Grade 7 Practice Problems: Numbers
Examples from Standards Revision and GLEs
7N-40) Answer: 2,304 total; 464 ketchup; 288 soda; 528 medicine; 656 salad dressing; 240 vinegar; 128 milk
Ronelle's seventh-grade class went on a field trip to a bottle factory. The class enjoyed moving from room to room, watching the machines put out the glistening, brand-new bottles. The guide explained that out of every 144 bottles coming off the lines in the factory, 29 would be used by ketchup manufacturers, 18 would be used by soda factories, 33 would become medicine bottles, 41 would become salad dressing bottles, 15 would be used for vinegar, and only 8 would be used for milk, since most milk comes in cartons. On one shift, 2304 bottles came off the lines. How many bottles belonged to each category? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-39) Answer: 1872 pigs; 63,648 bunches of onions; 9,623,016 eggs
The Duke of Yolk is "eggstatic." His kingdom, which produces only pigs, eggs, and green onions, has been invited to display its products at the World Food Fair. The Duke asked his cook, Julia, to prepare ham and onion omelet’s for the visitors at the fair. She thought the idea was a bit cracked, but the Duke kept egging her on, so she agreed to do it. The attendance at the fair is expected to be 3,207,672 people, but the recipe in the royal cookbook only feeds 3,427 people. It calls for 856.75 dozen eggs, 72 pounds of ham, and 136 pounds of onion. (Tabasco is optional.) Each mature pig yields 36 pounds of ham and each bunch of onions from the royal farms weighs 2 pounds. How many eggs, how many pigs, and how many bunches of onions will Julia need in order to feed the visitors at the fair? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-38) Answer: 306
Ralph the mouse and his friends were ecstatic. The exhibition hall where they lived was having an International Cheese Convention. When the people departed, Ralph and the other mice wandered through the halls filled with hundreds of varieties of cheese. They finally collapsed in a corner, stuffed to the whiskers from cheese tasting. Ralph noticed that out of every 34 pieces of cheese they had tasted, 12 were American, 3 were English, 6 were Austrian, 9 were Swiss, 3 were Dutch, and 1 was Italian. After the mice had tasted 81 pieces of Swiss cheese, how many pieces of cheese had they tasted altogether? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-37) Answer: On the 14th week they will repeat the cycle (Cycle repeats every 13 weeks.)
In a faraway galaxy, on the planet Ortem, meteorologists are practicing climate control. They are producing four kinds of weather and have worked out a pattern of 3 hot days, then 2 mild days, followed by 4 cloudy days, and then 4 warm days. If there are 9 days to a week on Ortem, how many weeks would it be before they get back to a week beginning with three hot days? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-36) Answer: Jazz - 11; Country western - 11; Rock - 49; Reggae - 9; Soul - 22; Heavy metal - 14; Big band - 7; Total = 123
With the spring dance coming up, the dance committee did a survey to see what kind of band to get. They talked to 123 students and found that twice as many people wanted soul music as jazz; the number wanting heavy metal was 2/7 as many as the number wanting rock; 1/2 as many wanted the big band sound as heavy metal; 1/3 the combined total of jazz and soul wanted country western; 5 more than the combined total for jazz, country western, and soul wanted rock; and there were 2 fewer votes for reggae than jazz. How many votes did each band get? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-35) Answer: 11
The Sea-City shuttle is making the last run of the day. The bus leaves the terminal with some passengers already on board. At the city park, the first stop, the bus picks up the same number of passengers as the number that were on board before it stopped. Seven passengers get off here. At the second stop, the zoo, the bus picks up the same number of passengers as the number that was on board before the bus stopped. Nine passengers get off. At the football stadium, the last stop, no one gets on and 21 passengers get off. The bus returns empty to the terminal. How many passengers were on board when the bus left the terminal? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-34) Answer: Noon, May 30, 2001
Willard Van Winkle (distant cousin of Rip) woke up slowly and looked around. "These things don't exist," he said, "wait a minute. ..." Suddenly a voice said, "No, wait 6,000,000 minutes!" And so it was - Willard had in fact been asleep for 6,000,000 minutes, having fallen asleep on January 1, 1990 at 8 PM. What time did Willard wake up? Explain in detail how you found your answer using words, number, and/or pictures.
