Math Practice Problems to Teach Strategies for Seventh Grade

7S-9d) Strategy: Guess, check, and revise Answer: 64

"Seven eighths of the number, added to 72, doubles the number," read Soren. "Is this a joke?" Larry looked at the paper and said, "No, it's the number of my locker."   What is the number of Larry's locker?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-9c) Strategy: Guess, check, and revise Answer: white - 506, red - 251, blue - 390

It was time for the Fourth of July parade. Marty was helping to put helium in the balloons. When he was finished he had inflated 1147 balloons. There were 255 more white balloons than red ones. There were 116 fewer blue balloons than white ones. How many balloons of each color did Marty inflate?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-9b) Strategy: Guess, check, and revise Answer: 1500

The Split Ends are hot! They have played 20 live shows this week, and every record store in town is sold out of their albums. Their manager told reporters that over a thousand records were sold in one hour after the last concert. He said, "If you take 4/6 of the number and double it, that's 500 more than the number of records sold." Give the reporters a break. How many records were sold?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-9a) Strategy: Guess, check, and revise Answer: 36

Remember the princess and the pea? She had problems sleeping because of a pea under her mattress. Well, her problem was tiny compared with that of her cousin, the duchess. The duchess bought a radio, got it back to the castle, and discovered that it played only rock music. "Horrors!" she gasped. "Where is Bach? Where is Beethoven? What's all this screaming?" She took the radio back and exchanged it, only to have the same thing happen again. The duchess exchanged quite a few radios, until she finally found one that would pick up a classical station at the castle. She was glad the radio was on her Chopin Liszt, and she would be sure to Handel it with care, so that she wouldn't have to take this one Bach. You might be wondering how many radios the duchess took back before she found the right one. Here is a clue. The total number of radios, divided in half, added to 9, equals 3/4 the number. How many radios did she return? Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-8d) Strategy: Draw a picture Answer: 144

"Mercy!" exclaims Gertie Giraffe as she looks at her yards and yards of yarn. "What did I get myself into?" Winter is coming on, and Gertie is knitting neck-warmers for Geraldine and Geronimo and their cousins. Of all the neck-warmers that she plans to knit, 61 will be purple, 83 will be extra long, and 59 will be striped. Five of the warmers will be purple and extra long, but not striped; 22 will be striped and extra long, but not purple; and 10 will be purple and striped, but not extra long. There will be 11 purple, extra long, striped warmers. How many neck-warmers does Gertie plan to knit?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-8c) Strategy: Draw a picture Answer: 3^rd trip

Venski is fascinated by the ice-cleaning machine as it scrapes the ice between periods at the hockey game. The hockey rink is a rectangle, 120 feet by 60 feet. The scraper cleans a 4-foot-wide strip. If the machine starts at one corner and moves around and around the rink toward the center, on which trip around will it have half the area of the rink clean?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-8b) Strategy: Draw a picture Answer: 3^rd trip

C-623 and C-279 are Cyborgs, who work together on interstellar developments for the Cosmos Construction Company. Their last job was to clear a small rectangular area 200 feet wide and 600 feet long for a new dance club. They used a special planet planer, a bulldozer-type machine, to clear loose rocks and smooth the surface. The planet planer covers an area 20 feet across. If C-623 begins at a corner, and works his way into the center, on which trip around will he clear his half of the area?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-8a) Strategy: Draw a picture Answer: 14,570

The demand for earthworm specialties at Elliot's Underground Gourmet Shop is growing. During the past month Elliot sold 7,584 glasses of mud milk, 7,872 orders of fried flies, and 8,712 bug burgers. He had 2,866 customers buy all three on the combination plate; 2,108 bought just the sawdust salad platter; 894 bought fried flies and a glass of mud milk; 2,769 bought a bug burger and some fried flies; and 2,311 bought mud milk and a bug burger. How many customers visited Elliot's Gourmet Shop in the past month?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-7c) Strategy: Act out the problem or use objects Answer: row 1 – Italy, England, Russia; row 2 – Spain, Japan, Germany; row 3 – Ireland, France, Austria

Blanca dreams of traveling all over the world.  She collects travel posters and tacks them up to the ceiling above her bed so she can lie in bed and look at them.  For her last birthday Blanca’s aunt, a travel agent, gave her a poster of Italy.  Blanca rearranged the posters to make room for the new one.  She put Japan between Spain and Germany as well as between England and France.  She put Italy above Spain and to the left of England.  She did not put Ireland next Germany, or Russia next to France.  Austria was the last poster she put up.  How did Blanca arrange the posters on the ceiling? Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-7b) Strategy: Act out the problem or use objects Answer: North - Louis Jones; East - Lulu Anderson; South - Lily Anderson; West - Lee Jones

