Grade 3 Practice Problems: Strategies
Expectations from Standards Revision and Strategy Description
3S-8c) Strategy: Guess, check and revise Answer: 18 tiger lilies, 33 dandelions
Zoobee has two kinds of flowers in his garden: dandelions and tiger lilies. Zoobee planted only tiger lilies, but dandelions came up too. There are 51 flowers in Zoobee's garden, and there are 15 more dandelions than tiger lilies. How many of the flowers are tiger lilies and how many are dandelions? Write to help explain your best thinking using words, numbers, or pictures.
3S-8b) Strategy: Guess, check and revise Answer: Danny 11 cents; Celia 26 cents
"Let's buy this frog mask," croaked Danny to Celia. The frogs both took out their money. Together they paid 37 cents for the mask. Celia paid 15 cents more than Danny did. How much money did each frog pay? Write to help explain your best thinking using words, numbers, or pictures.
3S-8a) Strategy: Guess, check and revise Answer: 25
I am thinking of a number. Add the number to itself. Then subtract 13. The answer is 37. What is the number? Write to help explain your best thinking using words, numbers, or pictures.
3S-7d) Strategy: Draw a picture Answer: 15
The kitten climbed its first tree and got stuck on the top branch. First it went up the trunk of the tree and on up to the 6th branch. A big squirrel scared the kitten and it climbed down 3 branches. A bird flew at the kitten and scared it again. Now it climbed up 10 branches. The kitten climbed back down 2 branches and then went up 4 branches to the very top of the tree. How many branches were in the tree? Write to help explain your best thinking using words, numbers, or pictures.
3S-7c) Strategy: Draw a picture Answer: 17
Jim is looking for friends to play softball. His friends all live on his side of the street. First he goes down the hill 4 houses to get Lenny. Lenny lives in the first house on the block. Then Jim goes up the hill 6 houses to get Raul. From here he goes down the hill 3 houses to find Terry. Next he goes up the hill 13 houses to get Renata. She lives in the last house on the block. How many houses are on Jim's side of the street in his block? Write to help explain your best thinking using words, numbers, or pictures.
3S-7b) Strategy: Draw a picture Answer: (path)
Juanita and Cole discovered a note in a bottle. It said, "Start at the Boat Dock on Toad Road. Go forward 3 blocks on Toad Road to Snake Street. Turn left and go forward 5 blocks to Snail Trail. Turn right and go forward 4 blocks to Mud Street. Stay there. Use your eyes. Look for a secret message under a big white rock." Can you show the path from the Boat Dock to the secret message? Write to help explain your best thinking using words, numbers, or pictures.
3S-7a) Strategy: Draw a picture Answer: (drawing)
Harvey started drawing a map for Sue, who wants to get to Al's house. Harvey said, "Here we are at the corner of Story Road and Long Street. Go forward 3 blocks on Long Street. Turn right on Bay Road and go forward 3 blocks. Turn left on Dry Street. Go forward 4 blocks to Lamb Road. Al's house is on the corner of Lamb Road and Dry Street." Can you show Sue's path to Al's house? Write to help explain your best thinking using words, numbers, or pictures.
3S-6b) Strategy: Act out the problem or use objects Answer: (drawings)
Marcy is making a big banner to hang on a wall. She has 3 red, 3 white stars, and 3 blue stars to put on the banner. She is going to put the stars in 3 rows and 3 columns. How can she place the stars so that she has a red star, a blue star, and a white star in each row and in each column? Write to help explain your best thinking using words, numbers, or pictures.
3S-6a) Strategy: Act out the problem or use objects Answer: (Cathy/Bobby) (Eric/Dorothy) (Abby/Forrest)
Donna was putting six new bears in the display case at the toy store. The case had three shelves, one on top of the other, with two spaces on each shelf. Each bear had a name: Abby, Bobby, Cathy, Dorothy, Eric, and Forrest. Donna put Dorothy next to Eric and above Forrest. She did not put Bobby next to Eric or Forrest. She did not put Abby next to Bobby. Where did Donna put each of the bears? Write to help explain your best thinking using words, numbers, or pictures.