7N-33) Answer: 4 days
For the next 144 days, Earth's newest space colony will be floating through the area between Mars and Jupiter known as the asteroid belt. Most of the asteroids, which will be constantly bombarding the colony, are no larger than a baseball. But there are five huge asteroids, which scientists have named Alpha, Beta, Cephalon Delta, and Erthon, which will occasionally orbit the colony. The scientists are advising everyone to stay inside during any time that all of these huge asteroids orbit the colony at the same time. Alpha will orbit the colony every 6 days, Beta every 4 days, Cephalon every 9 days, Delta every 12 days, and Erthon every 18 days. How many days will the inhabitants of the space colony have to spend inside in the next 144 days? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-32) Answer: 4 tables for 8 and 9 tables for 10; 9 tables for 8 and 5 tables for 10; 14 tables for 8 and 1 tables for 10
You are in charge of setting up the cafeteria for an awards banquet. A total of 122 people will attend. The tables you are setting up seat either 8 or 10 people. No empty seats are allowed. How many of each size table will you need to use to make sure everyone has a seat? List all combinations. Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-31) Answer: 6 players
16 players are on a baseball squad. 6 can pitch. 8 can play second base. 4 can do both. How many can neither pitch nor play second base? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-30) Answer: 150 oranges
A local market buys oranges at 3 for 10 cents and sells them at 5 for 20 cents. How many oranges must it sell in order to make a profit of $1.00? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-29) Answer: $54
A man spent 1/3 of his money and then lost 2/3 of the remainder. He was left with $12.00. How much did he start with? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-28) Answer: Nancy $1,460; Amy $220
Amy and Nancy bought three sets of golf clubs at the Golfland going-out-of-business sale. All three sets of clubs are of equal value. They paid $1,680 in all. Nancy paid $900 and Amy paid $780. They took the clubs to an auction for resale. One set was sold for $1,680. At the end of the auction, Amy decided to take the remaining two sets for herself. How should they divide the cash equitably? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-27) Answer: about 46%
Ann and David poured a 48-ounce container of school lunch gravy through a strainer. After straining, the gravy weighed in at 26 ounces. Approximately what percent of the gravy would not go through the strainer? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-26) Answer: Steve 1st; Jesse 2nd; Steve was seven beans closer
At the county fair, there are 873 jellybeans in a jar. People guess the number in the jar, and two prizes are given for the closest guesses. Jesse and Steve were the winners. Jesse guessed 909 jellybeans and Steve guessed 844 jellybeans. Who won first prize? Who won second prize? How much closer to the exact number was the first-prize winner than the second-prize winner? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-25) Answer: 70+50 = 120 flyers
Billy and Maria ordered flyers to advertise the school dance. Flyers cost $8.75 for the first 50 and $1.50 for each additional 10. The bill was $19.25. How many flyers did they order? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-24) Answer: $27,600
Georgette earned $500 a week for the first 20 weeks of the year. She then received a 10 percent raise. How much did she earn for the entire year? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-23) Answer: 15
If 75 were divided into three parts in the proportions 2 to 3 to 5, what is the smallest part? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-22) Answer: discount
In a warehouse you obtain a 20% discount but you must pay a 15% sales tax. Which would you prefer to have calculated first, discount or tax? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-21) Answer: Elevator #1 at 1:13
In an elevator bank of two elevators, the following schedule is installed: Elevator #1 takes two minutes between floors, whereas Elevator #2 takes only one minute between floors. The elevator that arrives at a given floor first must wait three minutes before leaving. No waiting time is required of the elevator that arrives second at a given floor. Both elevators leave the sixth floor on a downward trip at exactly 1:00. Which elevator arrives at the ground floor first, and at what time? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-20) Answer: 82
Janice has an average of 74 on the first three tests in her algebra class. On the final four tests, she scored 92, 90, 94, and 76. What was her average for the entire year? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-19) Answer: 29 fish
Loretta owns a pet shop that specializes in exotic tropical fish. In April, Loretta doubled the number of fish she had on hand, and then sold 30 of them. In May, she tripled the number of fish she had on hand, and then sold 54 of them. In June, she quadrupled the number of fish she had, and then sold 72 of them. She now had 48 fish left. How many fish did she start with? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-18) Answer: $9
Mike, Ray, and Lucy went into the record store for the big "Dollars Only Sale." Mike bought 2 CDs and 1 cassette for $16. Ray bought 1 CD and 2 cassettes for $11. Lucy bought 1 CD and 1 cassette. How much did she pay? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-17) Answer: three 5-pound boxes and one 3-pound box
