Transcript Math design template

Unit 1:
Integers and
Absolute Value
0011 0010 1010 1101 0001 0100 1011
Test Review
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1. Blake bought 20 oranges from the farmer’s
market. Which of the following actions would
make his net change in the amount of oranges he
0011 0010 1010 1101 0001 0100 1011
owns 0? Select all that apply.
•
In this question, remember that he begins with 20
oranges. For each answer choice, you need to
remember that he has those 20 oranges.
A. He stored 20 oranges in the fridge.
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Start with the 20 Blake has, then he stored (+) 20
more, so 20 + 20 = 40. This DOES NOT give us a net
of 0.
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B. He bought 20 oranges from the store.
Start with the 20 Blake has, then he bought (+) 20
more, so 20 + 20 = 40. This DOES NOT give us a net
of 0.
1. Blake bought 20 oranges from the farmer’s
market. Which of the following actions would
make his net change in the amount of oranges he
0011 0010 1010 1101 0001 0100 1011
owns 0? Select all that apply.
•
In this question, remember that he begins with 20
oranges. For each answer choice, you need to
remember that he has those 20 oranges.
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C. He drank juice made from 20 oranges.
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Start with the 20 Blake has, then he drank juice of (-)
20 more, so 20 - 20 = 0. This DOES give us a net of 0.
D. He gave 20 oranges to his local food pantry.
Start with the 20 Blake has, then he gave away (-) 20
more, so 20 - 20 = 0. This DOES give us a net of 0.
1. Blake bought 20 oranges from the farmer’s
market. Which of the following actions would
make his net change in the amount of oranges he
owns
0?0001
Select
that apply.
0011 0010 1010
1101
0100all
1011
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In this question, remember that he begins with 20
oranges. For each answer choice, you need to
remember that he has those 20 oranges.
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E. His family ate 10 oranges and then bought 10
more.
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Start with the 20 Blake has, then his family ate (-) 10,
then bought (+) 10 more, so 20 – 10 + 10 = 20. This
DOES NOT give us a net of 0.
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F. His daughter gave 40 oranges to her friends at
school.
Start with the 20 Blake has, then his daughter gave (-)
40 oranges, so 20 - 40 = -20. This DOES NOT give us a
net of 0.
2.
In Earnest’s yard, the grass grew 2 inches. The
next week, Earnest cut 2 inches off of the grass.
The total change was 0 inches. Which of the
0011 0010 1010
1101 0001
0100 1011 also has a total change of 0?
following
situations
A. It rained 2 inches on Tuesday. Then it rained 2
inches on Wednesday.
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2 inches of rain (+2), and 2 more inches of rain (+2) is
2 +2=4. This DOES NOT give us a total change of 0.
B. It snowed 4 inches last week. Then, 8 inches of
snow melted during this week.
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4 inches of snow (+4), then 8 inches of snow melted (-8)
is 4 – 8 = -4. This DOES NOT give us a total change of
0.
2.
In Earnest’s yard, the grass grew 2 inches. The
next week, Earnest cut 2 inches off of the grass.
The total change was 0 inches. Which of the
0011 0010 1010
1101 0001
0100 1011 also has a total change of 0?
following
situations
C. I put 5 pounds of birdseed in the feeder. Then,
birds ate 5 pounds of birdseed.
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5 pounds of birdseed in (+5), then birds ate 5 pounds
(-5) is 5 – 5 = 0. This DOES give us a total change of 0.
D. A farmer sold 3 bushels of apples last week.
Then she sold 6 bushels of apples this week.
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3 bushels of apples sold (-3) and another 6 bushels sold
(-6) is -3 – 6 = -9. This DOES NOT give us a total
change of 0.
2. In Earnest’s yard, the grass grew 2 inches. The next
week, Earnest cut 2 inches off of the grass. The
total change was 0 inches. Which of the following
0011 0010situations
1010 1101 0001
also0100
has1011
a total change of 0?
E. 3 feet of growth was cut from a tree branch last
year. Then the tree branch grew 3 feet this year.
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3 feet cut (-3), then grew 3 feet (+3) is -3 + 3 = 0. This
DOES give us a total change of 0.
F. My family painted a 300 square foot barn on
Saturday. Then on Sunday, we painted a 300
square foot garage.
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300 square foot barn painted (+300) and 300 square foot
garage painted (+300) is 300 + 300 = 600 . This DOES
NOT give us a total change of 0.
3. A number line is shown below.
A
B
-2
2
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Using the terms additive inverse and absolute value,
explain the relationship between A and B.
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A and B are additive inverses because when you add them
together, they equal 0. We also refer to additive inverses as “zero
pairs”. -2 + 2 = 0
A and B have the same absolute value of 2 because they are the
same distance from zero on the number line. Absolute value is
always positive because it tells the distance of a number from 0
on the number line.  2  2 and 2  2
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4. Which of the following situations could be
represented by the expression -20 + 5?
A. Sue borrowed $20 from her mom and earned $5
0011 0010 1010 1101 0001 0100 1011
for mowing the neighbor’s lawn.
Sue borrowed $20 (negative value) and earned $5
(positive value), so this CAN be represented by -20 + 5.
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B. David earned $20 for doing his chores and spent
$5 for lunch.
David earned $20 (positive value) and spent $5
(positive value), which is 20 – 5. Therefore, this CAN
NOT be represented by -20 + 5.
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4. Which of the following situations could be
represented by the expression -20 + 5?
C. Juan gave 20 M&M’s to his friend Julie and 5
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more to his other friend Kyle.
