and another for $8 and takes away a bill
for $7 and a check for $6. Am I richer or poorer, and by how much?
5. (a)
2+2
2+1
2+0
2 + (−1)
2 + (−2)
2 + (−3)
2 + (−4)
2 + (−5)
113
=
=
=
=
=
=
=
=
4
3
2
1
0
−1
−2
−3
(b)
3+1
2+1
1+1
0+1
(−1) + 1
(−2) + 1
=
=
=
=
=
=
4
3
2
1
0
−1
(c)
4−2
4−1
4−0
4 − (−1)
4 − (−2)
=
=
=
=
=
2
3
4
5
6
(d)
5−3
5−4
5−5
5−6
5−7
=
=
=
=
=
2
1
0
−1
−2
9−7
8−7
7−7
6−7
5−7
=
=
=
=
=
2
1
0
−1
−2
OR
(h)
3×3
2×3
1×3
0×3
(−1) × 3
(−2) × 3
114
=
=
=
=
=
=
9
6
3
0
−3
−6
6. (a) 3 − 2 + (−6) − (−1) = −6
(b) (−4) + (−3) − (−2) + 5 = 0
(c) (−1) − (−3) + 2 − 5 = −1
(d) (−1) + (−3) − 2 + (−5) = −11
7. (a) He starts on positive 5, faces left and walks forward 9 steps, then faces right and
walks backward two steps, ending on -6.
(b) He starts on -3, faces left and walks backward 4 steps, then remains facing left and
walks forward 1 step, ending on 0.
(c) He starts on 2, faces right and walks backward 5 steps, remains facing right and
walks forward 6 steps, and finally faces left and walks forward 4 steps, ending on
-1.
(d) He starts on -1, faces left and walks forward 3 steps, then faces right and walks
backward 2 steps and finally faces left again to walk backward 6 steps, ending on
0.
115