This graph shows a proportional relationship between the number of tulips and the number of daffodils in gardens planned by the Lindy Landscaping Company.

What is the constant of proportionality?

Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you find the best answer to the question.

Which cylinder pressure will Jillian need if she plans to fill 90 balloons?

Nancy created a graph to predict the pay she will take home after taxes are taken from her income. Using the information on the graph, what is the constant of proportionality?

The rate at which an airplane flew was $$\frac{700\ miles}{2\ hours}$$  . How can the unit rate be determined?

Ming used the calculations shown to find out how much he would spend on 6 pounds of ground beef if 10 pounds of ground beef cost $25.00.

What was Ming’s error?

According to the information in the table, who is the fastest typist?

In which of these cases is each stamp worth the most?

Which is equivalent to “12 chairs for every 3 tables”?

Holly earns $30 for babysitting 5 hours. She earns $28 when she does chores for 4 hours. Which compares the unit rates?

Each serving of a cereal is 80 calories. Which expression can be used to find the number of calories in 3 servings?

Byron earns $11.00 per hour. How many hours will Byron have to work to earn $143.00?

Josiah’s parents pay him for each chore he completes. He created a table to show his earnings each week for the past month.

Which graph correctly depicts his earnings including the last week?

Aimee noticed her plant grew of $$\frac{2}{3}$$  an inch every week since it sprouted. She created this graph to show its growth.

Which statement about Aimee’s graph is true?

Breanna set up her media player and created a graph to show what she saved on it. What does point A represent on the graph?

Enjoli is making cupcakes for a party. She needs 45 cupcakes but the recipe makes 15.

If she does not want any leftovers, which point should Enjoli use to determine the amount of strawberries she will need to make her cupcakes?

Geraldo gets paid the same amount for each hour he works. The graph shows the amount he is paid, y, as it relates to the number of hours he works, x. Yesterday, when he worked 6 hours, he was paid $84.

Which ordered pair could represent the number of hours and amount Geraldo is paid today at the same hourly wage?

Mrs. Santos is buying binders for the students in her class. She determined that 15 binders would cost $22.50.

If all of the binders cost the same amount, which statement is true?

What is the constant of proportionality in the equation $$y=\frac{x}{9}$$  ?

Consider the two graphs below.

Which statement best describes the graphs?

The table below shows the total cost of buying printer ink cartridges for both members and nonmembers of a shopping club.

Which statement is supported by the table?

Which equation represents the same proportional relationship as the graph?

Merrida wrote the table of points below.

Which explains whether or not Merrida has described a proportional relationship, and why?

If the relationship is proportional, what is the missing value from the table?

Rosa earns $12 per hour. In 7.5 hours, she will earn x dollars.  Which is a valid proportion that can be used to solve the problem?

What is the value of x in the proportion below?

$$\frac{180\ kilometers}{3\ hours}=\frac{540\ kilometers}{x}$$  

What is the value of x in the proportion below?

$$\frac{\frac{2}{3}}{5}=\frac{x}{15}$$  

Brian can type $$1\ \frac{1}{3}$$  pages every 20 minutes. How many pages can he type in 2.5 hours?

Which is equivalent to 3.25%?

Which diagram shows a percent equivalent to $$\frac{3}{5}$$  ?

Maxwell used the diagram below to help determine 75% of 24. Which expression could Maxwell have used to find 75% of 24?

Twenty percent of the 640 pitches Kendall threw last year were strikes. Which table can be used to find the number of strikes she threw?

Gregory sees an $80.00 jacket on sale at 30% off. How much will it cost after a 7% sales tax is applied?

Antoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00. Tess says, “It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $$\text{4.60 + 4.60 = 9.20}$$  for the 15% gratuity.”How should Antoine respond to Tess’s method?

Paul needs to find 310% of 72. Which expression should he use?

Mrs. Garcia’s students were asked to find 220% of 75. Each of the students had a different method.

