Resources

Resources

Quantities that combine to zero: word problems

In which story is the answer to the question

0

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(A) Kendra took a hot air balloon ride from the bottom of a canyon to the top. The hot air balloon started at an elevation of

-90

feet. When the ride ended, Kendra was at an elevation of

90

feet. How much did Kendra's elevation change from the start of the hot air balloon ride to the top of the canyon?

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(B) Kendra took a hot air balloon ride from the bottom of a canyon to the top. The hot air balloon started at an elevation of

-90

feet. When the ride ended, Kendra was

90

feet higher in elevation than she was when the ride started. At what elevation did the hot air balloon ride end?

In which story is the answer to the question

0

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(A)Kurt hiked through a canyon on a trail that began at an elevation of

-35

feet. When he stopped to rest at noon, his elevation had decreased by

35

feet from the start of his hike. At what elevation was Kurt when he stopped at noon?

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(B)Kurt hiked through a canyon on a trail that began at an elevation of

-35

feet. When he stopped to rest at noon, his change in elevation had increased by

35

feet from the start of his hike. At what elevation was Kurt when he stopped at noon?

In which story is the answer to the question

0

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(A) Darren visited Denmark last year and participated in a polar plunge, a challenge where people jump into icy cold seawater! On the day of the challenge, the temperature in the air was

-10^\circ\text{C}

. Darren jumped into the water, which had a temperature of

10^\circ\text{C}

. How much warmer was the water than the air?

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(B) Darren visited Denmark last year and participated in a polar plunge, a challenge where people jump into icy cold seawater! On the day of the challenge, the temperature in the air was

-10^\circ\text{C}

. Darren jumped into the water, which was

10^\circ\text{C}

warmer than the air. What was the temperature of the water?

In which story is the answer to the question

0

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(A)Caleb and Maureen competed in a trivia game where they earned points for correct answers and lost points for incorrect answers. Caleb ended the game with

-30

points. Maureen ended with

30

more points than Caleb. How many points did Maureen end the game with?

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(B)Caleb and Maureen competed in a trivia game where they earned points for correct answers and lost points for incorrect answers. Caleb ended the game with

-30

points. Maureen ended with

30

fewer points than Caleb. How many points did Maureen end the game with?

In which story is the answer to the question

0

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(A) Zeke was flying a drone at the park. He flew the drone

8

feet above the ground. Then, his sister took the remote control from his hands and the drone fell

8

feet below where Zeke was flying it before. How many feet above the ground was the drone in the end?

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(B) Zeke was flying a drone at the park. He flew the drone

8

feet above the ground. He wanted to test how high it could go, so he flew the drone

8

feet higher than where he was flying it before. How many feet above the ground was the drone in the end?

In which story is the answer to the question

0

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(A)In Montana, where Lexi lives, the lowest temperature recorded is

-70\degree\text{F}

. Yesterday, the temperature was

70\degree\text{F}

. How much higher was yesterday's temperature compared to the lowest temperature recorded?

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(B)In Montana, where Lexi lives, the lowest temperature recorded is

-70\degree\text{F}

. Yesterday, the temperature was

70\degree\text{F}

higher than the lowest temperature recorded. What was yesterday's temperature?

In which story is the answer to the question

0

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(A)Caleb's science teacher awards Classroom Bucks to students who show leadership in class. Last week, Caleb earned

200

Classroom Bucks for leading a debate. Later in the week, Caleb earned

200

Classroom Bucks for organizing a recycling project. How many Classroom Bucks did Caleb end with last week if he started with none?

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(B)Caleb's science teacher awards Classroom Bucks to students who show leadership in class. Last week, Caleb earned

200

Classroom Bucks for leading a debate. Later in the week, Caleb spent

200

Classroom Bucks on a homework pass. How many Classroom Bucks did Caleb end with last week if he started with none?

In which story is the answer to the question

0

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(A) Eva belongs to an outdoor recreation club that is building a new walking trail. The elevation of the trailhead is

-30

feet. Eva is digging out a section of the trail at a location

30

feet higher in elevation than the trailhead. At what elevation is Eva digging?

