Grade 4 Practice Problems: Strategies
Expectations from Standards Revision and Strategy Description
4S-8d) Strategy: Guess, check and revise Answer: 31 silver, 18 copper
Ana has 49 copper and silver coins in her collection. She got quite a few of them on her birthdays. She has 13 fewer copper coins than silver coins in her collection. How many coins does she have of each kind? Write to help explain your best thinking using words, numbers, or pictures.
4S-8c) Strategy: Guess, check and revise Answer: Amy 7, Marcus 3.5
Together Alice and Mark walked a total of 10.5 miles in the School walk-a-thon. Alice walked twice as far as Mark and she had blisters to prove it. How many miles did Alice and Mark each walk? Write to help explain your best thinking using words, numbers, or pictures.
4S-8b) Strategy: Guess, check and revise Answer: 265 fish, 140 eels
In the huge fish tank there are fish and eels. There are 405 marine animals altogether, and there are 125 more fish than eels. How many marine animals of each kind are there? Write to help explain your best thinking using words, numbers, or pictures.
4S-8a) Strategy: Guess, check and revise Answer: 9
I am thinking of a number. Subtract 5. Then add 18. The answer is 22. What is the number? Write to help explain your best thinking using words, numbers, or pictures.
4S-7h) Strategy: Draw a picture Answer: (map)
Kim and Leadra programmed Rosie The Robot to travel around the school. They sent her out of their classroom, had her turn right and go straight down the hall 6 classrooms and then turn left. They had her go straight 4 classrooms and then turn right. She went ahead 6 classrooms and turned right. She went ahead 7 classrooms and then she suddenly stopped and started to beep! Can you draw a map and show where Rosie started to beep? Write to help explain your best thinking using words, numbers, or pictures.
4S-7g) Strategy: Draw a picture Answer: 20
The big old house in the center of town was called the House of Stairs. Years ago, someone who was crazy about stairs built the house with 4 different stairways from the first floor to the second floor, and 5 different stairways from the second floor to the third floor. How many different ways could you get to the third floor from the first floor in the House of Stairs? Write to help explain your best thinking using words, numbers, or pictures.
4S-7f) Strategy: Draw a picture Answer: 16
The Riverboat Kids explore rivers. This summer they went from one end of Pepper River to the other. They started out at Duck Harbor and rowed 7 miles south to one end of the river. The next day they rowed 9 miles north to Rooster Cove. When a storm came up, they turned around and rowed 5 miles south to Scooter Park. They camped there overnight. The next day they rowed 12 miles north to the other end of the river. How many miles long is Pepper River? Write to help explain your best thinking using words, numbers, or pictures.
4S-7e) Strategy: Draw a picture Answer: 12
Marty and Ramon want to ride the new Skystreak roller coaster at the amusement park. The boys can go into the park through three different gates. They must stop at the main ticket booth that is just inside the gates, and they can take four different walkways from the ticket booth to the Skystreak. How many different paths can Marty and Ramon take from outside the park to the Skystreak? Write to help explain your best thinking using words, numbers, or pictures.
4S-7d) Strategy: Draw a picture Answer: 10
A model of a dinosaur stands in a glass case in a museum. Its four legs and tail touch the floor. Last night a mouse went through one of the two doors into the glass case. The mouse ran up one of the dinosaur's legs, onto the body, and up the neck to its head. How many different paths could the mouse take from outside the glass case up to the dinosaur's head? Write to help explain your best thinking using words, numbers, or pictures.
4S-7c) Strategy: Draw a picture Answer: 8 steps
A fireman stood on the middle step of a ladder. As the smoke cleared, he climbed up three steps. The fire got worse so he had to climb down five steps. Then he climbed up the last six steps and was at the top of the ladder. How many steps were in the ladder? Write to help explain your best thinking using words, numbers, or pictures.
4S-7b) Strategy: Draw a picture Answer: (drawing)
From a large sheet of postage stamps, three attached stamps can be torn off in six different ways. Make drawings to show the six ways. Write to help explain your best thinking using words, numbers, or pictures.