Amy: “I multiplied 2.20 by 75 to find my answer.

”Braden: “I created a table with columns for 100%, 100%, 20%, and 220%. Then I filled in the table and added the values.”

Colton: “I created a table with columns for 100%, 10%, 10%, and 220%. Then I filled in the table and added the values.”

Danielle: “I divided 75 by 5 to find 20%. Then I added 75 twice to what I found to get my final answer.”If all of the students completed their steps accurately, which student got the answer wrong?

A roller coaster at an amusement park rises to a height of 196 feet above the ground. So far, it has risen 36% of this height. To estimate the height the roller coaster has risen so far, Jake did the following.

1. Rounded 36% to 40%

2. Rounded 196 to 200

3. 10% of 200 is 20

4. $$20\left(4\right)=80$$  

5. 36% of 196 is about 80

However, Jake’s estimate was too high by almost 10 feet. Why was his estimate off by so much?

A distance runner is running an 18-mile race. So far, she has run 43% of the race.

Which would be the best way to estimate the number of miles the runner has run so far?

Gloria’s hotel bill came to $296 plus an 11% tax, which means that she will pay 111% of her bill.

Which is the best estimate of the total amount Gloria will pay?

To estimate 103% of 63, Rich rounded 103% down to 100%, 63 down to 60, and multiplied 60 by 1 to get 60. Which of these statements is correct?

Jack works at a sporting goods store and makes a commission of 20 percent. His sales for each week are shown below. How much did Jack make in total in commission during all four weeks?

Which of the purchases would be the least expensive?

A $120 wagon is on sale for 15 percent off. What is the sale price of the wagon?  

Zenaida is shopping and wants to purchase a $320 stereo system. The store is offering an incentive of 10 to 30 percent off when you spin the discount wheel. Zenaida spins the wheel and receives 20 percent off. How much will the stereo system cost?

A store is marking down the price of a television 25 percent from the original price of $250. Which expression can be used to find the marked down price? 

The snack bar at the school purchases water bottles at wholesale and then marks them up to make a profit. It marks up the water bottles by $$33\ \frac{1}{3}$$  percent, an amount of $0.28.

What was the wholesale price of each water bottle?

Sales tax in Birmingham, AL, is the highest in the nation at 10 percent. Pete paid $9.44 in sales tax for an item in Birmingham, AL.

What was the price of the item before tax was included?

A store purchases an item wholesale for $60 and marks it up by 70 percent. If there is a 7 percent tax on the item, how much will the item cost?

A frozen dinner at a grocery store is purchased for $2.20 wholesale and is marked up by 40 percent. A customer wants to buy four frozen dinners. How much will the customer pay, including paying 9 percent sales tax? Round your answer to the nearest cent.

A frame is marked down by 22 percent from an original price of $14.50. What is the new price?

Raj was friends with his waitress so he left her a 90 percent tip.

If his tip was $27.54, what is the value of x in the table above?

Luca is planning to pay the restaurant bill for his coworkers. The bill was $193.75. A 4% tax was then added by the waiter. If Luca wants to leave a 16% tip on the total amount including the tax, how much should Luca pay?

Which term is a word for an initial amount of money that is borrowed or invested?

Renee used the values in the table to calculate simple interest.

Which interest rate is missing from Renee’s table?

The office manager of First Tech Support borrowed $25,000 to purchase new computers for employees. The bank charges 6 percent interest for 4 years. How much interest will the company pay in all?

After 3 years, a $1,500 investment is worth $1,680. What is the interest rate on the investment?

Antonio predicted that he would sell 60 rugs, but he actually sold 82 rugs. Which expression would find the percent error? Use the table below to help answer the question.

Pedro predicted that he would sell 128 novels. He actually sold 150 novels. What are the values of a and b in the table below?

Bescha predicted that she would sell 500 handmade vases at a flower show. When the show was over, she had 50 vases left. What was the percent error in the estimate? Round the answer to the nearest tenth.