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(B) Eva belongs to an outdoor recreation club that is building a new walking trail. The elevation of the trailhead is

-30

feet. Eva is digging out a section of the trail at a location with an elevation of

30

feet. How much higher in elevation is Eva digging than the trailhead?

In which story is the answer to the question

0

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(A)Gabe and Ellie played a pick-up basketball game where players earn a point for making a shot and lose a point for missing a shot. Gabe ended with

-8

points. Ellie ended with

8

more points than Gabe. How many points did Ellie end with?

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(B)Gabe and Ellie played a pick-up basketball game where players earn a point for making a shot and lose a point for missing a shot. Gabe ended with

-8

points. Ellie ended with

8

points. How many more points did Ellie have than Gabe?

In which story is the answer to the question

0

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(A)Ethan, a chemist, was experimenting with the melting point of mercury in his lab. The mercury sample started at

-40^\circ\text{F}

. Ethan used a burner to raise the temperature of the mercury to

40^\circ\text{F}

. How much warmer was the mercury at the end of the experiment than it was at the beginning of the experiment?

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(B)Ethan, a chemist, was experimenting with the melting point of mercury in his lab. The mercury sample started at

-40^\circ\text{F}

. Ethan used a burner to raise the temperature of the mercury by

40^\circ\text{F}

. What was the temperature of the mercury at the end of the experiment?

In which story is the answer to the question

0

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(A)At Bear Country Ski Resort, the West Hammer chairlift starts at an elevation

130

meters below the main lodge. Arianna rides the chairlift, which increases her elevation by

130

meters, and then gets off. How many meters above the lodge is Arianna when she gets off?

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(B)At Bear Country Ski Resort, the West Hammer chairlift starts at an elevation

130

meters below the main lodge. Arianna rides the chairlift up to an elevation

130

meters above the lodge. What is the change in elevation from where the chairlift started to where Arianna got off?

In which story is the answer to the question

0

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(A)Hanson learned a new dice game this week, where you earn or lose points based on the number you roll. At the end of the game, Hanson had

-12

points. Hanson's friend Brenda ended with

12

more points than Hanson ended with. How many points did Brenda have at the end of the game?

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(B)Hanson learned a new dice game this week, where you earn or lose points based on the number you roll. At the end of the game, Hanson had

-12

points. Hanson's friend Brenda ended with

12

fewer points than Hanson ended with. How many points did Brenda have at the end of the game?

In which story is the answer to the question

0

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(A)Some marine life researchers are in a submarine that is resting at an elevation of

-115

feet. They detect movement above and ascend

115

feet in elevation to capture rare video footage of a western gray whale. At what elevation is the submarine now?

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(B)Some marine life researchers are in a submarine that is resting at an elevation of

-115

feet. They detect movement below and descend

115

feet in elevation to capture rare video footage of a western gray whale. At what elevation is the submarine now?

In which story is the answer to the question

0

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(A) Destiny went on an RV trip in South America. In the first week, she visited Laguna del Carbón, a lake with an elevation of

-344

feet. During the second week, she went camping near the Andes Mountains at an elevation that was

344

feet higher than Laguna del Carbón. At what elevation was Destiny camping?

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(B) Destiny went on an RV trip in South America. In the first week, she visited Laguna del Carbón, a lake with an elevation of

-344

feet. During the second week, she went camping near the Andes Mountains at an elevation of

344

feet. How much higher was the elevation where Destiny went camping than the elevation of Laguna del Carbón?

In which story is the answer to the question

0

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(A) A scuba diver was exploring a shipwreck in the Caribbean Sea. He swam from his boat down to an elevation of

-110

feet to photograph the shipwreck. After he was finished, he swam back up to his boat

110

feet above. What elevation did the scuba diver end at?

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(B) A scuba diver was exploring a shipwreck in the Caribbean Sea. He swam from his boat down to an elevation of

-110

feet to photograph the shipwreck. After he was finished, he swam back up to his boat

110

feet above. How far below his boat did the scuba diver swim to the shipwreck?

In which story is the answer to the question

0

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(A)Last Sunday, Bonnie deposited a check for

\$40

that she earned from babysitting. Later in the week, she deposited another

\$40

from watching her neighbor's dog. How much did her account balance change?

