Grade 8 Practice Problems: Numbers
8N-44) Answer: 6666
A palimage of a natural number is the number that has the same digits as the given number but in reverse order. For example, 659 and 956 are palimages; so are 1327 and 7231. Now add 354 and its palimage. Call this sum X. Add X and its palimage. Call this sum Y. Add Y and its palimage. Call this sum Z. What is the value of Z? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-43) Answer: 24
Sir Dwayne is in charge of dragon designs at the King's Toy Factory. He hopes that his new designs will please the king. "Your Highness," he says. "I have the plans for the toy dragons. If it pleases you, every 6th dragon shall have glowing eyes, every 4th dragon shall breathe fire, every 3rd dragon shall billow clouds of smoke through its nostrils, and every 8th dragon shall have a tail with spikes on it. I shall make 100 dragons." The king asks, "Sir Dwayne, how many dragons shall have more than one of these characteristics?" Sir Dwayne doesn't have the answer. Can you help him answer the king before he is thrown into the dungeon? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-42) Answer: 20
Sarah, the chimney sweep, cleans fireplaces. She uses a super vacuum cleaner to remove the soot that she brushes down the chimney. Sarah doesn't want to take the noisy cleaner inside a customer's home, so she leaves the cleaner outdoors and runs a hose from it to the fireplace. The distance from the cleaner to the fireplace is different at each home, so she has sections of hose that she can snap together to make the length of hose she needs. She has 3 sections each of these lengths: 8 feet, 10 feet, 12 feet, 16 feet, and 24 feet. Sarah is ready to clean a fireplace and needs a 100-foot hose. How many different combinations of hose sections could she use? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-41) Answer: 89
Craig and his friends are on a 2-week backpacking trip in the mountains. They took their time traveling the 35 miles from the park ranger's office to Black Hawk Summit. They stopped along the way to fish and to explore old mines. Now they are on their way back to the ranger's office, and they can travel faster because their packs are lighter. The hikers have only three days left and they still have to cover 24 miles. They don't plan to cover more than 12 miles or less than 1 mile each day, but they will cover a whole number of miles every day. What are all the different ways they could divide the 24 miles for their three days of hiking? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-40) Answer: Loa and Lara - days 12,24,36; Lola and Pam - days 8, 16, 24, 32, 40
Lara, Lola, and Pam work out at the Fitness Center after school. Lara goes every 3 days, Lola every 4 days, and Pam plays in the band, so she can only go every 8 days. On what days in the next six weeks will Lola and Lara be at the Fitness Center on the same day? On what days in the next six weeks will Lola and Pam be at the Fitness Center on the same day? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-39) Answer: 78
Although many people are aware that Indians used shells in their trading, few people know that Indians, especially West Coast Indians, also used feathers. To the traders, it was important that the birds from whom the feathers came still be soaring among the clouds. The feathers had to be collected from dangerous perches along the beach cliffs. The most popular feathers came from birds that were common along the coast: seagulls, pelicans, and sandpipers. The feathers were all given equal value. A blanket or a piece of jewelry that cost 11 feathers could be paid for with any combination of 11 feathers from one or more of the three kinds of birds. How many different combinations of feathers could the traders have used for that purchase? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-38) Answer: yes
Some friends decided to make a week-long bike trip, with some of them leaving or joining the trip along the way. Two-thirds of the group wanted to try to go the entire distance. After the first day 1/3 of the bikers left. On the second day, they got 8 new bikers. At the end of the second day, they lost 3/7 of the group. On the third day they gained 2 new bikers and at the end of the day 2/5 of the group left. Five new bikers joined up on the fourth day and they lost 3 at the end of the day. On the fifth day, they picked up 4, and then lost 1/4 of the total group. On the sixth day they got 4 new ones and at the end of the day 6 departed. On the seventh day, 7 bikers finished the trip. Did the group that wanted to go the whole way make it? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-37) Answer: 13 at $57, 12 at $.98, 12 at $1.06, 16 at $1.33, 15 at $2.78