Last year, Theodora estimated that she would sell 96 bracelets. But at the end of the year, she had 16 bracelets left over. Which explains how Theodora can find the percent error of her estimate?

Jerry is comparing –8 and –10 on a number line. Which is true regarding their locations on the number line?

Paloma plotted two different integers with the same absolute value on a number line. The distance between the two numbers must be

Denver is about 5,200 feet above sea level. Which number line best represents this integer?

Carly withdraws $18 from her bank account. Which number line represents this amount?

Renee is simplifying the expression $$\left(7\right)\left(\frac{13}{29}\right)\left(\frac{1}{7}\right)$$  . She recognizes that 7 and $$\frac{1}{7}$$  are reciprocals, so she would like to find their product before she multiplies by $$\frac{13}{29}$$  .  Which property will allow Renee to do this without changing the value of the expression?

Dylan is evaluating the expression $$13+19+7+10$$  . At one step in his work, Dylan rewrites the equation as $$13+7+19+10$$  . Which property of addition must Dylan have used when he evaluated the expression?

Which statement illustrates the distributive property?

Julia is evaluating the expression $$17\left(144\right)$$  . If she uses the distributive property to rewrite the expression with friendlier numbers, which expression can be a step in her work?

Which tiles should be added to the model below to make zero?

Kyle wants to buy a new laptop that has an original price of $540. The store is having a sale, so the laptop is 10 percent off, which amounts to a discount of $54. If sales tax is 8 percent on the final price of the laptop, how much tax will he need to pay?

Jillian is using integer tiles to add $$7+\left(-2\right)$$  . She uses the steps below.

Jillian has made an error. In which step does it occur?

The position of a swimmer below sea level is represented by –5 meters. The diver descends an additional 3 meters below sea level. Which expression describes the new position of the diver?

Helene, a hiker, starts at an elevation of 27 feet above sea level and descends 32 feet during her hike to base camp. Which describes the elevation of base camp?

A-1 Deli sells jugs of iced tea that they have marked up 150% above their wholesale cost of $0.80 per jug. They also charge sales tax of 9%. What is the total cost of a jug of iced tea from A-1 Deli?

The student store sells pencils that have a markup of 120 percent above their wholesale cost of $0.50 each. They also charge sales tax of 8 percent. What is the total cost of a pencil from the student store?

Dimitri is paid 8 percent commission on his total sales every pay period. Last pay period, he sold $6,300 worth of items. After a state tax of 6 percent is deducted from his commission, how much is left to the nearest dollar?

What is the solution to  $$-1-7$$  ?

Antwan determines the distance between the points –7 and 2 on a numberline. Maggie determines the difference between the numbers –7 and 2. How are Antwan’s and Maggie’s solutions related?

Kale is hiking 2,345 feet above sea level. The peak of the mountain he is climbing is 3,283 feet above sea level. What is the vertical distance between Kale and the mountain peak?

Vicky records the low temperature for three consecutive days. Between the first and second days the temperature increased 6 degrees. Between the second and third days the temperature decreased 3 degrees. On the third day the low temperature was –6º. What was the low temperature on the first day?

How is the product of 2 and –5 shown using integer tiles?

Which point on the number line represents the product $$\left(5\right)\left(-2\right)\left(-1\right)$$  ?

At 4 p.m., the temperature started to change drastically. Each hour, for three hours, the temperature decreased by 7°F. Which word in the problem indicates that a negative integer should be used?

Katrina's mother is 2 inches shorter than her father, Katrina is 2 inches shorter than her mother, and Katrina's brother is 2 inches shorter than Katrina. Which best represents the change in height from Katrina's father to her brother?

What is the quotient?

$$36\div6$$  

Using the order of operations, what should be done first to evaluate $$\left(-4\right)^2+6\div\left(-3+4\right)\left(2\right)-5$$  ?

Using the order of operations, what should be done first to evaluate $$6+\frac{\left(-5-7\right)}{2}-8\left(3\right)$$  ?