Mr. Homeowner wants to put fresh grass seed down on his front lawn. Grass seed is available in three-pound boxes and in five-pound boxes. A three-pound box costs $4.50, and a five-pound box costs $6.58. Mr. Home-owner needs 17 pounds of the grass seed. How many of each size box should he purchase to get the best buy? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-16) Answer: $65
Mr. Rafaelo runs a bicycle store. He sells a bike for $165, including the tax. To determine his selling price, he added $10 to the cost of the bike for a child's seat on the back. Then he doubled the total for his own markup. Last, he added $15 for sales tax. How much did the bike cost Mr. Rafaelo? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-15) Answer: $100
Pam has decided to open a special money-market account. She noticed a bank advertising a new investment plan. The bank will double the amount of money in an account on the last day of the month. On the first of the next month, however, it will charge a $100 service fee. Pam deposited $100 on the 15th of January. How much money is in her account on January 15th of the following year? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-14) Answer: 90
The arithmetic mean of George's 10 tests was 87. His teacher decided to discard the best and worst grades, a 95 and a 55. What was George's new arithmetic mean? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-13) Answer: 56
The Art Club at the Carroll School decided to exchange gifts at the end-of-school party. Each of the eight members brought a gift for each of the other members. How many gifts were exchanged? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-12) Answer: $126 profit
The Audio Store decided to sell its entire stock of audio tapes, and reduced the price from $5 to $3 per tape. During the first day of the sale, they sold one-half of their stock of tapes. On the second day of the sale, they lowered the price to $2, and sold one-half of their remaining tapes. On the third day of the sale, they reduced the price to $1, and sold the remaining 90 tapes. If each tape cost them $1.90, how much did they make or lose during the three-day sale? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-11) Answer: two children under five
The eight members of the Mendoza family went to the movies last Saturday evening. Adult tickets cost $6.50 each; children's tickets cost $3.20 each. Children under five years old are free. The total cost for the tickets was $29.10. How many children under five years old were there? (Don’t assume an even number of adults.) Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-10) Answer: Tuesday
The local pool is open Monday through Friday. Swimming classes meet every day except Tuesday. Diving classes meet every Monday, Wednesday, and Friday. Water polo games are played every day except Monday and Wednesday. Water ballet classes are held on Thursday. Scuba diving instruction is held every day. Which is the least busy day at the pool? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-9) Answer: Sally's score is 64; Steve had 5 correct
There were 10 problems on the math test. You receive 10 points for each one you have correct. You lose 2 points for each one you have wrong. Sally had 7 correct. What was her score? Steve scored a 40. How many did he get right? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-8) Answer: $7.75 saved
This data shows the cost of birthday cards in Mrs. Henry's Card Shop: Number of Cards - Cost per Card; 1 to 3 - $2.50; 4 to 6 - $2.25; 7 to 9 - $2.00; 10 to 12 - $1.65; 13 or more - $1.50. Mrs. Ross went into the store in the morning and bought 5 cards. That same afternoon, Mr. Ross bought 8 cards. How much could Mr. and Mrs. Ross have saved if they had made their purchase together? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-7) Answer: Saturday, January 13th and Thursday, January25th
Three trains pass through the town of Centerville. The Blue Arrow passes through every other day. The Pacific Sunrise passes through every third day; that is, on Monday, Thursday Sunday, and so on. The Red Rocket passes through the town every fourth day; that is, on Monday, Friday, Tuesday, and so on. All three trains passed through the town on Monday, January 1st. On what days and dates in January will all three pass through the town? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-6) Answer: Fran
Fran, Frankie, and Jo are trying to guess the number of jellybeans in a jar. Jo guesses 132. Frankie guesses 127. Fran guesses 115. One guess is off by 12 jellybeans. One guess is off by 17 jellybeans. One guess is correct. Who was correct? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-5) Answer: 800 earrings
In a certain Eskimo village, there are 800 women. Three percent of the women wear one earring. Half of the remainder wears two earrings and half wear none. How many earrings are worn by all of the women? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-4) Answer: 16 pennies
John has less than 20 pennies. When he puts them in piles of 5, he has 1 left over. When he puts them in piles of 3, he also has 1 left over. How many pennies does he have? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-3) Answer: one possible solution: top row: 1/6, 11/12, 5/12; middle row: ¾, ½, ¼; bottom row: 7/12, 1/12, 5/6.
Put one of the fractions 1/12, 1/6, 1/4, 5/12, 1/2, 7/12, 3/4, 5/6, and 11/12 in each of the boxes of a 3x3 grid so that the sum of the fractions in each row and column is 3/2. Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-2) Answer: $8.45
Ronni, her mother, and her grandmother are all going to the local movie. Children under 12 must pay $1.80. Adult tickets cost $3.50, but senior citizens get a 10% discount. If Ronni is 9 years old and her grandmother is a senior citizen, how much do they spend for the 3 tickets? Explain in detail how you found your answer using words, numbers, and/or pictures.
