Grade 5 Practice Problems: Strategies
Expectations from Standards Revision and Strategy Description
5S-8d) Strategy: Guess, check and revise Answer: 6 crayfish & 4 turtles; 6 crayfish & 9 turtles; 2 crayfish & 14 turtles
Oozy Pond is filled with crayfish and mud turtles who are there for an egg-laying contest. Betsy Beaver says she doesn't know how many crayfish and turtles there are, but she counted 76 legs in all. Each crayfish has 10 legs, and each turtle has 4 legs. How many crayfish and how many turtles could there be in Oozy Pond? Write to help explain your best thinking using words, numbers, or pictures.
5S-8c) Strategy: Guess, check and revise Answer: Monica 75; Marty 30
Monica and Marty are llamas at the petting zoo. They like to count their visitors, and the number of people who pet them. After visiting hours on Sunday Monica reported that 105 people in all had petted both of them. She bragged that 2 1/2 times as many people petted her as petted Marty. How many people petted Monica and how many petted Marty? Write to help explain your best thinking using words, numbers, or pictures.
5S-8b) Strategy: Guess, check and revise Answer: 45 tomato plants, 7 pumpkin vines
The gremlins' garden has special tomato plants and pumpkin vines. Every tomato plant has 5 tomatoes on it and every pumpkin vine has 4 pumpkins on it. If the gremlins have a total of 253 tomatoes and pumpkins in their garden, how many tomato plants and how many pumpkin vines do they have? Write to help explain your best thinking using words, numbers, or pictures.
5S-8a) Strategy: Guess, check and revise Answer: 14
I am thinking of a number. Multiply the number by 2. Then add 11. The answer is 39. What is the number? Write to help explain your best thinking using words, numbers, or pictures.
5S-7e) Strategy: Draw a picture Answer: 12
Zork is looking for friends to play spaceball. His friends all live in his galaxy. Zork leaves his planet and flies 5 planets west to get Zeek. Zeek lives on the first planet in the galaxy. Then Zork flies east 8 planets to get Zook. From here he flies west 6 planets to find Zurk. Then he flies east 9 planets for Zack. Zack lives on the last planet in the galaxy. How many planets are in Zork's galaxy? Write to help explain your best thinking using words, numbers, or pictures.
5S-7d) Strategy: Draw a picture Answer: (map)
The animals were having a meeting at the Big Oak. Roger gave Rachel Raccoon directions to the Big Oak from the tallest redwood tree. "Stand to the left of the redwood tree. Go ahead 6 trees, turn right and go ahead 9 trees and then turn left. Go straight until you see the eagle's nest, which is in the 12th tree ahead on your left. Turn left there and look for the mark a hunter made on the tree, 4 trees ahead on your left. Look to your right and you'll be at the Big Oak." Can you make a map to show how Rachel got to the Big Oak? Write to help explain your best thinking using words, numbers, or pictures.
5S-7c) Strategy: Draw a picture Answer: 36
Hugo the Horrible lived in a castle with a moat around it. Anyone who had to see him could enter the castle yard over 3 different drawbridges. From the castle yard they could enter the castle through 4 different gates. Finally, they could go into Hugo's throne room through 3 different doors. How many different ways could some poor unfortunate person take from outside the moat to Hugo's throne room? Write to help explain your best thinking using words, numbers, or pictures.
5S-7b) Strategy: Draw a picture Answer: 27 minutes
Your mother asked you to cut a 20 foot long log into 10 equal lengths for the fireplace. How long will it take you if each cut takes 3 minutes? Write to help explain your best thinking using words, numbers, or pictures.
5S-7a) Strategy: Draw a picture
Two hunters came to a river. They met three youngsters who had a small boat. The boat could hold two youngsters or one adult. How did all five persons get across the river? How many trips will be necessary? Write to help explain your best thinking using words, numbers, or pictures.
5S-6c) Strategy: Act out the problem or use objects Answer: (orange juice-ice cream-pizza)/(vegetables-French fries-fish)
Dana's mother was telling her where to find things in the six sections of aisle E at the supermarket. Her mother said that the orange juice and pizza were at opposite ends of the same side of the aisle. She said the fish was across from the pizza and next to the French fries. She said the vegetables were not on the same side as the pizza. Where did Dana find the pizza, French fries, ice cream, orange juice, fish, and vegetables on aisle E? Write to help explain your best thinking using words, numbers, or pictures.
5S-6b) Strategy: Act out the problem or use objects Answer: (sketch)
Ingrid and Kirsten are making the art room very colorful. They are painting one wall with squares of red, green, blue, and yellow. They divided the wall into 4 columns with 4 rows. Before painting they marked each square with an R, G, B, or Y. They didn't want any color to be repeated in the same row or in the same column. How did Ingrid and Kirsten arrange the colors in the squares on the wall? Write to help explain your best thinking using words, numbers, or pictures.