Fernando evaluated the expression below.

What was Fernando’s error?

A dolphin went 15 feet below sea level to catch a fish. A shark went twice as deep, then swam down an additional 10 feet to catch a larger fish. Which expression represents the shark’s position in relation to sea level?

Jasmine and Carlotta are sisters, and each have their own savings. Together, they borrowed $28 from their brother to go to the movies. Each girl has to pay back an equal amount. Carlotta also owes her brother $6. Which expression represents the change in Carlotta’s savings after she repays her brother?

The temperature in Coast City is 3 degrees below zero on the Fahrenheit scale (). The temperature in Dodge City is colder than a temperature that is twice as cold as Coast City’s temperature. What is the temperature in Dodge City?

A bank teller notices that an account was overdrawn and had a balance that can be represented by $-324 . The account holder then deposited 3 checks for $150 each and made 4 withdrawals of $20 each. The teller used the steps below to find the new balance for the account.

In which step did the teller make the first error?

Charla is finding points on a number line.

Which point could represent $$\frac{2}{3}$$  ?

Which expression is equivalent to –21.8 – (–18.3)?

What is the sum of 16.87 + (–98.35)?

Which point on the number line most closley represents $$1.66666$$  ?

Which pair of rational numbers are equivalent?

Martin measured the lengths of five shoes in his closet. Their lengths were 10.252 inches, 9.894 inches, 10.455 inches, 9.527 inches, and 10.172 inches. Which two estimation techniques will give the same result for the total number of inches for all five shoes?

Before sunrise, the temperature was 22.4°F below zero. By noon, it had risen 12.8°F. What expression can be used to find the temperature at noon?

Amira needs $$24\ \frac{3}{10}$$   feet of fencing material to make a fence for her small garden. Which number represents the additive inverse of this number?

What is the quotient?

$$-3.22\ \div-5$$  

The quotient of 7.3 divided by –7.3 is

Mika taught her sister the steps for dividing a decimal by a decimal. Which instructions are correct?

What is the quotient?

$$-\frac{3}{8}\div-\frac{1}{4}$$  

Kari estimated the quotient of $$-12\ \frac{1}{5}\div4\ \frac{2}{5}$$   to be –8. Which best describes her error?

Water flowed out of a tank at a steady rate. A total of $$18\ \frac{1}{2}$$   gallons flowed out of the tank in $$4\ \frac{1}{4}$$  hours. Which expression determines the quantity of water leaving the tank per hour?

Two swim clubs are having a membership sale. Aqua Plus is offering a two-year membership for $479.76. Water World is offering an 18-month membership for $350.00. Which describes the swim club that has the lower-priced offer?

Ramon needs to simplify the expression below.

$$\frac{3.5\cdot2\div0.4}{8.1+1.5-4}$$  

Which operation should he perform first?

The temperature fell from 0 to $$6\ \frac{3}{5}$$   below 0 in $$2\ \frac{1}{5}$$  hours. What was the temperature change per hour?

What is the value of the expression below?

$$1.2+0.8\div4-3\left(0.7-0.5\right)$$  

What is the simplified value of the expression below?

$$\frac{4\left(-8+4.5\right)}{6.25+\left(-8.25\right)}$$  

On a cold January morning, the radiator fluid in Kuri’s car is ° F. With the engine running, the temperature rises by 2.5°F per minute. How long before the radiator temperature reaches 40°F?

What is the difference of the fractions? Use the number line to help find the answer.

$$\frac{4}{7}-\frac{10}{7}$$  

What is the difference of the fractions? Use the number line to help find the answer.

$$\frac{1}{2}-1\ \frac{1}{5}$$  

Johnny rode his bike of $$\frac{4}{7}$$   a mile from his house to the lake on a straight path. Then, he turned around and rode his bike $$3\ \frac{1}{8}$$  miles in the opposite direction. About how far is Johnny from his house?