"What?" gasped Old Mother Hubbard when she opened her cupboard to get her poor doggie a bone." STILL bare? I'm going to the butcher." Off she went, and the dog could not have agreed more. Mother Hubbard made the mistake of taking the dog with her. The dog, you see, had saved Mother Hubbard's daughter from an oncoming train many years earlier, and he had learned to use that act of bravery to his every advantage. When Mother Hubbard started to walk out of the butcher shop with bones that cost only $.57 each, the dog began tapping his claws on the floor. Mother Hubbard returned to the counter and bought more bones, some at $.98 each and some at $1.06 each. This time, the dog began making sounds like a train, just as a reminder. This so unnerved Mother Hubbard that she bought more bones, some at $1.33 each and some at $2.78 each. She gave the butcher a $100-bill for her package of 68 bones, and she received 3 pennies, 1 dime, and a $5-bill for change. How many bones at each price had the dog persuaded Old Mother Hubbard to buy? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-36) Answer: 5 hours; 1-ride 24 miles, walk 12; 2-ride 12 miles, skate 16, walk 8
Mario and Min were delivering mail in the mountains. On their route, which covered 36 miles, they traveled by pony, by skates, and by walking. They shared the pony named Pete, who traveled at 12 miles an hour. They could each skate 8 miles an hour and they walked 4 miles an hour. They each finished their rounds in the same amount of time. They could only exchange Pete or the skates on the hour, and no one had time to wait for the other. They agreed to share Pete. If one of them wasn't using the skates, they could just carry them, but they had to arrive at the same time. How long did it take them and how far did each one walk, ride, and skate? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-35) Answer: R1 - 21, 42 points; R2 - 19, 76 points; R3 - 17, 187 points; R4 - 15, 255 points; R5 - 13, 494 points; Raider Robot - 7,1190 points
Kara is playing Raider Robot, trying to beat the best score. Finally, she sets a new record after 6 minutes and 8 seconds. For every blue robot that Kara is able to turn red, she gets points, depending on whether it's an R1, R2, R3, R4, R5, or Raider Robot. R1 is worth 2 points, R2 is worth 4 points, R3 is 11 points, R4 is 17 points, R5 38 points, and Raider Robot is worth 170 points. Kara changed a total of 92 robots from blue to red for a total of 2,244 points. How many robots of each kind did she turn to red, and how many points did she get for each kind? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-34) Answer: 3.9
If Melissa earns a grade point average of 2.1, 2.9, and 3.1, what does her 4th quarter GPA need to be to raise her grade to a 3.000 cumulative grade point average? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-33) Answer: swim 40k, raft 80k
"Amadeo! Hey, Amadeo! Aren't you coming for practice?" Amadeo put down the newspaper and looked out the window. Raul was outside, his softball and bat in hand. "Be there in a minute!" Amadeo shouted, "I'm reading this incredible story." In the paper was a story about three friends, all marathon swimmers, who had tried to go around the world in a boat they built together. When they were 120 kilometers from their first shore stop for provisions, the boat sank. They rescued two one-man rafts and a wetsuit. After trying to put two men on a raft and having it sink, they made a plan: They would take turns riding on the rafts and swimming with the wetsuit. The rafters would keep pace alongside the swimmer. The agreement was that each man would swim as short a distance as possible (while trying to keep their swimming distances equal) and each man would raft as long a distance as possible (while rafting equal distances) until they reached shore. How did they work this out and how far did each one raft and each one swim? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-32) Answer: 2 cows
It is graduation day at Moo U., and the cows are waiting patiently to receive their degrees. The university clerk is watching as each graduate shakes hoofs with the university president. The clerk notices that every third candidate receives a BBA (Bachelor of Bovine Arts), every seventh graduate receives a CCD (Doctorate of Cud-Chewing) degree, every fourteenth a BS (Beef Science) degree, every ninth an HHA (Honorary Hoof Award), and every twenty-first an MA (Moo Award). Any cow who receives all five degrees and awards will win the coveted UB (Utterly Brilliant) award. How many cows out of the 260 graduating class will receive the UB award? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-31) Answer: 30 minutes