Lily tosses and turns, too excited to go to sleep. Tomorrow is the Rose Bowl parade.   Lily, her sister Lulu, Lily's boyfriend Lee, and his brother Louis will be riding on a huge float made up of hundreds of flowers. One person will be on the north side, one on the east, one on the south, and one on the west, each one facing away from the center of the float. Lulu will be to the left of Lee's girlfriend. Lee's brother will be to the right of Lily's boyfriend. Each member of the Jones family will be across from a member of the Anderson family. There will not be an Anderson on the west side and Louis will be riding on the north side. What is the name and position of each person who will be riding on the float?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-7a) Strategy: Act out the problem or use objects Answer: table l clockwise: Mary Black, Suzanne Green, Paul White, Allen Brown      Table 2 clockwise: John Green, Jennifer White, Arlene Brown, Peter Black

The Blacks, the Browns, the Whites, and the Greens, four married couples, are playing a card game. If they are arranged at two separate tables, where is each one sitting? ü No Black is across from a Green or a Brown. ü Married couples are not at the same table. ü Mary is across from Jennifer's husband. ü John's wife is to Mary's left and across from Arlene's husband. ü John is opposite Allen's wife. ü Paul's wife is on John's left and across from Mary's husband. ü John's partner is a Brown. ü Peter's wife is on Suzanne's right. ü Mary's partner is not a Black.  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-6f) Strategy: Make a table or chart Answer: Nine objects changed to 2 metals (36, 48, 63, 72, 84, 96, 108, 112, 126); only one changed to 3 metals  (144)

King Midas is well known for his golden touch, but Millicent Metals hasn't gotten such good press. She also changed many of the things she touched, but not into gold. Every 12th object she touched turned to platinum. Every 16th object became silver, every 9^th object turned to copper, and every 7th object changed to brass. She kept count of the objects she touched, and found that the 36th object turned into a combination of platinum and copper. If Millicent touched 150 objects in all, how many of them changed to combinations of 2 metals, and how many changed to combinations of 3 metals?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-6e) Strategy: Make a table or chart Answer: 606

Marta made out the order for Jaguar Jeans. She ordered 7 pairs of jeans for every jacket, 1 shirt for every 2 pairs of jeans, 3 sweaters for every jacket, 2 pairs of shoes for each 3 sweaters, and 1 belt for every 3 jackets. If Marta ordered 36 jackets, how many items did she order altogether?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-6d) Strategy: Make a table or chart Answer: 812

Q4T4 is the number one Martian vehicle manufacturer. They make six different forms of transportation for sweeping around the Martian countryside. For every 12 Crater Crawlers they make 4 Canal Cruisers; 3/4 the number of Dusty Dippers as Crawlers; 4 1/2 times as many Ice Cap Crunchers as Cruisers; one-half as many Rocket Rollers as Crunchers; and 2 Rotating Ribbits for every 4 Crawlers. If in one year Q4T4 produced 252 Ice Cap Crunchers, how many vehicles did they make altogether?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-6c) Strategy: Make a table or chart Answer: 2 days

Yesterday afternoon Jason fed all of the fish in his fish tanks. He has five different fish, and each one is on a different feeding schedule. He feeds the Glassfish every 2 days, the Black Molly every 3 days, and the Catfish every 5 days. He feeds the Eel every 2 1/2 days, and the Angelfish every 1 1/2 days. On how many days in the next 30 days will Jason feed at least 4 fish?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-6b) Strategy: Make a table or chart Answer: 270 total: 45 with long necks and stripes; 60 with short necks and spots; 75 with short necks, stripes, long legs; 90 with long necks, spots, short legs

Scientists are agog over the news that a herd of strange new animals has been discovered in the Plains of Abunk. Apparently the animals are a cross between a zebra and a giraffe. It seems that out of every 18 zegraffes, 3 have long necks and stripes; 4 have short necks and spots; 5 have short necks, stripes, and long legs; and 6 have long necks, spots, and short legs. Scientists from the University of Abunk corralled a group of zegraffes in order to study them. After a walk among the animals, the scientists reported that they had counted 45 zegraffes with long necks and stripes. How many zegraffes were in the group, and how many zegraffes were there of each kind?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-6a) Strategy: Make a table or chart Answer: 166