Bruno uses a piece of wrapping paper with dimensions $$1\ \frac{1}{4}$$  feet by 3 feet to wrap a gift. What is the total area of the paper used to wrap the gift?

Noa was walking in the forest and measured the circumference of two trees that he found. The first tree measured $$37\ \frac{5}{8}$$  inches around, and the second tree measured $$45\ \frac{1}{3}$$  inches around. Noa wanted to find the difference of the circumferences of the two trees. He recorded his steps in the table.

In which step did Noa first make an error?

What is the product of $$-\frac{2}{7}$$  and $$-\frac{3}{7}$$  ?

What is the product of $$\frac{3}{4}$$  and $$-\frac{6}{7}$$  ?

Which expression represents the same solution as $$\left(4\right)\left(-3\ \frac{1}{8}\right)$$  ?

Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. Which value represents the probability that he will win the election?

Viktoria knows that it is impossible to remove a red marble from her bag that has no red marbles in it. If she reaches into the bag and pulls out a marble without looking, what is the probability that the marble will be red?

Which value cannot represent the probability of an event occurring?

The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. A juice box is selected at random. What is the probability of the complement of choosing an orange juice box?

The spinner is divided into 8 equal sections.

What is the probability of spinning blue or green?

Which event has a probability other than $$\frac{1}{2}$$  ?

Daniel’s spinner is divided into 8 equal sections.

He plans to spin it 80 times. Which equation predicts the number of times that he could spin green?

Catherine has a 6-sided number cube that is numbered from 1 through 6. She plans on rolling the number cube 60 times. About how many times should she expect to roll a number that is greater than 4?  

Herky found that 8 out of every 100 beans in his garden were nibbled by rabbits. How many beans can he expect to be damaged if there are 450 beans in his garden?

Which statements about experimental probability are true?

Kiesha’s quality-control manager told her she must have 97% of her clocks functioning properly. She found a report that said 6 out of 300 clocks tested were not working properly. Kiesha predicts that she will have enough working clocks to please the manager. Which statements are true about Kiesha’s prediction?

A number cube was rolled as part of an experiment. The results are in the table below. The fraction $$\frac{1}{x}$$   is the experimental probability of rolling a 3. What is x?

A standard deck of 52 cards contains four suits: clubs, spades, hearts, and diamonds. Each deck contains an equal number of cards in each suit. Rochelle chooses a card from the deck, records the suit, and replaces the card. Her results are shown in the table.

How does the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart?

Walter is conducting an experiment using a spinner with 4 equal sections. Which number of trials will lead to experimental outcomes that are most similar to his predicted outcomes?

Josiah conducts an experiment that has 4 possible outcomes. Sally conducts an experiment that has 10 possible outcomes. The students conduct 50 trials each. Which statement best compares the two experiments?

A cube is numbered 1 through 6. If the cube is rolled twice, how many of the possible outcomes will have two even numbers?

Byron bought a keyless entry door lock that has the digits 0 through 9 on the keypad. He wants to choose a three-digit entry code. How many different combinations are possible, if the digits can be repeated?

A jar contains only one blue tile, one green tile, one red tile, and one yellow tile. If a tile is chosen at random and then replaced in the jar, and then a second tile is chosen at random, how many of the possible outcomes contain at least one red tile?

A set of cards contains the numbers 1 through 20. Mathieu chooses a card at random, records the number of the card, and then returns the card to the set. He conducts 200 trials of this event. Based on the theoretical probability, how many times can Mathieu expect to choose a multiple of 5?

Keisha has a bag that contains one red marble (r), one yellow marble (y), one green marble (g), and one orange marble (o). She makes the table below to show the different ways that she can choose two marbles—by first choosing one marble, replacing it, and then choosing another marble.

What outcome is missing from Keisha’s table?

The table below shows the possible outcomes of rolling a six-sided number cube and flipping a coin.

What is the probability of getting a number less than 3 and a tails?

Which describes dependent events?