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(B)Last Sunday, Bonnie deposited a check for

\$40

that she earned from babysitting. Later in the week, she withdrew

\$40

to go to the mall with her friends. How much did her account balance change?

In which story is the answer to the question

0

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(A)Rita lives in Chicago, Illinois, and her pen pal lives in Cheyenne, Wyoming. One January, the lowest temperature recorded in Chicago was

-11^\circ\text{F}

. In Cheyenne, the lowest temperature that month was

11^\circ\text{F}

warmer than Chicago's lowest temperature. What was the lowest temperature recorded in Cheyenne that January?

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(B)Rita lives in Chicago, Illinois, and her pen pal lives in Cheyenne, Wyoming. One January, the lowest temperature recorded in Chicago was

-11^\circ\text{F}

. In Cheyenne, the lowest temperature that month was

11^\circ\text{F}

. How much warmer was the lowest temperature in Cheyenne than the lowest temperature in Chicago that January?

In which story is the answer to the question

0

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(A)When Liz climbed Mount Rainier, the windchill temperature was

-4^\circ\text{C}

. The actual temperature outside was

4^\circ\text{C}

warmer than the windchill temperature. What was the actual temperature outside?

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(B)When Liz climbed Mount Rainier, the windchill temperature was

-4^\circ\text{C}

. The actual temperature outside was

4^\circ\text{C}

. How much warmer was the actual temperature outside than the windchill temperature?

In which story is the answer to the question

0

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(A)Washington Tunnel was built at an elevation of

-6

meters. Lincoln Tunnel was built at an elevation of

6

meters. How much higher is the elevation of Lincoln Tunnel than the elevation of Washington Tunnel?

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(B)Washington Tunnel was built at an elevation of

-6

meters. Lincoln Tunnel was built at an elevation

6

meters above Washington's Tunnel. At what elevation was Lincoln Tunnel built?

In which story is the answer to the question

0

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(A)Last weekend, Reagan filled her pool with water for the summer. On Saturday, it was really hot, and

2

centimeters of water evaporated from the pool. On Sunday, the pool lost

2

more centimeters of water during a water polo game. What is the difference between the pool's water level now and the water level when Reagan first filled it?

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(B)Last weekend, Reagan filled her pool with water for the summer. On Saturday, it was really hot, and

2

centimeters of water evaporated from the pool. On Sunday, the water level rose

2

centimeters after a rainstorm. What is the difference between the pool's water level now and the water level when Reagan first filled it?

9

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A weather station recorded the amount of rain that fell during an

8

-hour time frame using a rain gauge. The findings are recorded in the graph below.

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Amount of Rain in Rain Gauge

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Between which hours was the rate at which the rain fell greater than the rate at which the rain fell between hours

0

1

Santos wants to know what percentage of people who get married in his county knew each other in school.

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Which of the following survey methods will allow Santos to make a valid conclusion about the percentage of couples married in his county who knew each other in school?

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1

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(A) Get a list of the

30

couples most recently married in his county, then ask them.

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(B) Sort a list of couples married in his county into a random order, then ask the first

30

couples on the list.

Ron intends to survey spectators at the Quidditch World Championship to find out which team has the most spectators' support.

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Which of the following survey methods will allow Ron to make a valid conclusion about which team has the most spectators' support?

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1

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(A) Put the names of all of the spectators who speak the same language as Ron does into a cauldron, mix them up, draw out

75

names, and survey those spectators.

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(B) Put the names of all of the spectators into a cauldron, mix them up, draw out

75

names, and survey those spectators.

Which of the following is a correct interpretation of the expression

-6+9 ?

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1

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(A) The number that is

9

-6

on the number line

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(B) The number that is

9

to the right of

-6

on the number line

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(C) The number that is

6

-9

on the number line

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(D) The number that is

6

to the right of

-9

on the number line

Which of the following is a correct interpretation of the expression

-3-5

\newline

1

\newline

5

on the number line and move

3

\newline

5

on the number line and move

3

\newline

-3

on the number line and move

5

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-3

on the number line and move

5

Which of the following are true statements about the expression

-8+8 ?