3S-5i) Strategy: Make a table, chart, or organized list Answer: snail
A snail and a turtle both started out on Monday toward a pond 32 inches away. An owl was watching them and told us how far they were at the beginning of each day of the race. By Tuesday both the snail and the turtle had traveled 1 inch. By Wednesday the snail had traveled 2 inches and the turtle had crawled 7 inches. By Thursday the snail was 4 inches from the start, and the turtle was 13 inches from it. By Friday the snail was 8 inches from the start, and the turtle was 19 inches from it. If the snail and the turtle kept moving in the same ways, which one reached the pond first? Write to help explain your best thinking using words, numbers, or pictures.
3S-5h) Strategy: Make a table, chart, or organized list Answer: 24, 28, 42, 48, 82, 84
Anthony came home from school with a puzzle for his sister Teresa. He gave her three cards. One card had a 2 on it; one card had a 4 on it; and one card had an 8 on it. Anthony asked, "Teresa, how many 2-digit numbers can you make with these three cards?" Teresa surprised Anthony. She made six different 2-digit numbers. What numbers did Teresa make? Write to help explain your best thinking using words, numbers, or pictures.
3S-5g) Strategy: Make a table, chart, or organized list Answer: (12 answers)
Laura is buying a sundae at Mario's Ice Cream Store. She wants one scoop of ice cream, one kind of sauce, and one kind of topping. Here are the flavors of ice cream and kinds of sauces and toppings Laura can choose from: *Ice Cream: peanut butter, chocolate *Sauces: carmel, chocolate, strawberry *Toppings: nuts, coconut. What are all the different sundaes that Laura could order? Write to help explain your best thinking using words, numbers, or pictures.
3S-5f) Strategy: Make a table, chart, or organized list Answer: 18
The Chin family is planning a summer vacation. They are trying to decide whether to travel by plane, train, or car. They will go to Yosemite National Park, Yellowstone National Park, or the Grand different trips that the Chins could plan? Write to help explain your best thinking using words, numbers, or pictures.
3S-5e) Strategy: Make a table, chart, or organized list Answer: 6
Angelina's club is having a meeting. They have decided that everyone should have a secret number. They will use just the numerals 1, 3, and 5 in their numbers, but each number will be different. Each numeral can be used only once in any number. If they use all the different three-digit numbers that you can make with the numerals 1, 3, and 5, how many members does Angelina's club have? Write to help explain your best thinking using words, numbers, or pictures.
3S-5d) Strategy: Make a table, chart, or organized list Answer: 24
The Cars For Kings Company is putting out the new models. They want to put a 4-digit number on the back of each new model car. They have decided to use only the numerals 2, 5, 7, and 8. Each numeral can only be used once in a number. How many different numbers can the Cars For Kings Company put on the backs of the new model cars? Write to help explain your best thinking using words, numbers, or pictures.
3S-5c) Strategy: Make a table, chart, or organized list Answer: (several answers)
Carla and Nick were playing a factors game. Carla would name a factor of 24 and Nick had to give the other factor. Show the ways Carla and Nick could play the game. Write to help explain your best thinking using words, numbers, or pictures.
3S-5b) Strategy: Make a table, chart, or organized list Answer: AET,ATE,EAT,ETA,TAE,TEA - three
You have the three letters A,E, and T. List all the 3-letter combinations you can make using each letter once. How many of the combinations are actually words? Write to help explain your best thinking using words, numbers, or pictures.
3S-5a) Strategy: Make a table, chart, or organized list Answer: (list of 12 suppers)
At camp these are the choices for supper: * Meat: steak, trout * Potatoes: mashed, baked, French fries * Vegetable: corn, green beans. List the 12 different suppers a camper could choose. Write to help explain your best thinking using words, numbers, or pictures.