Tillie the tuna is giving her first concert. The underwater amphitheater is full and waiting for Tillie, Sharleen Shark, and the Fluke Wellington Orchestra. The concert will end with the choir of Angelfish. Molly Marlin is behind the curtain, peeking out at the audience, as Tillie begins singing. Molly notices that in the first five minutes of Tillie's performance, the entire front row of 60 fish get up, swim off, and demand their money back! Molly doesn't want to carp, but she is afraid that if this continues, the concert will flounder. To Molly's horror, 114 fish leave in the next five minutes, 90% more than the number of fish that left in the first five minutes. If this same rate of departure continues, how long will it take before all 2,200 patrons are gone? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-30) Possible Answers: 31, 10, 10, 10 OR 15, 5, 31, 10 OR 9, 10, 11, 31
James hit the dartboard shown with 4 darts. His score was 61. How might he have done this? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-29) Answer: cheese - 72; pepperoni - 10; vegetarian - 128
Pizza-making is a family affair at Lucca Pizza Parlor. Angelo, Paoli, and Lucia Lucca are helping their parents make pizzas for an especially busy day of orders. Angelo makes the cheese pizzas, Paoli makes the pepperoni pizzas, and Lucia makes the vegetarian pizzas. During the first hour Angelo made 6 pizzas, Paoli made 5, and Lucia made 2. The next hour Angelo made 12, Paoli made 2, and Lucia made 8. The third hour Angelo made 8, Paoli made 7, and Lucia made 4. The next hour Angelo made 16, Paoli made 4, and Lucia made 16. The fifth hour Angelo made 12, Paoli made 9, and Lucia made 8. During the last hour of their very long day, they made a total of 210 pizzas. After 10 hours, how many of the pizzas were cheese, how many were pepperoni, and how many were veggie? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-28) Answer: 44 resembled owners; 66 fell asleep; 110 refused to obey; 132 were uncombed; 154 growled; 176 performed perfectly
Canine City is typical of any large city, with one rather remarkable exception: The city is made up entirely of dogs who own humans, rather than human residents who own dogs. It is a rather fitting turn of the table, and the dog residents seem to like it just fine. Once a year the dogs get together and have a Human Show. Ribbons are awarded for the best-groomed, the best-behaved, and the most-alert humans, and for the humans who can do the most tricks. This year Spot, the dalmation, and Prince, the collie, have entered their own humans-Sid and Gladys. While grooming their humans at intermission, Prince observed how unruly the batch of humans seemed this year. Spot agreed and noted that out of every 31 humans in the show, 2 bore an alarming resemblance to their dog owners; 3 fell asleep right on the show tables; 5 simply refused to obey commands; 6 were uncombed; 7 growled constantly; and 8 performed perfectly. Out of 682 humans entered in the show, how many were there in each of the categories that Spot and Prince observed? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-27) Answer: Saturday, May 15, 9:20 am
Sherlock Homes was listening to a strange tape that had been left at the home of Lady Webberly: "At the sound of the tone the time is 7:00 PM. exactly, Monday, May 3,1987. In precisely 16,700 minutes you must be under the oak tree behind the Somerset library, or you will be in grave danger." Sherlock instructed Lady Webberly to follow the instructions and that he would follow behind at a discreet distance. On what day and at what time was Lady Webberly to be under the oak tree behind the library? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-26) Answer: 21 adult swans, 21 young swans, 21 adult ducks, 21 ducklings
The ugly duckling grew up to become a beautiful swan, and his brothers and sisters grew up to be ordinary ducks. Everyone got married and raised ducklings and baby swans. One day the swans and ducks decided to have a reunion for old times' sake. They rented a hall next to a pond, and everyone had a great time. There were four sizes of swans and ducks at the reunion. The adult swans each weighed 35 pounds; the young swans each weighed 8 pounds; the adult ducks each weighed 16 pounds; and the ducklings each weighed 4 pounds. After the birds had eaten and were getting ready to go swimming, the photographer they had hired for the event got everyone together for a family photograph. There were 84 birds in the picture, with a combined weight of 1,323 pounds. How many adult swans, young swans, adult ducks, and ducklings were in the family photo? Explain in detail how you found your answer using words, numbers, and/or pictures.
Franky Flightright invented the flingwinger, a flying machine. The flingwinger has a rectangular body, made up of 10 compartments in this arrangement:
In order to fly, the combined weight of the passengers must be the same in compartments A-B-C as in compartments C-D-E-F, as in compartments F-G-H, and as in compartments H-l-J-A. There must be at least 1 person in each compartment. On the first flight of the flingwinger, there were 56 passengers, who all weighed the same. How could Franky have seated the passengers in the flingwinger?