4S-7a) Strategy: Draw a picture Answer: Bobbi Sue, Dobbin, Electricity, Crazyhorse, AppleEater
In a horse race: Crazyhorse finished 1 length ahead of AppleEater. AppleEater was not the last place horse. BobbiSue finished 7 lengths ahead of Electricity. Crazyhorse finished 7 lengths behind Dobbin. Electricity finished 3 lengths behind Crazyhorse. What was the finishing position of each horse? Write to help explain your best thinking using words, numbers, or pictures.
4S-6c) Strategy: Act out the problem or use objects Answer: (orange-blue-green) (red-pink-yellow)
Mandy folded her T-shirts and put them in two stacks in her drawer. She put three T-shirts in each stack. She put the green shirt under the blue shirt. She put the yellow shirt on the right side of the green shirt. She put the orange shirt on top of the blue shirt. Finally Mandy put the pink shirt between the yellow shirt and the red shirt. Where did Mandy put each T-shirt in her drawer? Write to help explain your best thinking using words, numbers, or pictures.
4S-6b) Strategy: Act out the problem or use objects Answer: top (Dominoes-Crazy Cards-Chinese Checkers); bottom (Beetles-Chess-Sly Spy)
Rico keeps his games on a shelf that makes a 2x3 grid in his wall. Sly Spy is below of Chinese Checkers. His Chess game is on the left side of Sly Spy. Crazy Cards is between Chinese Checkers and Dominoes. Dominoes is above the Beetles game. Where is each game on Rico's shelf? Write to help explain your best thinking using words, numbers, or pictures.
4S-6a) Strategy: Act out the problem or use objects Answer: (drawings)
Here are 9 hamburgers on a 3x3 grill. One hamburger has cheese on it in the upper left corner. Put cheese on 5 more hamburgers, but be sure to leave 1 hamburger without cheese in each row and in each column. Which hamburgers did you put cheese on? Write to help explain your best thinking using words, numbers, or pictures.
4S-5k) Strategy: Make a table, chart, or organized list Answer: 4
With my new spray formula, trees grow 1 foot a day and ferns grow 2 feet a day. Today I found a trees 1 foot high and a fern 7 feet high. In how many days will the fern be three times as high as the tree? Write to help explain your best thinking using words, numbers, or pictures.
4S-5j) Strategy: Make a table, chart, or organized list Answer: eleven 15-pt.; five 10-pt.
Big Burger is giving away gold and silver coupons. The gold coupons are worth 15 points and the silver coupons are worth 10 points. Owen is saving coupons so he can get free Super-Big Burgers. So far Owen has coupons worth 215 points. How many gold coupons and how many silver coupons does Owen have? Write to help explain your best thinking using words, numbers, or pictures.
4S-5i) Strategy: Make a table, chart, or organized list Answer: 8 pounds
Three boxes of 4 lb. Snake Powder weighs the same as one box of 4 lb. Snake Powder and a can of Lizard Tears. How many pounds does one can of Lizard Tears weigh? Write to help explain your best thinking using words, numbers, or pictures.
4S-5h) Strategy: Make a table, chart, or organized list Answer: 5 red coupons - 6 green coupons
Kara and Dora are collecting red coupons and green coupons from cereal boxes. The red coupons are worth 5 points and the green coupons are worth 2 points. As soon as they have coupons worth 50 points, they can send in for a prize. Right now they have 11 coupons that are worth 37 points. How many coupons of each color do they have? Write to help explain your best thinking using words, numbers, or pictures.
4S-5g) Strategy: Make a table, chart, or organized list Answer: (62, 66, 67, 68, 72, 76, 77, 78, 82, 86, 87, 88)
The people in the Land of Few make up their own telephone numbers. The only numerals they use are 2, 6, 7, and 8. Their telephone numbers are two digits long. This is what the telephone book looks like now: (Name, Telephone Number)(Adams,22) (Bears, 26) (Cricket, 27) (Dim, 28) What other telephone numbers can be made by the people in the Land of Few? Write to help explain your best thinking using words, numbers, or pictures.