3S-4d) Strategy: Look for a pattern Answer: 6th day
On her first day of vacation, Angela found 2 sand dollars on the beach. She put them in an old sock. The next day she found 4 sand dollars, and she put them in her sock. On each day of her vacation, Angela found 2 more sand dollars than she had found the day before. On what day did she have 42 sand dollars in the sock? Write to help explain your best thinking using words, numbers, or pictures.
3S-4c) Strategy: Look for a pattern Answer: 4th hour
There were 30 campers in Crazy Creek Park on Saturday when it started to rain. In the first hour of rain, 3 campers took down their tents and went away. In the second hour, 6 campers took down their tents and left the park. The rain kept pouring down. Every hour 3 more campers left than during the hour before. In what hour did the last campers leave the park? Write to help explain your best thinking using words, numbers, or pictures.
3S-4b) Strategy: Look for a pattern Answer: 33
Mona is wearing her magic cape again. The first time she wore it, she found 5 pennies in a crack of the sidewalk. The next time she wore it, she discovered 9 pennies under an old barrel. The third time she wore it, she found 13 pennies in some sand. The fourth time she wore it, she discovered 17 pennies under the bleachers in a ball park. If Mona keeps finding pennies in this way, how many will she find when she wears her cape the eighth time? Write to help explain your best thinking using words, numbers, or pictures.
3S-4a) Strategy: Look for a pattern
Write the next three numbers in each sequence: *2,3,6,__,__,__ * 1,4,7,10,__,__,__ * 1,2,4,8,16,__,__,__ * 1,2,4,7,11,16,__,__,__ Write to help explain your best thinking using words, numbers, or pictures.
3S-3a) Strategy: Use logical reasoning Answer: $18
One crab and one shark cost the same as 4 crabs. If one crab costs $6, then how much does one shark cost? Write to help explain your best thinking using words, numbers, or pictures.
3S-2c) Strategy: Work backward Answer: 3
Porcupines, skunks, and opossums live in Wooly Woods. There are 5 fewer opossums than skunks, and half as many skunks as porcupines. When danger is near, the opossums lie down and play dead. The 16 porcupines raise their quills to frighten away their enemies. How many opossums live in Wooly Woods? Write to help explain your best thinking using words, numbers, or pictures.
3S-2b) Strategy: Work backward Answer: 4 lbs.
The Jolly Giant weighed some of the vegetables that grew in his garden. He weighed a tomato, an ear of corn, a turnip, and a carrot. The carrot was 8 pounds less than the turnip, and the turnip was 3 pounds more than the ear of corn. The ear of corn weighed half as much as the tomato. The Jolly Giant rolled the tomato onto the scale. It was 18 pounds! How much did the carrot weigh? Write to help explain your best thinking using words, numbers, or pictures.
3S-2a) Strategy: Work backward Answer: 40
Someone broke a bag of peanuts on Peep Street. Pigeons came from all over the city to feast on the peanuts. They ate lots of the nuts on Monday. They ate 2 fewer nuts on Tuesday than on Monday. They came back again on Wednesday, Thursday, and Friday. Each day they ate 2 fewer peanuts than the day before. On Friday they cleaned up the last 4 peanuts. How many peanuts in all did the pigeons eat? Write to help explain your best thinking using words, numbers, or pictures.
3S-1a) Strategy: Make it Simpler Answer: 34
Mr. and Mrs. Jeremy Mouse sell square tins of cheese buns in their shop. Right now they have 12 tins of buns in the shop. They stack the tins on the shelf, 2 tins in each stack, and the stacks touch sides. Every day Mr. Mouse dusts the sides of the tins that are not touching the shelf or another tin. How many sides must he dust on 12 tins of buns? Write to help explain your best thinking using words, numbers, or pictures.
Expectations of Core Processes from the 2008 Mathematics Standards Revision (draft) – Grade 3
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 physical objects, pictures, words, 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 (3S-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 (3S-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 (3S-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 (3S-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 (3S-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 (3S-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 (3S-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 (3S-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.