8N-24) Answer: 588
The manager of Majestic Ski Slopes was counting the number of skiers at the resort one day. He discovered that there were twice as many people in the lodge as on the expert slopes. The same number of people were on the expert slopes and the advanced slopes. There were 1/3 as many advanced skiers as intermediate skiers. He found that there were 6/7 as many intermediates as beginners. There were twice as many beginners as racers. There were 84 racers that day, exactly 21/147 of the total number of skiers. How many people were skiing at the Majestic Ski Slopes that day? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-23) Answer: 107 bins of meteorite dust, 535 bins of asteroid fragments, 101 bins of electronic parts, 404 bins of scrap metal
Barok and Zanna opened their B & Z Recycling Station one month ago, and already they have 7,000 tons of galactic debris for sale. They have collected five times as many 4-ton bins of asteroid fragments as 2-ton bins of meteorite dust. They have in storage four times as many 10-ton bins of scrap metal as 6-ton bins of electronic parts. How many bins do they have of each kind of galactic debris? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-22) Answer: 6
The Star Sports Company is organizing a canoe trip. When Blaine signs up for the trip he discovers a small problem. Each canoeist can only carry supplies for eight days, but it will take 14 days to reach the trip destination. Blaine has asked some friends to help out. Each friend can only carry supplies for eight days as well. How many friends will need to begin the trip with Blaine, so he can finish the trip? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-21) Answer: 39
The old woman who lived in a shoe with her many children awoke one morning and set out the bread, salami, cheese, and tomatoes for her children's sandwiches, as she always did. She put on an aerobics workout tape and began making the sandwiches in time to the music, as she always did. But then she did something she never did. She got so caught up in the music that she lost track of the number of sandwiches she was making. When the tape finished 45 minutes later, she found herself surrounded by stacks and stacks and stacks of sandwiches. "RATS!" she said. "What shall I do now?" She found that 294 of the sandwiches had salami, 294 had cheese, and 368 had tomatoes; 87 had salami and cheese, 65 had salami and tomatoes, 152 had cheese and tomatoes; and 50 had salami, cheese, and tomatoes. The woman decided to freeze the sandwiches and thaw some out each school day. If she had 18 children, and each child ate one sandwich a day, how many days did the sandwiches last? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-20) Answer: Do-it-yourself - 150; New - 300; Business - 210; Entertainment - 120; Programming modules - 20; Cleaning - 100; Special task - 5; Total = 905
Leo and Castor were off to the robotics convention. They wandered around, trying to take in some of the 905 robots on display. There were 50% as many do-it-yourself robots as new robots; 4/5 as many entertainment robots as do-it-yourself kinds; 1/3 as many cleaning robots as new ones; 1/6 as many robots with programmable modules as ones for entertainment; 1/4 as many robots for special tasks as with programmable modules; and twice as many business robots as the combined total for cleaning and special task robots. If Leo and Castor covered all the displays at the convention, how many of each type of robot did they see? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-19) Answer: Snakes - 52, Hamsters - 26, Mountain lions - 32
Harvey's Heavenly Helpers supply aid and assistance for any job: large, small, or out of the ordinary. During the last year they had 1.4% more jobs searching for stray mountain lions than looking for stolen hamsters; twice as many requests for building fences as washing windows; 3.5 times more jobs moving pianos than searching for hamsters; 1/4 as many calls for finding hamsters as washing windows; twice as many jobs washing windows as locating lost snakes; and 52 lost snake cases which was 10.4% of their business. If they successfully completed each job, how many snakes, hamsters, and mountain lions did they locate? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-18) Answer: 11
Þ Subtract 3
Þ Multiply by 4
Þ Add 8
Þ Result 40
What number in the "start" box will yield the result 40? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-17) Answer: 2 large boxes, 15 small boxes
A dealer packages marbles in two different box sizes. One size holds 5 marbles and the other size holds 12 marbles. If the dealer packaged 99 marbles and used more than 10 boxes, how many boxes of each size did he use? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-16) Answer: Total - 41,472; eating dinner - 13,824; watching television - 6,912; on vacation - 3,456; refused to answer door - 1,728; never heard of Goldilocks - 864; invited her to dinner - 864; pretended to be asleep - 9,216; sent bill - 2,304; gave teddy bear - 1,152; called police - 576; asked if she did windows - 576