4S-5f) Strategy: Make a table, chart, or organized list Answer: 35
Marvin Monkey wanted to start a school. So he counted all the young monkeys in his jungle. When Marvin finished counting, he gave these clues:
There were more than 25.
There were fewer than 40.
I said the number when I counted by fives.
I didn't say the number when I counted by tens.
How many young monkeys did Marvin count? Write to help explain your best thinking using words, numbers, or pictures.
4S-5e) Strategy: Make a table, chart, or organized list Answer: 6 pounds
Carol's cat weighs 2 pounds. Doug's dog weighs 14 pounds. Both pets are gaining about a pound a month. If they keep on gaining weight like that, the dog will soon weigh three times as much as the cat. How many pounds will the cat weigh then? Write to help explain your best thinking using words, numbers, or pictures.
4S-5d) Strategy: Make a table, chart, or organized list Answer: 6
Meredith got on the bus and dropped her coins into the money meter. Her bus fare was 15 cents. How many different groups of coins could Meredith have used to pay for her bus fare? Write to help explain your best thinking using words, numbers, or pictures.
4S-5c) Strategy: Make a table, chart, or organized list Answer: 27
I need to decide what to do with my friends. We can bike, walk, or go by skateboard to the park. We can go swimming, play catch, or fly a kite at the park. Then we will go get ice cream, popcorn, or a soda. What are all the different plans we can make for afternoon? Write to help explain your best thinking using words, numbers, or pictures.
4S-5b) Strategy: Make a table, chart, or organized list Answer: in 5 years
Mike is 4 years old and Andy is 13 years old. When will Andy be twice as old as Mike? Write to help explain your best thinking using words, numbers, or pictures.
4S-5a) Strategy: Make a table, chart, or organized list Answer: 800, 802, 804, 806, 808, 810, 812, 814, 816, 818, 900, 902, 904, 906, 908, 910, 912, 914, 916, 918
Pat was playing "Guess the Number" and gave these clues: üThe number has 3 digits. üThe digit in the 100's place is greater than 7. üThe digit in the 10's place is less than 2. ü The number is even. What are the possibilities for the number? Write to help explain your best thinking using words, numbers, or pictures.
4S-4e) Strategy: Look for a pattern Answer: Saturday
At noon on Monday, 51 caterpillars met for lunch on the leaves of the old tree. On Tuesday, only 42 caterpillars came to the tree for lunch (The rest of the caterpillars were building cocoons.) On Wednesday, only 33 caterpillars came to the tree. The number of caterpillars coming for lunch kept decreasing in the same way each day. On what day did only 6 caterpillars come to the tree? Write to help explain your best thinking using words, numbers, or pictures.
4S-4d) Strategy: Look for a pattern Answer: 7
I had 500 jellybeans and hand out 50 jellybeans on the first day of the month. On the second day I hand out 62 jellybeans, 12 more than the first day. On the third day they hand out 74 jellybeans, 12 more than the second day. If I hand out all the jellybeans at this rate, how many days will it take to hand them all out? Write to help explain your best thinking using words, numbers, or pictures.
4S-4c) Strategy: Look for a pattern Answer: 12
Yolanda and Willie found that they were getting more and more snails in their garden. On the first day they counted 9 snails, then on the second day there were 17. On the third day they counted 24, 32 on the fourth day, and 39 on the fifth day. On what day did they count more than 90 snails? Write to help explain your best thinking using words, numbers, or pictures.
4S-4b) Strategy: Look for a pattern Answer: The sum of the first two numbers equals the third number; 12, 14, 12
Find a rule that gives the third number from the first two numbers. Fill in the blanks: ü 8, 3, 11 ü9 , 5, 14 ü 4,8,___ ü6,__, 20 ü __, 7, 19 Write to help explain your best thinking using words, numbers, or pictures.