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2

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(A) The expression describes the number that is

8

-8

on the number line.

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(B) The expression describes the number that is

8

to the right of

-8

on the number line.

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(C) The expression equals

-16

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(D) The expression equals

0

Which of the following is a correct interpretation of the expression

-2-7

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1

\newline

-2

on the number line and move

7

\newline

-2

on the number line and move

7

\newline

7

on the number line and move

2

\newline

7

on the number line and move

2

Which of the following are true statements about the expression

-9+9

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2

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(A) The expression describes the number that is

9

-9

on the number line.

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(B) The expression describes the number that is

9

to the right of

-9

on the number line.

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(C) The expression equals

-18

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(D) The expression equals

0

Which of the following is a correct interpretation of the expression

6-13

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1

\newline

13

on the number line and move

6

\newline

13

on the number line and move

6

\newline

6

on the number line and move

13

\newline

6

on the number line and move

13

Which of the following are true statements about the expression

-7+7

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2

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(A) The expression describes the number that is

7

-7

on the number line.

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(B) The expression describes the number that is

7

to the right of

-7

on the number line.

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(C) The expression equals

-14

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(D) The expression equals

0

Which of the following is a correct interpretation of the expression

3+(-7) ?

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1

\newline

7

on the number line and move

3

\newline

7

on the number line and move

3

\newline

3

on the number line and move

7

\newline

3

on the number line and move

7

Which of the following is a correct interpretation of the expression

5-8

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1

\newline

5

on the number line and move

8

\newline

5

on the number line and move

8

\newline

8

on the number line and move

5

\newline

8

on the number line and move

5

Which of the following is a correct interpretation of the expression

-4+13

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1

\newline

(A) The number that is

4

-13

on the number line

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(B) The number that is

4

to the right of

-13

on the number line

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(C) The number that is

13

-4

on the number line

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(D) The number that is

13

to the right of

-4

on the number line

Which of the following is a correct interpretation of the expression

-7-(-11) ?

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1

\newline

-7

on the number line and move

11

\newline

-7

on the number line and move

11

\newline

-11

on the number line and move

7

\newline

-11

on the number line and move

7

Which of the following is a correct interpretation of the expression

-3+(-5) ?

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1

\newline

(A) The number that is

5

-3

on the number line

\newline

(B) The number that is

5

to the right of

-3

on the number line

\newline

(C) The number that is

3

5

on the number line

\newline

(D) The number that is

3

to the right of

5

on the number line

Lara is a wildlife researcher. They were analyzing the mean and median lengths of

7

fish their team had observed. The fish all had different lengths between

15 \mathrm{~cm}

33 \mathrm{~cm}

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Lara found out that they were misreading the longest length. It was actually

88 \mathrm{~cm}

33 \mathrm{~cm}

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How will this length increasing affect the mean and median?

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1

\newline

(A) Both the mean and median will increase.

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(B) The mean will increase, and the median will stay the same.

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(C) The mean will increase, and the median will decrease.

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(D) The mean will stay the same, and the median will increase.

Gabe is mapping out important family events. He uses negative numbers to represent time before he was born and positive numbers to represent time after he was born. For example, Gabe's mom was given a special coin in year

-20

, and Gabe's sister was born in year

7

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0

\newline

1

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(A) The year Gabe's mom was given a special coin

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(B) The year Gabe was born

\newline

(C) The year Gabe's sister was born

Geographers use negative numbers to represent points below sea level and positive numbers to represent points above sea level. For example, the lowest point in New Orleans is at

-2

meters, and the highest point is at

6

\newline

0

meters represent?

\newline

1

\newline

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(B) The highest point in New Orleans

\newline

(C) The lowest point in New Orleans

In a board game, negative number cards represent moving backward and positive number cards represent moving forward. For example, Nuha drew a card with

4

and moved forward

4

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Raha draws a card with

0

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0

represent in the board game?

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1

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(A) Going back to the starting space

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(B) Not moving any spaces

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(C) Losing all points

Four players are playing a game together. They each gain or lose points based on their actions.

\newline

50

points for finding a green mushroom.

\newline

100

points for completing a level.