An elderly woman, claiming to be Goldilocks, has been making the rounds on the talk shows. She is advertising her just-published book, Too Hot, Too Cold, Just Right: My Life as a Drop-In. It is the story of how her chance visit to the home of a family of bears, and their rejection, led her to a lifetime of compulsive "dropping-in" on total strangers. "Oh, yes," she reminisces, "once I got started, there was no stopping me. I dropped in on many lovely people in my nearly eighty years on the road." She smiles and settles back in her chair. "One third were eating dinner when I arrived; 1/6 were watching television; 1/12 were away on vacation; 1/24 refused to answer the door; 1/48 had never heard of me (Imagine that!); 2/96 invited me back; 2/9 pretended to be asleep; 1/18 sent me a bill; 1/36 gave me a teddy bear; 1/72 called the police (Mercy, what a fuss!) and 576 asked me if I did windows. I assured them I didn't." Too Hot, Too Cold, Just Right leaves the reader with two burning questions: Just how many people did Goldilocks drop in on, and how many people were in each category? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-15) Answer: 93,500 gallons
Ms. Dixie Drinkwater, chairperson of the Parch City Beverage Advisory Board, calls the annual meeting of the members to order. The citizens of Parch City pride themselves on the number of gallons of healthful beverages they consume every year. It is the Board's job to verify the figures before the report is published in the newspaper. Everyone is waiting effervescently: "Well," begins Ms. Drinkwater dryly, "16% of the total amount of beverages consumed was orange juice; 5% was mineral water; 11% was mango juice; 8% was cactus milk; 24% was broth; 7% was carrot juice; 13% was celery juice; 3% was banana shake; 9% was prune juice, and 3740 gallons of milk were consumed. End of report. Let's break for tea." How many total gallons of beverages were consumed by the thirsty residents of Parch City that year? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-14) Answer: 15, 21, 35
There are many numbers which divide 109 with a remainder of 4. List all two-digit numbers that have that property. Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-13) Answer: 1,403
Nathaniel and Daniel are attending the local skateboard competition. They think it is a "totally rad" event, but they chuckle to themselves, sure that many of the adult spectators do not know what most of the skateboard maneuvers are called. To find out, they handed out questionnaires at the beginning of the freestyle competition. Now, just before the street style competition begins, they are tallying the results. They discover that 410 spectators know what an "ollie" is, 462 know what a "copergrind" is, and 552 know what a "rail slide" is. Ninety-one spectators can identify both an "ollie" and a "copergrind"; 105 can identify both a "copergrind" and a "rail slide"; and 42 can identify a "rail slide" and an "ollie". Only 25 spectators know what all three maneuvers are called, and 192 cannot identify any of the three maneuvers. How many spectators filled in a questionnaire for Nathaniel and Daniel? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-12) Answer: 12 darts
A dartboard has sections labeled 2, 3, 5, 11, and 13. Patti scored exactly 150. What is the minimum number of darts she might have thrown? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-11) Answer: 63
A mooring rope that is 1 inch thick and 63 feet long is being coiled on the dock. The first coil took 12 inches of rope, the second coil took 24 inches, the third took 48 inches, and so on. How many coils are needed for the entire rope? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-10) Answer: 15 shots
Ann is the weakest foul shooter on the girls' basketball team. Out of her first 30 foul shots, she made only 50 percent. Her coach had her go through several practice sessions. She raised her season's percent to 60 percent after 20 more foul shots in the next three games. How many of these 20 shots did she make? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-9) Answer: 3, 3, 8
During the recent census, a man told the census taker that he had three children. When asked their ages, the man replied, "The product of their ages is 72. The sum of their ages is the same as my house number." The census taker ran to the door and looked at the house number. "I still can't tell," she complained. The man replied, "Oh, that's right. I forgot to tell you that the oldest one likes chocolate pudding and the twins like butterscotch." The census taker promptly wrote down the ages of the three children. How old are they? (Consider only integral ages). Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-8) Answer: 2:1
In a group of men and women, the average age is 40. The average age of the men is 50 and the average age of the women is 35. What is the ratio of women to men in the group? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-7) Answer: 42 and 43
Jaime opened his mathematics textbook and multiplied the two page numbers that were facing him. Their product was 1806. To what pages was the book opened? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-6) Answer: same number
Jenny has a nickel-box with 40 nickels in it, and a penny-box with 50 pennies in it. Her younger brother took 10 coins from the nickel-box, put them into the penny-box, and mixed them all up. Then he took 10 coins from the penny-box, put them into the nickel-box, and mixed them all up. Are there more pennies in the nickel-box, or more nickels in the penny-box? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-5) Answer: 50 days
Miguel and Charles started their new jobs on the same day. Miguel's schedule provides for 3 workdays, followed by 1 day off. Charles's schedule provides for 7 workdays followed by 3 days off. On how many of their first 500 days will they both have a day off on the same day? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-4) Answer: 2.5 hours