Juan gave 20 M&M’s (negative value) and gave 5 more
(negative value), which is -20 – 5. Therefore, this CAN
NOT be represented by -20 + 5.
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D. In the morning, Olivia noticed the temperature
had dropped 20° overnight. After an hour, the
temperature increased by 5 °.
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Temperature dropped 20° (negative value) and then
increased 5° (positive value), so this CAN be
represented by -20 + 5.
4. Which of the following situations could be
represented by the expression -20 + 5?
0011 0010 1010 1101 0001 0100 1011
E. A football team lost 20 yards. Then they gained 5
yards.
Football team lost 20 yards (negative value) and gained 5
yards (positive value), so this CAN be represented by -20
+ 5.
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F. A scuba diver dove 20 feet below sea level. Then
swam up 5 feet.
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Scuba diver dove 20 feet below sea level (negative value)
swam up 5 feet (positive value), so this CAN be
represented by -20 + 5.
5. When x is a nonzero integer, the sum of 3 + x is
sometimes negative and sometimes positive.
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1010 1101a0001
0100
A. Identify
value
of1011
x for which the sum of 3 + x is
negative. Explain.
Think about how many
negatives I would need to add in
order to make a negative value
+
-
+
-
+
-
*In order to get the maximum
credit for this question, you
need to give 2 examples.
= -1
-
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I would need -4 in order to
make a negative value, so x can
be -4.
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Any value that is less than -4
(more negatives) would also
work. Examples: -5, -6, -7…
5. When x is a nonzero integer, the sum of 3 + x is
sometimes negative and sometimes positive.
0011 0010
1010 1101a0001
0100
B. Identify
value
of1011
x for which the sum of 3 + x is
positive. Explain.
Can x be a negative value?
+
-
+
+
-
*In order to get the maximum
credit for this question, you
need to give 2 examples.
=1
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If I add -2, I will still have a
positive value, so x can be -2.
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X can also be any value that is
greater than -2 (fewer negatives
and all positive numbers) would
also work. Examples: -1, 1, 2,
3…
6. The temperature on a cold winter day in Chicago
was -10°F. Which of the following situations could
explain how the temperature became -10°F ?
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A. The temperature reached 15°F, then dropped
overnight 25°F .
Started at +15°F, then dropped (negative value) 25°F, so
15°F – 25°F = -10°F. This COULD explain how it became 10°F.
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B. The temperature was 12°F, then increased by 22°F.
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Started at 12°F, then increased (positive value) by 22°F, so
12°F + 22°F = 32°F. This COULD NOT explain how it
became -10°F.
6. The temperature on a cold winter day in Chicago
was -10°F. Which of the following situations could
explain how the temperature became -10°F ?
0011 0010 1010 1101 0001 0100 1011
C. The temperature was 3°F, then dropped by 13°F.
Started at +3°F, then dropped (negative value) 13°F, so
3°F – 13°F = -10°F. This COULD explain how it became 10°F.
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D. The low temperature for the day was -15°F, then
increased by 5°F.
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Started at -15°F, then increased (positive value) by 5°F, so
-15°F + 5°F = -10°F. This COULD explain how it became
-10°F.
6. The temperature on a cold winter day in Chicago was
-10°F. Which of the following situations could
explain how the temperature became -10°F ?
0011 0010 1010 1101 0001 0100 1011
E. The high temperature for the day was 10°F, then it
decreased by 10°F.
Started at 10°F, then decreased (negative value) by 10°F,
so 10°F - 10°F = 0°F. This COULD NOT explain how it
became -10°F.
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F. The temperature was 9°F, then dropped by 19°F.
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Started at +9°F, then dropped (negative value) 19°F, so
9°F – 19°F = -10°F. This COULD explain how it became 10°F.
7. Which of the following expressions is equal to
-32? Select all that apply.
Use1010
and 1101
N/P chart
to organize
0011 0010
0001 0100
1011
A. -20 –(-63) – 11
Opposite of
-63 is + 63
So, -31 + 63 = 32
So, -63 + 31 = -32
Correct answer
P
-20
+63
-11
Incorrect answer
B. -63 + 20 –(-11)
N
Opposite of
-11 is + 11
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N
-63
P
+20
+11
7. Which of the following expressions is equal to
-32? Select all that apply.
Use1010
and 1101
N/P chart
to organize
0011 0010
0001 0100
1011
A. 11 –63 – (-20)
Opposite of
-20 is + 20
N
P
-63
+11
So, -63 + 31 = -32
Correct answer
B. -20 - 63 +11
So, -83 + 11 = -72
Incorrect answer
1
+20
2
4
N
-20
-63
P
+11
7. Which of the following expressions is equal to
-32? Select all that apply.
Use1010
and 1101
N/P chart
to organize
0011 0010
0001 0100
1011
A. 63 –20 – 11
So, -31 + 63 = 32
Incorrect answer
B. 11 + 20 -63
So, -63 + 31 = -32
Correct answer
N
P
-20
-11
+63
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N
-63
P
+11
+20
8. The temperature at noon on a cold winter day in Alaska
was -18°F. By evening, the temperature had dropped by
4°F. Jack thinks that the temperature for the evening could
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found
by0001
subtracting
4 from 18. Sam thinks that -4
should be added to -18 Their methods are shown in the
expressions below.
Jack: -18 – 4
Sam: -18 + (- 4 )
Are these two expressions equivalent? Explain.
These two expressions ARE equivalent because in both
expressions, both integers are negative. In other words,
you start with a negative value, then get more negative.
You can see it as subtracting a positive or adding a
negative.
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