\newline

100

points for getting hit by a fireball.

\newline

75

points for stepping on a spike.

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Which two friends had the same amount of change to their scores?

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1

\newline

(A) Amani and Ajeet

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(B) Damian and Julius

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(C) Amani and Julius

\newline

(D) Ajeet and Damian

Water freezes at

0^{\circ}

Celsius. Four friends test the temperature of their water.

\newline

Miko's water is

3^{\circ}

\newline

-8^{\circ}

\newline

Rocky's water is

4^{\circ}

\newline

Leon's water is

-1^{\circ}

\newline

Which friend's water has a temperature closest to the freezing point?

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1

\newline

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Four players are playing a game together. They each gain or lose points based on their actions.

\newline

5

points for letting a fish get away.

\newline

10

points for collecting a mushroom.

\newline

100

points for disturbing a bear.

\newline

80

points for building a fire.

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Whose action has the greatest effect on their scores?

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1

\newline

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At the beginning of the week, Josh had

32

computer games,

133 \%

as many computer games as Peter had. By the end of the week, Josh gave

25 \%

of his computer games to Peter. How many computer games did Josh and Peter each have by the end of the week?

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1

\newline

8

games; Peter had

24

\newline

24

games; Peter had

8

\newline

24

games; Peter had

32

\newline

32

games; Peter had

24

28 x^{2}

(14 x)\left(2 x^{2}\right)

\newline

Yasmin factored

28 x^{2}

(7 x)(4 x)

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Which of them factored

28 x^{2}

\newline

1

\newline

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(B) Only Yasmin

\newline

(C) Both Jude and Yasmin

\newline

(D) Neither Jude nor Yasmin

Sophia factored

81 y^{6}

\newline

\left(9 y^{3}\right)\left(9 y^{2}\right) \text {. }

\newline

81 y^{6}

\left(3 y^{6}\right)(27 y)

\newline

Which of them factored

81 y^{6}

\newline

1

\newline

(A) Only Sophia

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(C) Both Sophia and Ahmed

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(D) Neither Sophia nor Ahmed

Emily thinks the perfect tomato sauce has

15

cloves of garlic in every

6 \mathrm{~L}

of sauce. Raphael's tomato sauce has

25

cloves of garlic in every

9 \mathrm{~L}

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What will Emily think of the amount of garlic in Raphael's tomato sauce?

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1

\newline

(A) Raphael's tomato sauce has too much garlic.

\newline

(B) Raphael's tomato sauce has too little garlic.

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(C) Raphael's tomato sauce is perfect.

Kermit's favorite iced tea uses

15

tea bags in every

2

liters of water. Peggy made a

12

-liter batch of iced tea with

90

tea bags. Peggy and Kermit keep the bags in the water the same amount of time.

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What will Kermit think of Peggy's iced tea?

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1

\newline

(A) Peggy's iced tea is too strong.

\newline

(B) Peggy's iced tea is too weak.

\newline

(C) Peggy's iced tea is just right.

Lashawn makes scrambled eggs with

3

spoonfuls of salsa for every

2

eggs. Gilberta adds

7

spoonfuls of salsa for every

5

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Whose scrambled eggs have a stronger salsa taste?

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1

\newline

(A) Lashawn's eggs

\newline

(B) Gilberta's eggs

\newline

(C) The dishes of scrambled eggs have equal salsa tastes.

Nayeli lights a

4 \mathrm{~m}^{2}

12

candles. Citlali lights a

10 \mathrm{~m}^{2}

30

of the same type of candles.

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Whose space is lit brighter?

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1

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(A) Nayeli's area

\newline

(B) Citlali's area

\newline

(C) The spaces are equally bright.

Ari thinks the perfect milkshake has

5

scoops of ice cream for every

3

spoonfuls of caramel. Freeze Zone makes batches of milkshakes with

10

scoops of ice cream and

7

spoonfuls of caramel.

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What will Ari think about the amount of caramel in Freeze Zone's milkshakes?

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1

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(A) Freeze Zone's milkshakes have too much caramel.

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(B) Freeze Zone's milkshakes have too little caramel.

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(C) Freeze Zone's milkshakes are just right.