Mitchell and Jane are going to race their racing cars around an oval track. Mitchell takes 25 minutes to complete a lap and Jane takes 30 minutes to complete a lap. How long will it take Mitchell to lap Jane's car (that is, to overtake her car) if they start together at the same point? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-3) Answer: $41.00
The Shoe Shop is having a big 20%-off sale on all athletic shoes. Mr. Klutz bought a pair of running shoes that were originally priced at $45, a pair of basketball shoes that were originally $85, and a pair of golf shoes that were originally $75. How much did he save by buying the shoes on sale? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-2) Answer: 24 points
During the third quarter of the Bulls' game, four players scored all of the points. Michael Jordan scored 1/2 of the Bulls' points, Scottie Pippen scored 1/3 of the Bulls' points, Luke Longley made one three point basket, and Dennis Rodman scored the last point by sinking one three throw. How many points did the Bulls score in the third quarter? Explain in detail how you found your answer using words, numbers, and/or pictures.
8N-1) Answer: 25 gallons
If a truck gets 5 miles per gallon of gasoline in the city and 10 miles per gallon on the highway, how many gallons would it use to make a 200 mile trip that is 75% highway driving and the rest city driving? Explain in detail how you found your answer using words, numbers, and/or pictures.
Know the square roots of the perfect squares from 1 through 225 and estimate the square roots of other positive integers.
Represent numbers in scientific notation and interpret problem situations involving numbers expressed in scientific notation.
Expectations and Examples of Operations from the 2008 Math Standards Revision (draft) – Grade 8
Simplify expressions involving positive integer exponents using the laws of exponents and the order of operations.
Examples of Number Sense from the 2006 GLEs – Grade 8
Explain the meaning of integers raised to whole number exponents and provide examples.
Explain the meaning of an integer squared and provide examples.
Explain the meaning of square root of a whole number and provide examples.
Order rational numbers including integers, whole number powers, and square roots, and explain why one rational number is greater than, equal to, or less than another.
Order rational numbers including integers, whole number powers, and square roots based on a picture of a real world model, locations on a number line, or symbolic representation.
Explain why one given rational number including integers, whole number powers, and square roots is greater than, equal to, or less than another rational number.
Demonstrate the distributive property of multiplication over addition using an area model or picture.
Use the distributive property to simplify expressions that include integers.
Use the distributive property to factor expressions.
Represent or evaluate the application of the addition and multiplication properties on rational numbers including integers.
Use the addition and multiplication properties, including the distributive property, to assist with computations.
Determine an unknown value for a dimension or a number of events or objects using ratio or proportion.
Determine an unknown value for a dimension or a number of events or objects using percents.
Select and use the most advantageous representation of ratios or percents in a given situation.
Determine a ratio or percent in a given situation.
Explain the meaning of multiplication and division of integers including remainders using words, pictures, or models.
Explain the meaning of taking whole number powers of integers or square roots of whole numbers using words, pictures, or models.
Represent a situation involving multiplication or division of integers, whole number powers of integers, or square roots of whole numbers.
Explain how the result of dividing a rational number by a fraction between 0 and 1 is different from the result of dividing the same number by a fraction greater than 1.
Translate a given situation, picture, or illustration into a numeric expression or equation involving decimals, fractions, integers, whole number powers, and square roots of whole numbers.
Select and/or use an appropriate operation to show understanding of whole number powers and square roots.
Convert between equivalent forms of rational numbers including whole number powers and square roots of perfect squares.
Compute with rational numbers using order of operations.
Compute using whole number powers and/or square roots of perfect squares.
Interpret and apply the concept of remainder in a given situation.
Complete multi step computations using two or more different operations with rational numbers.
Select and justify 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 mental computation with integers using powers and square roots.
Select, explain, and justify situations involving rational numbers where estimates are sufficient and others for which an exact value is required.
Use a variety of estimation strategies to predict results prior to computation.
Use a variety of estimation strategies 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 decimals, fractions, and integers, using +, -, x, ÷, powers, and square roots.