4S-4a) Strategy: Look for a pattern Answer: Find the difference between the first two numbers then subtract 1 to get the third number (9, 6, 23)
Find a rule that gives the third number from the first two numbers. Fill in the blanks: ü10,4,5 ü 15,7,7 ü19,9,__ ü7,__,0 ü __,11,11 Write to help explain your best thinking using words, numbers, or pictures.
4S-3e) Strategy: Use logical reasoning Answer: fish-cups; snail-can; crab-sneaker; worm-bottle
An old sneaker, a cup, a bottle, and a can fell off Drew's Dock and dropped to the bottom of the water. Along came a fish, a snail, a crab, and a worm who were looking for homes. The worm slithered into the bottle. The crab crawled into the sneaker. The fish wouldn't go near the can. What did each sea animal choose as its home? Write to help explain your best thinking using words, numbers, or pictures.
4S-3d) Strategy: Use logical reasoning Answer: Sheldon-space; Lorna-lemon; Della-banana; Jess-apple
Sheldon, Lorna, Della, and Jess each ate a different kind of muffin for breakfast this morning. Their mother had put four different muffins on the table: apple, banana, lemon, and spice. Lorna ate the lemon muffin. Jess hates banana flavor, and Sheldon doesn't like any fruit flavors. Which muffin did each child eat? Write to help explain your best thinking using words, numbers, or pictures.
4S-3c) Strategy: Use logical reasoning Answer: Gina-animal trainer, Evan-clown, Amelia-juggler, Collin-trapeze artist
Alice, George, Evan, and Collin were dreaming about the circus. They wanted to be an animal trainer; a clown, a juggler; and a trapeze artist. George is training her dog to be a seeing-eye dog for the blind. Evan is always telling jokes, and Alice is afraid of heights. Which job in the circus do you think each friend would choose? Write to help explain your best thinking using words, numbers, or pictures.
4S-3b) Strategy: Use logical reasoning Answer: $7
At the dime store, 3 planea and one bird-cage cost the same as 5 planea. If one plane costs $3.50, then what does a bird-cage cost? Write to help explain your best thinking using words, numbers, or pictures.
4S-3a) Strategy: Use logical reasoning Answer: glok, yuk, bah, ick, ugh
A yuk is more than an ugh. A bah is not the least of the whole group. A yuk is not the greatest. Only one thing is less than an ick. A glok is more than a bah. More than one thing is greater than a bah. Put the yuk, ugh, bah, ick, and glok in order from largest to smallest. Write to help explain your best thinking using words, numbers, or pictures.
4S-2b) Strategy: Work backward Answer: 55
The Kingdom of Ketchupia is famous for its tomato sauce. One day the recipe for the sauce disappeared. The king ordered some of his Red Knights to search throughout the kingdom for the recipe. They did not return. On the second day the king sent out 4 more knights than he had sent out the first day. Each day the king kept sending out 4 more knights than he had sent the day before. Nineteen knights left the castle on the fifth day. How many knights in all did the king send out into his kingdom? Write to help explain your best thinking using words, numbers, or pictures.
4S-2a) Strategy: Work backward Answer: 3
I saw three more rabbits than birds. I saw one half as many birds as kittens. There were one third as many kittens as puppies. I took a long look at the 36 cute puppies. How many animals did I look at altogether? Write to help explain your best thinking using words, numbers, or pictures.
4S-1b) Strategy: Make it Simpler Answer: 20
I have 6 blocks together in a row on a table and spray paint on the blocks. Every block has 6 sides. The sides that touch the table or sides of other blocks don't get painted. How many sides of the blocks in a row get painted? Write to help explain your best thinking using words, numbers, or pictures.
4S-1a) Strategy: Make it Simpler Answer: 44
We are having a party and are putting square tables together in a long row for the party. We can put two chairs on each side of a table. The tables are all the same size. If we put together ten tables in a row, how many people can sit down? Write to help explain your best thinking using words, numbers, or pictures.
Expectations of Core Processes from the 2008 Mathematics Standards Revisions 9draft) - Grade 4
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 (4S-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 (4S-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 (4S-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 (4S-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 (4S-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 (4S-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 (4S-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 (4S-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.