Maggie’s bank has assigned her a temporary 3-digit PIN to use with her ATM card. Each digit is a number from 1 to 5, inclusive, and no digit can be used more than once in the PIN. Which multiplication problem can be used to determine the probability that the PIN she was assigned was 123?

To win the game, Eitan has to roll a sum of 11 or more using two six-sided number cubes.

Asher has a better probability of winning than Eitan has. Which could be the outcome that Asher needs to win the game?

The student government wants to determine the theme for the eighth-grade dance. Which group would it be best to take a sample from?

An employer asks the survey question “How much money do you spend on gasoline per week to get to work?” of her employees that drive to work. Which best describes why she chose to only ask the employees that drive to work rather than all of her employees?

Kristin wants to ask the managers of the fast food restaurants in a large city “How do you retain employees?” What condition must be true to justify surveying only a sample of the managers instead of surveying the entire population of managers?

When is choosing a sample from a population least likely to be appropriate?

At Lawson Middle School, Mr. Hernandez asked 90 randomly selected students from each grade level for their favorite subject, and 28 chose social studies as their favorite. He used this data to draw the inference that out of the 250 middle school students, about 20% prefer social studies. Did he make a reasonable inference?

Out of a population of 700 students, 120 were asked by a random sampling to choose the green vegetable they would like to have served in the cafeteria. Their responses are shown in the table below.

Using proportional reasoning, about how many students out of the 700 would you expect to request broccoli to be served?

Geraldo wants to start a group bike ride on Sunday mornings for students at his school. He asked 30 students in the lunchroom how many miles they ride their bikes each month. He obtained the following results.

8, 3, 0, 1, 2, 3, 6, 3, 0, 4, 13, 1, 3, 12, 15, 2, 1, 3, 2, 2, 0, 3, 4, 2, 6, 7, 12, 8, 4, 0

The fraction $$\frac{x}{30}$$  shows the ratio of the number of students who ride their bikes more than 10 miles each month to the number of students surveyed. What is the value of x?

The student government at the local middle school surveyed students to help plan the end-of-year party. For the first sample, they surveyed every other person at sports practice after school. For the second sample, they surveyed every fifth person entering the cafeteria where all students eat. Which statement about the samples is true?

Lawrence performs a survey to determine the average number of minutes of exercise seventh-grade athletes get in one week. He gets a list of sports and the seventh-grade students participating in each sport. He then chooses 10 people from each list to complete the survey. How can Lawrence’s sample be improved to be more representative of the population?

Administrators surveyed students enrolled in a new school to choose the school mascot. The results are shown in the table below. What is the average number of students that chose grizzlies for both samples?

Out of a population of 1,000 students, 80 were asked by a random sampling what color they would prefer for their first car. Their responses are shown in the table below.

Using proportional reasoning, how many students out of the 1,000 would you expect to prefer a silver car?

A town’s athletic league contains 18 baseball teams. The board members of the league want to survey adults attending games to determine if they believe the athletes are showing good sportsmanship. The board members attended one game and surveyed an equal number of adults supporting each of the two teams. Which best explains the validity of the results?

The wildflower commonly known as Ute Ladies’ Tresses is threatened. Some sample counts were taken of local populations of the flower as part of monitoring and protecting its population. These counts are displayed in the table below. What is the average number of plants at site 2 for both samples?

Louden County Wildlife Conservancy counts butterflies each year. Data over the last three years regarding four types of butterflies are shown below. What is the average number of Variegated Fritillaries for all three samples?

Vickie conducts a survey of home builders to determine the average cost of building a new home. She samples 10 home builders who are building in the town in which she lives. Under which conditions will her sample be a representative sample?

Kai, a seventh grader, wants to determine the average number of times the families in his neighborhood visit the pool during the summer. He samples the families of four of his classmates. Which improvements could Kai make to his sample to increase the validity of the results?

If Benito is selecting samples of five values from the table, which row will result in the greatest mean?