It is a very hot summer in the desert, and there is a shortage of water. The sheiks began lining up their camels, at 3:00 this morning for a fill-up at the self-serve water station, which opens at 6:00 A.M. There are two lines of camels: one for Dromedary (one-hump) camels and one for Bactrian (two-hump) camels. At 3:00 A.M. there were 4 camels in the Dromedary line and 6 in the Bactrian line; by 3:15 there were 5 in the Dromedary and 7 in the Bactrian;  by 3:30 there were 7 in the Dromedary and 9 in the Bactrian; by 3:45 there were 10 in the Dromedary and 12 in the Bactrian. It is now 4:00, and there are 14 camels in the Dromedary line and 16 in the Bactrian.  At that rate, how many camels will be waiting at the water station when the attendants open it at 6:00 A.M.?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-5e) Strategy: Make an organized list Answer:

Arturo is selling ads for his school paper, The Gab Gazette. Burger Binge, Cobbies' Fish & Chips, and Doolittle Donuts all want to buy ads, but Arturo has only one page left to fill. The sizes of his ads are 1/2, 1/4, 1/8, and 1/16^th of a page. Before Arturo sells the ads to the restaurants, he has to figure out all of the different combinations of his ads that would fill one page. How many combinations can you find?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-5d) Strategy: Make an organized list Answer:

Laura is in charge of lighting the Rock Palace for an upcoming concert. Each light fixture supplies exactly 1,000 watts of power to light the bulbs in the fixture. Laura can use any combination of 150-watt, 100-watt, 75-watt, or 60-watt bulbs, but the total number of watts must be 1,000. How many different combinations of bulbs can you find that Laura could use in a light fixture?   Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-5c) Strategy: Make an organized list Answer: 93

Sanjay spent a long time searching for just the right birthday card for his mother. He narrowed his choice down to two different cards, a humorous one and a serious one. He finally decided to buy both, for a total of $3.34. He gave the clerk $4.00. How many  possible combinations of coins can you find for Sanjay’s change?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-5b) Strategy: Make an organized list Answer: 46

It's the 5th Annual Fernwick Frog-Jumping Contest! Claudette and her frog Clementine have been practicing many weeks for this big event. Each frog gets a certain number of tries. A try is made up of three jumps, and the score for the try is the total of the scores for those three jumps. In the Fernwick Contest today, Clementine jumped a total of 12 feet on each of her tries. Her shortest jump was 1 foot, her longest jump was 8 feet, and she jumped a whole number of feet on each jump. How many different ways could Clementine have scored 12 feet in three jumps? (Remember that 2 + 3 + 7 is different from 3 + 7 + 2.)  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-5a) Strategy: Make an organized list Answer: 68 ways

The Four Bomber Brothers are the most popular act at the Dingaling Brothers' Circus. In shining helmets and padded vests, they climb a 50-foot ladder and take turns jumping into one of five buckets of water. Each bucket is labeled with a number: 1, 3, 5, 7, and 9. In each performance their four jumps must total 16 points. If the score doesn't equal 16 points, each brother gets a pie in the face. Assuming they never miss the buckets, how many different ways can the Bomber Brothers get a total of 16 points in four jumps?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-4d) Strategy: Look for a pattern Answer: 32 rows and 29 in the last row.

The fierce army of ants marches forth to battle. The general makes up the whole first row. Two colonels make up the second row. Three lieutenant colonels form the third row. Four majors make up the fourth row. Five soldiers form the fifth row, and so on, row after row. If the army consists of 525 ants, how many rows are there, and how many are in the last row?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-4c) Strategy: Look for a pattern Answer: 136

"This is Dino, your dynamite D.J. from radio station KLOT," announced the familiar voice. "All you listeners out there, our Rock Trivia Contest begins today, and we're giving away a LOT of prizes. We're giving one first prize, two second prizes, three third prizes, and so on. Call in and be a winner Good luck! Go for it!" How many winners will there be by the time the sixteenth-place prizes have been awarded?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-4b) Strategy: Look for a pattern Answer: 120

Mele is designing a tree for her 7th grade holiday play. Since the play takes place in a futuristic society, Mele is designing a futuristic tree made entirely of stars. The first, or top, branch will have just one star; the second branch will have two stars; the third branch will have three stars, and so on. Mele will make the stars herself from foil. If her tree has 15 branches, how many stars will Mele need to make?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-4a) Strategy: Look for a pattern Answer: 19