5S-6a) Strategy: Act out the problem or use objects
Ashley is a spy and she knows she is being watched. This week she has to meet with 5 spies: A, B, C, D, and E. She has to meet with each spy for one hour every day and she wants to make sure that she doesn't meet with the same spy at the same hour on any other day of the week. She will meet with them between 9:00 and 2:00. What is one way Ashley could meet with the spies this week? Write to help explain your best thinking using words, numbers, or pictures.
5S-5m) Strategy: Make a table, chart, or organized list Answer: 9
Dr. Feather is trying to find out how many birds are feeding in the marsh. The first week he counts 5 long-necked farlings and 5 short-beaked fuzzlings. The next week he counts 10 farlings and 6 fuzzlings. In the third week he counts 14 farlings and 8 fuzzlings. In the fourth week he sees 19 farlings and 11 fuzzlings. At the end of the fifth week he counts 23 farlings and 15 fuzzlings. When did Dr. Feather count the same number of farlings and fuzzlings again, if the birds continue coming at the same rate? Write to help explain your best thinking using words, numbers, or pictures.
5S-5l) Strategy: Make a table, chart, or organized list Answer: August
Guests at the Shadow Inn have reported seeing ghosts in room F and in S, the attic room. In January, 7 people reported seeing a ghost in room F and 7 people reported seeing a ghost in room S. In February, there were 12 reports for room F and 9 reports for room S. In March, 11 people reported a ghost in room F and 12 reported a ghost in room S. In April, there were 16 reports for room F and 14 for room S. And in May they had 15 reports for room F and 17 for room S. If the reports continued at this same rate, what would be the next month that they would have the same number of ghosts reported for room F and room S? Write to help explain your best thinking using words, numbers, or pictures.
5S-5k) Strategy: Make a table, chart, or organized list Answer: 8 witches; 5 ghosts
At the Halloween Carnival Tora is throwing balls at witches and ghosts. She gets 5 points for every witch she hits and she gets 8 points for every ghost. She can win a black cat by getting 100 points. Tora has hit 13 witches and ghosts altogether and she has 80 points. How many ghosts and how many witches did she hit? Write to help explain your best thinking using words, numbers, or pictures.
5S-5j) Strategy: Make a table, chart, or organized list Answer: 6 toads - 4 frogs
"Warty Toads and Smooth Frogs. I will pay 3 cents for each toad, and 5 cents for each frog." claimed Professor Q in a news ad. Bert and Bruno saw the professor's ad, so they brought a sack of 10 toads and frogs to her. The professor looked at the animals and then gave the boys 38 cents. How many of the animals were toads and how many were frogs? Write to help explain your best thinking using words, numbers, or pictures.
5S-5i) Strategy: Make a table, chart, or organized list Answer: 33
The guards of Clock Castle open the two gates at the same time every hour to let visitors go into the castle. The guards keep track of how many people they let in through their gates. This is what they wrote today: (King-Queen Gates) -- 8 am (1-1), 9 am (5-4), 10 am (9-9), 11 am (13-12), 12:00 (17-17). The guards kept letting visitors go into the castle in the same ways all day. How many visitors went through Queen's Gate at the time that 33 visitors went through King's Gate? Write to help explain your best thinking using words, numbers, or pictures.
5S-5h) Strategy: Make a table, chart, or organized list Answer: 5 years old
Ellen is 10 years old now and Cheryl is 15. A few years ago, when Cheryl was twice as old as Ellen, Cheryl taught Ellen how to swim. How old was Ellen when she learned to swim? Write to help explain your best thinking using words, numbers, or pictures.
5S-5g) Strategy: Make a table, chart, or organized list Answer: 45
Ariel rides the Starlight Express from Misty Station to her home. The Starlight Express zooms past 100 stars an hour. Ariel will not tell us how far her home is from Misty Station, but she did give us these clues: Ú I ride past more than 39 stars. Ú I ride past fewer than 48 stars. Ú I ride past an odd number of stars. Ú One part of the number tells how many letters there are in my name. How many stars does Ariel pass on her way home? Write to help explain your best thinking using words, numbers, or pictures.
5S-5f) Strategy: Make a table, chart, or organized list Answer: 8
Julio is mailing a small package to Tony, who lives in another city. Julio has to put 18 cents worth of stamps on the package. Julio has 10 cent stamps, 4 cent stamps, and 2 cent stamps that he can use. How many different groups of stamps could Julio use on his package? Write to help explain your best thinking using words, numbers, or pictures.