7N-1) Answer: 21/28
The numerator and denominator of a fraction are in the ratio of 3:4. If 1 is subtracted from the numerator and 2 is added to the denominator, the value of the resulting fraction is equal to 2/3. Find the original fraction. Explain in detail how you found your answer using words, numbers, and/or pictures.
Expectations & Examples of Numbers from the 2008 Math Standards Revision (draft) - Grade 7
Illustrate the meaning of positive and negative integers using models, such as the number line or colored chips, and situations, such as elevation, temperature, or debt. Compare and order positive and negative rational numbers in both fraction and decimal forms using number lines, ordered lists, or the symbols <, >, or =.
Find the absolute value of a number and recognize that the absolute value represents the distance of the number from zero. |
Expectations and Examples of Operations from the 2008 Math Standards Revision (draft) – Grade 7
Represent addition, subtraction, multiplication, and division of positive and negative integers using numbers, pictures, or models, and translate among representations. Example:
Add, subtract, multiply, and divide positive and negative rational numbers. These four operations need not be taught or learned at the same time. Perform mental calculations involving positive and negative rational numbers. Example:
Students might approach this problem by regrouping and mentally combining fractions as shown below: I know that the sum of ¾ and ¼ is 1, so add 4 ¼ and 1 3/4 to get 6. Then 6 ½ and 7 ½ is 13 + 1 = 14. So the total is 6 + 14 + 3 = 23. Solve multi-step contextual problems involving rational numbers and justify the solution. |
Examples of Number Sense from the 2006 GLEs – Grade 7
Explain the meaning of fractions, decimals, and integers and give examples. Convert between equivalent forms of fractions, decimals, or percents. Explain or demonstrate that fractions may have multiple equivalent representations. Explain or demonstrate that decimals may have multiple equivalent representations. Order decimals, fractions, and/or percents and explains why one number is greater than, less than, or equal to another number. Order decimals, fractions and/or integers based on a picture of a real world model, locations on a number line, or symbolic representation. Explain why one integer, fraction, decimal, or percent is greater than, less than, or equal to another given number. Use the inverse relationship between multiplication and division to simplify computations. Use the inverse properties of addition and multiplication to simplify computations and explain why they work with integers, fractions, and decimals. Use, represent, or evaluate an application of the commutative, associative, and/or identity properties of addition on non negative decimals or fractions. Use, represent, or evaluate an application of the commutative associative, identity, and/or zero properties of multiplication on non negative decimals or fractions. Explain or illustrate the meaning of a ratio, percent or proportion. Express proportional relationships using objects, pictures, and symbols. Complete or write a proportion for a given situation. Predict a future situation using direct proportion Represent equivalent ratios and/or percents using pictures, diagrams, or symbols. Determine or use a ratio, percent, or proportion in a given situation. Explain or show the meaning of addition and subtraction of integers using words, pictures, or real world models. Translate a symbolic addition or subtraction of integers into a real life situation. Show addition and subtraction of integers using technology. Translate a given picture or illustration representing addition or subtraction of integers into an equivalent symbolic representation. Explain why multiplication of fractions involves multiplying denominators while addition of fractions requires finding common denominators. Select and/or use an appropriate operation to show understanding of addition and subtraction of integers. Find the product or quotient using non negative decimals and fractions. Use multiplication and division in real world situations involving non negative rational numbers. Multiply non negative decimals and fractions. Divide non negative decimal numbers by non negative decimal numbers to the hundredths place. Compute with non negative rational numbers using order of operations. Interpret and apply the concept of remainder in a given situation. Complete multi step calculations requiring two or more operations with non negative decimals and fractions. Select and use appropriate strategies and tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute in a given situation. Explain why a selected strategy or tool is more efficient or more appropriate than another strategy or tool for a situation. Describe strategies for mentally adding and/or subtracting integers and multiplying and/or dividing non negative decimals and fractions. Determine and explain when an approximation, estimation, or exact computation is appropriate and selects or illustrates a real life situation where estimation is sufficient. Use estimation strategies to predict an answer prior to operations on non negative rational numbers. Use estimation to verify the reasonableness of calculated results. Compute to check the reasonableness of estimated answers for a given situation. Explain an appropriate adjustment when an estimate and a computation do not agree. Explain or describe a strategy for estimation involving computation with non negative decimals and fractions. |