At 7:00 one summer morning, Tobie and Helene hopped into their speedy motorboat and left the Holloway dock. They arrived at Wickle Wharf 35 minutes later. During busy summer months, a car ferry departs from the Wickle Wharf every 5 minutes, beginning at 6:00 A.M. Tourists and local people crowd onto the ferry for the 55-minute ride to Holloway. If Tobie and Helene followed the route that the car ferries take between Wickle and Holloway, how many car ferries did they see on their trip?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-3g) Strategy: Use logical reasoning Answer: Albert

Albert, Bernard, Gina, Denise, and Elroy had all made it to the finals of the Chili Championship Cook-off. Their recipes were all top secret concoctions, some passed down from generation to generation. Three of their recipes called for ground beef, and two called for stew meat. Three of them used hot peppers and two used mild peppers. Bernard and Elroy used the same kind of peppers. Denise and Gina used the same kind of meat. Albert and Bernard didn't use the same kind of meat in their chili. Gina and Albert used different kinds of peppers. Who won the cook-off with a chili recipe that used stew meat and mild peppers?   Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-3f) Strategy: Use logical reasoning Answer: Edwin

Seven friends are standing by Loch Ness, gazing into the lake. Angie, Bess, Carl, Darcy, Edwin, Frank, and Gary are discussing Nessie, the legendary monster. Three of them think the creature should be captured and put into an aquarium, but the rest of them believe Nessie should remain in the lake. Three of them think the creature is a direct descendant of the dinosaurs, but four of them believe it is just a huge fish. Angie, Bess, and Carl don't want to capture Nessie. Gary and Frank have different opinions on that issue. Gary, Darcy, and Frank think Nessie is a huge fish. Bess and Angie have an argument about what Nessie is. Which one of the friends wants to put Nessie in an aquarium so people can see what ancient dinosaurs were like?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-3e) Strategy: Use logical reasoning Answer: 5

Randall, an outstanding rider for the pony express, braved all forms of adversity, believing that "The mail must go through!" One day Randall and his faithful pony got an important letter to deliver. The trip would take ten days over rocky terrain. Randall could only carry enough food for six days, so he requested help from the other riders. Each helper could only carry provisions for six days as well. How many riders were needed to begin the trip so that Randall would get his letter delivered?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-3d) Strategy: Use logical reasoning Answer: Percy--owl, mice; Louise--ocelot, red meat; Rita--otter, fish; Roger--elephant, hay

Poor Alex! He recently began his job at the zoo and today he can't find his morning feeding instructions for the ocelot, owl, otter, and elephant. He is trying to remember what Percy, Louise, Roger, and Rita eat. The possibilities are mice, raw meat, hay, or fish. This is all that Alex can remember: Louise and the otter are to be fed before the animals having mice or hay. Percy is next to the ocelot's cage and across from the animal having fish. Roger, who isn't the owl, is across from the otter and the animal that is eating raw meat. Rita and the owl are next to the animals that are eating hay and red meat. The ocelot doesn't eat hay. What was the name of each kind of animal and what was Alex supposed to feed each one?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-3c) Strategy: Use logical reasoning Answer: Allen, 25, veterinarian; Carrie, 24, police officer; John, 20, mail carrier; Gloria, 27, zoo keeper

Allen, Carrie, John, and Gloria hold these jobs in their city: veterinarian, mail carrier, police officer, and zoo keeper. Allen and Gloria work with animals. Carrie and John wear uniforms. John refuses to touch a gun. Gloria does not like dogs. The veterinarian is 5 years older than the mail carrier. Carrie, 24 years old, is 3 years younger than the zookeeper. The 20-year-old delivers letters. Can you match each person with an age and a job?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-3b) Strategy: Use logical reasoning Answer: Steven--football; Arnie--surfing; Renee-skateboarding; Paula--softball; Jack--ice skating; Enid--swimming

As everyone leaves the table after lunch, Steven chuckles and says, "I can't believe we're all brothers and sisters. We sure have different interests! Everyone laughs and agrees. Their favorite sports are football, surfing, skateboarding, softball, ice skating, and swimming; and each person participates in a different sport. Arnie, Renee, and Jack have an excellent sense of balance. Neither Jack nor Renee likes contact sports. Enid and Arnie love the water, but Enid is allergic to salt water. Jack likes cold weather sports best. Renee wears kneepads, and Paula always wears her cap backwards. Can you match each person with a sport?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-3a) Strategy: Use logical reasoning Answer: Emily