5S-5e) Strategy: Make a table, chart, or organized list Answer: 80
One summer Osha kept a record of how many kilometers she rode on her skateboard. She won't tell what the number is but she will give you these clues: Ú It is less than 100. Ú It is more than 44. Ú If you count by 4s, you say the number's name. Ú The number can be divided evenly by 5 and 8. How many kilometers did Osha go on her skateboard? Write to help explain your best thinking using words, numbers, or pictures.
5S-5d) Strategy: Make a table, chart, or organized list Answer: 160
In the movie "The Secret Step" the heroine, Pauline, is at the bottom of a pyramid. She has a note that tells her to climb the pyramid, carefully counting the steps. When she has climbed a special number of steps, she should look for a loose stone. Behind the stone is the treasure map. The note gives Pauline clues about the special number of steps she should climb up: üThere are more than 125. üThere are fewer than 180. üIf you count by 5s, you say the number's name. üThe number can be divided evenly by 4 and 8. How many steps did Pauline climb up? Write to help explain your best thinking using words, numbers, or pictures.
5S-5c) Strategy: Make a table, chart, or organized list Answer: 6
"We're hungry!" yelled Martina's sister and brothers. "Where are the pancakes?" Martina didn't pay any attention. She was trying to figure out how to measure out 24 ounces of milk. She had 3 different cans, marked 12 ounces, 6 ounces, and 4 ounces. Each can had just one number marked on it. How many different ways could Martina measure 24 ounces of milk? Write to help explain your best thinking using words, numbers, or pictures.
5S-5b) Strategy: Make a table, chart, or organized list Answer: 12
Allen was at a neighborhood garage sale. He was standing at a table with all sorts of comic books divided into 3 piles. One pile was marked 10 cents, the second 5 cents, and the third 1 cent. Allen had 26 cents. How many different combinations of comic books could Allen buy for 26 cents? Write to help explain your best thinking using words, numbers, or pictures.
5S-5a) Strategy: Make a table, chart, or organized list
You have a penny, a nickel, a dime, and a quarter. What amounts can you make if you use 1,2,3, or 4 of the coins? Write to help explain your best thinking using words, numbers, or pictures.
5S-4c) Strategy: Look for a pattern Answer: 7
"The Monsters of Muzz" opened on Monday. The first day there were 25 people who saw the movie. Word got out and on the second day 17 more people came than on the first day, so that 67 people had seen the movie after the second day. On the third day 59 people came, 17 more than on the second day. If each day 17 more people saw the movie than the day before, on what day would 500 people have seen the movie? Write to help explain your best thinking using words, numbers, or pictures.
5S-4b) Strategy: Look for a pattern Answer: 76
In Furland, the king of the Fuzzies was sad to hear that there was an outbreak of flu. On the first day 58 Fuzzies came down with the flu. On the second day 68 Fuzzies got sick, and 60 got sick on the third day. On the fourth day 70 Fuzzies got sick, and 62 new cases were reported on the fifth day. If the Fuzzies kept getting the flu at this same rate, how many Fuzzies would come down with the flu on the 10th day? Write to help explain your best thinking using words, numbers, or pictures.
5S-4a) Strategy: Look for a pattern
Find answers for 1x8+1=____, 12x8+2=___, 123x8+3=___, 1234x8+4=___. Predict the answer for 123,456x8+6=_____. Write to help explain your best thinking using words, numbers, or pictures.
5S-3c) Strategy: Use logical reasoning Answer: Luis-"Trolls From Outer Space," Trina-"Singing in the Snow," Ai-"The Yellow Ghost," Roxanne-"The Lost Pelican"
Trina, Avi, Luis, and Roxanne are trying to decide whether to go see "Trolls From Outer Space, The Lost Pelican," "The Yellow Ghost," or "Singing In The Snow." Luis loves to read books on science fiction. Trina likes singing and dancing in the school plays, and Roxanne hates scary programs on television. Which movie do you think each one of them would choose? Write to help explain your best thinking using words, numbers, or pictures.
5S-3b) Strategy: Use logical reasoning Answer: 36 oz
There are cans and bottles of Lemon Lite at the store. 2 cans and one bottle of Lemon Lite weigh the same as 5 cans of Lemon Lite. If a can of Lemon Lite weighs 12 ounces, then what does a bottle of Lemon Lite weigh? Write to help explain your best thinking using words, numbers, or pictures.
5S-3a) Strategy: Use logical reasoning
Larry, Curly, and Moe left the theater together. Each one was wearing the jacket and the shoes of someone else. Curly was wearing Moe's jacket and Larry's shoes. Whose jacket and whose shoes was each one wearing? Write to help explain your best thinking using words, numbers, or pictures.