Five cousins are camping together in the mountains. Two of the cousins are Pattersons and three are Andersons. Two of them are from Montana, and three are from Wyoming. Irene and Yvonne are from the same state. Michael and Emily are from different states. Leo and Michael have the same last name. Emily and Yvonne do not have the same last name. The Patterson from Montana awakes in the middle of the night to discover a raccoon rummaging through the food pack. What is that cousin's first name?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-2c) Strategy: Work backward Answer: 6 lb mushrooms, 36 lb carrots, 54 lb potatoes, 12 lb chicken wings, 72 lb frogs legs, 76 lb fruit bats

Fran was demonstrating her specialty on KRTB, Fruit-Bat Soup for a crowd. First she threw in her prime ingredient, giant fruit bats. Then she added 6 times as many pounds of frog legs as chicken wings. She added 2/9 as many pounds of chicken wings as potatoes, 1 1/2 as many pounds of potatoes as carrots, and 6 times as many pounds of carrots as mudflat mushrooms. The mudflat mushrooms were 3/128 of the total ingredients, which amounted to 6 pounds. How many pounds of each ingredient did she add?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-2b) Strategy: Work backward Answer: yes

In order to graduate from the Easter Bunny University and be an official egg-delivering rabbit, Riley Rabbit has to pass a final "eggsamination."  He has to hop ten miles through the heart of downtown traffic (at rush hour) with a basketful of decorated eggs. At three stations along the way a judge will match each uncracked egg with a decorated egg and remove the cracked eggs. To pass the exam, Riley must arrive at the fourth station with at least twice the number of uncracked eggs that he began with. Here is what happened: Riley arrived at Station 1 with no cracked eggs. His eggs were matched with decorated ones. On the way to Station 2, however, he cracked 10 eggs. At Station 2 the uncracked eggs were matched and the cracked ones removed. On the way to Station 3 Riley cracked 14 eggs, which were removed and the uncracked ones matched. On the way to Station 4 he cracked 2 eggs. Riley arrived at Station 4 with 90 uncracked eggs. Did Riley graduate?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-2a) Strategy: Work backward Answer: 61

Maresa and her brother Andrew are on a dinosaur dig in New Mexico. Each day they dig for fossils, and then check in with the resident paleontologist at the end of the day. He helps them to separate the fossils, those for the museum and those they can keep. At the end of the first day 2/5 of the total goes to the museum. On the second day they find 6 new ones and then 3/8 of the total goes to the museum. On the third day they find 13 new fossils and that night the museum keeps 2/7 of the total. On the fourth day they add 7 and 4/9 goes to the museum. On the fifth day they find 3 and the museum keeps 5/6 of their total. They add 12 on the sixth day, and the museum keeps 1/3 of their collection. At the end of their dig they have 10 fossils to take home. How many new fossils did they collect for the museum?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-1c) Strategy: Solve a simpler or a similar problem Answer: April 17, 2035, at 8 am

Pegasus is flying in today for a checkup. He needs to have his coat brushed and his wings cleaned. He's logged in 4,740,000 minutes of flying time since his last checkup at 4 PM on April 12, 2026.  What is the present checkup time and date?  (Remember 2028 and 2032 will be leap years.  When the last two digits are divisible by four, the year is a leap year.)  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-1b) Strategy: Solve a simpler or a similar problem Answer: $2,400,100

On a large planet in a distant galaxy lives Mr. Alphotec with his collection of 85,800 exotic animals. He has one-half as many auples as burfuls, one-third as many burfuls as curlaps, and one-fourth as many curlaps as drolops.  Auples have soft patches of fur dotting their tubular bodies. Blue burfuls have gold spots all over their pyramid-shaped bodies. Curlaps have metallic green plates covering their egg-shaped bodies, and drolops have thick, pointed hairs all over their short, stubby bodies. If an auple is worth $43.50, a drolop sells for $12.50, a curlap is valued at $22.50, and a burful is worth $30.00, what is the value of Mr. Alphotec's collection?  Explain in detail how you found your answer using words, numbers, and/or pictures.

7S-1a) Strategy: Solve a simpler or a similar problem Answer requested

P.G. Andee takes her science class on a field trip to the local hydroelectric plant. After an interesting tour of the facilities, the guide explains to the class that there are four such plants in the northern part of the state. Power Plant A converts one half as many gallons of water per hour into electricity as Power Plant B, which converts one half as many per hour as Plant C, which converts one half as many per hour as Plant D. Last year all four plants together converted 262,800,000 gallons of water into electric power. The company made a profit of $.25 per gallon of water converted. How much profit was made per hour at each power plant?  Explain in detail how you found your answer using words, numbers, and/or pictures.