5S-2c) Strategy: Work backward Answer: 4 lbs
North Park was filled with people one Saturday. There were one third as many people skateboarding as there were biking. There were twice as many people biking as there were skating. There were one fourth as many people skating as there were playing softball. North Park was a popular place for softball. There were 60 people playing softball. How many people were skateboarding, biking, and skating? Write to help explain your best thinking using words, numbers, or pictures.
5S-2b) Strategy: Work backward Answer: 40
Slowly Katie peeked around the door. The huge monster wiped its mouth, smiled, went to sleep, and started to snore. Katie had been watching while the monster ate the cakes in the bakery. The first hour it ate 21 of all the cakes in the bakery; the second hour it ate 21 of all the cakes left; the third hour it ate 21 of what was left; and the fourth hour it ate 21 the cakes left again. Now there are 3 cakes left. How many cakes did the monster eat? Write to help explain your best thinking using words, numbers, or pictures.
5S-2a) Strategy: Work backward Answer: 150
Six lords came to live in the city of Gimiro. The first lord built himself a tower. The second lord built a tower that was 6 feet higher than the first lord's tower. The third lord built a tower 6 feet taller than the second lord's tower. Each lord built a tower 6 feet taller than the tower built by the lord before him. The sixth lord's tower was 40 feet high. If the six towers were piled on top of each other, how high would they reach? Write to help explain your best thinking using words, numbers, or pictures.
5S-1a) Strategy: Make it Simpler Answer: 344
Priscilla Pig loves pink. Everything she has is pink. She just built a brick wall and she is going to paint it pink. The wall has 14 bricks across and is 11 bricks high. She is going to paint each side of the bricks that are facing out. How many sides will Priscilla have to paint? Write to help explain your best thinking using words, numbers, or pictures.
Expectations of Core Processes from the 2008 Mathematics Standards Revision (draft) – Grade 5
Analyze a problem to determine the question(s) to be answered. Identify information that is essential, missing, or extraneous in order to solve a problem. Select and use strategies and procedures to find solutions to problems. Represent a problem using words, numbers, pictures, physical objects, or symbols. Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question. Recognize when a previously used solution process can be applied in a new context. Use informal and mathematical language to explain why certain strategies or procedures were used to find a solution. Example:
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GUESS, CHECK, AND REVISE (5S-8 …)
Guessing and checking is helpful when a problem presents large numbers or many pieces of data, or when the problem asks students to find one solution but not all possible solutions to a problem. When students use this strategy, they guess the answer, test to see if it is correct and if it is incorrect they make another guess using what they learned from the first guess. In this way, they gradually come closer and closer to a solution by making increasingly more reasonable guesses. Students can also use this strategy to get started, and may then find another strategy which can be used.
DRAW A PICTURE (5S-7 …)
For some students, it may be helpful to use an available picture or make a picture or diagram when trying to solve a problem. The representation need not be well drawn. It is most important that they help students understand and manipulate the data in the problem.
ACT IT OUT OR USE OBJECTS (5S-6 …)
Some students may find it helpful to act out a problem or to move objects around while they are trying to solve a problem. This allows them to develop visual images of both the data in the problem and the solution process. By taking an active role in finding the solution, students are more likely to remember the process they used and be able to use it again for solving similar problems.
MAKE AND USE AN ORGANIZED LIST, TABLE, CHART OR GRAPH (5S-5 …)
Making an organized list, table, chart or graph helps students organize their thinking about a problem. Recording work in an organized manner makes it easy to review what has been done. Students keep track of data, spot missing data, and identify important steps that must yet be completed. It provides a systematic way of recording computations. Patterns often become obvious when data is organized. This strategy is often used in conjunction with other strategies.
LOOK FOR A PATTERN (5S-4 …)
A pattern is a regular, systematic repetition. A pattern may be numerical, visual, or behavioral. By identifying the pattern, students can predict what will "come next" and what will happen again and again in the same way. Sometimes students can solve a problem by recognizing a pattern, but often they will have to extend a pattern to find a solution. Making a number table often reveals patterns, and for this reason is frequently used in conjunction with looking for patterns.
USE LOGICAL REASONING (5S-3 …)
Logical reasoning is really used for all problem solving. However, there are types of problems that include or imply various conditional statements such as, "if.. then," or "if.. then.. else," or "if something is not true, then...” The data given in the problems can often be displayed in a chart or matrix. This kind of problem requires formal logical reasoning as a student works his or her way through the statements given in the problem.
WORK BACKWARD (5S-2 …)
To solve certain problems, students must make a series of computations, starting with data presented at the end of the problem and ending with data presented at the beginning of the problem.
SOLVE A SIMPLER OR A SIMILAR PROBLEM (5S-1 …)
Making a problem simpler may mean reducing large numbers to small numbers, or reducing the number of items given in a problem. The simpler representation of the problem may suggest what operation or process can be used to solve the more complex problem.