Grade 1 Practice Problems: Reasoning, Problem Solving & Communication
Expectations from Standards Revision and Strategy Description
1P-46) Directions for Drawing: Tell students they may use the following shapes to represent the
hat 
skirt 
and blouse
1P-45) Fiona has a green hat and a purple hat. She has a white blouse and a red blouse. She also has a yellow skirt and a brown skirt. Fiona is amazed at the number of outfits she can create by combining her new clothes. How many different hat, blouse, and skirt outfits could Fiona wear? Draw all the outfits.
1P-44) There are 5 cats on a fence. There are 3 cats in the tree. Jeff says there are 2 cats in all. Kate says there are 8 cats in all. Who is right? How do you know?
1P-43) Write a subtraction number story about these cats. Tell where each number came from.
1P-42) Use the number 10. Write an addition story problem that has the number 10 for the answer.
1P-41) Finish this story. Fill in the blanks with numbers so the story makes sense.
There were 8 birds on a fence.
There was a loud noise, so ____________ birds flew away.
There were ____________ birds left on the fence.
Draw a picture to show your story.
1P-40) Make pictures of a man, pig, and a dog. Which one doesn't belong? Why?
1P-39) Jess and Jed jog. Jim and Jill jump. Jeff and Jen just sit. How many children in all?
1P-38) 9 fish swim in a tank. 7 fish are red. The rest are black. How many fish are black?
1P-37) Chet chops 6 logs. Chad chops 2 more logs than Chet chops. How many logs does Chad chop?
1P-36) Jeff ate 3 pancakes. Russ ate 1 more pancake than Jeff ate. Rachel didn't eat any pancakes. How many pancakes were eaten?
1P-35) Max, Tom, and Sam have a contest. Max is the fastest. Sam is the slowest. Who arrives first? Who arrives last?
1P-34) Make pictures of a frog, a crab, and a crib. Which two go together and why?
1P-33) 8 men sit in a boat. To float, the boat can only hold 6 men. How many men need to get off the boat?
1P-32) 3 men slowly row a big boat. Each man has 2 paddles. How many paddles are in the boat?
1P-31) We need 5 kids for a basketball team. We have 4 kids. How many more kids do we need?
1P-30) Jared planted 5 bean plants and 3 pepper plants. Hank planted 2 bean plants and 4 pepper plants. Jed planted 1 bean plant and 6 pepper plants. Who planted the most plants?
1P-29) 4 whales swim in the sea. 2 little fish are swimming next to each whale. How many little fish are there?
1P-28) Tim has 3 lemons and 4 melons. Van has 2 lemons and 3 melons. Wes has 1 lemon and 7 melons. Who has the most fruit? Who has the least?
1P-27) It takes 2 pilots to fly each big airplane. 4 airplanes are ready for takeoff. How many pilots do we need?
1P-26) Barbara picked 3 red flowers, 2 purple flowers, and 1 pink one. She gave Kim 2 red flowers and 1 purple one. How many flowers does Barbara have left?
1P-25) Dad boils water for hot chocolate. 4 boys each want to drink 2 cups of hot chocolate. How much water must Dad boil?
1P-24) The robin has 4 babies in the nest. She brings 8 worms back to the nest. If each baby gets an equal number of worms, how many worms does each baby get?
1P-23) We are playing volleyball. The red team has 5 children. The blue team has 7 children. How can we make the volleyball teams equal?
1P-22) We are drinking milkshakes. Each of us wants 2 straws. There are 3 of us. How many straws do we need?
1P-21) Wayne had 9 dollars in his wallet. He spent 3 dollars at the toy store. He spent 1 dollar at the candy store. He bought a book for 4 dollars. He wanted to buy a kite for 2 dollars. Did he have enough money?
1P-20) Betsy is tiny. Randy is little. Sally is bigger, and Tony is the biggest. Is Randy littler than Sally?
1P-19) We have 8 trees in the orchard. 2 are apple trees, 3 are peach trees, and the rest are orange trees. How many trees are orange trees?
1P-18) The king has a golden crown. There are 2 emeralds at each point on the crown. The crown has 5 points. How many emeralds are in the crown?
1P-17) Ann has 8 dollars. She spent 3 dollars on lunches, 2 dollars on bus fare, and 1 dollar on flowers. How much money does she have left?
1P-16) Planes were at the airport. 8 planes were taking off. 6 planes were landing. How many more planes were taking off than landing?
1P-15) Fern wanted to measure the windows. The first window was 3 feet wide. The second window was twice as wide. How wide was the second window?
1P-14) Each woman washed 2 shirts. 8 shirts are now clean. How many women are washing?
1P-13) 9 friendly monsters appeared in my dream. A friend made almost all of them disappear. Only 1 monster was left. How many disappeared?
1P-12) 2 basketball teams get ready in the gym. There are 5 women on each team. How many women get ready to play?
1P-11) 3 ladies were dancing in the ballet. Each lady had a partner. How many people were dancing?
1P-10) Here is Ruth's math paper. It has 4 addition problems. It has 2 division problems. She got 2 problems wrong. All the rest are right. How many did she get right?
1P-9) We have an orchestra at our school. 2 people are playing the violin. Twice as many people are playing the trumpet. How many people are playing the trumpet?
1P-8) 7 snakes rest on the rocks. 1 snake slithers away. The rest of the snakes stay. How many snakes stay?
1P-7) 9 balloons. 5 balloons fly in the sky. The rest go into the pond. How many balloons go into the pond?
1P-6) Grandpa baked cupcakes. He gave the cupcakes to Ben, Bess, and Bill. Each of them ate 2 cupcakes. All the cupcakes were eaten. How many cupcakes did Grandpa bake?
1P-5) Len and Peg went fishing. Len got 5 fish. Peg got 1 more fish than Len got. How many fish did Peg get?
1P-4) Ann has 5 beanbags. Nan has 1 black beanbag and 3 red ones. Dot has 2 black beanbags and 2 red ones. Fran has 3 black beanbags and 2 red ones. Who has the same number of beanbags as Ann?
1P-3) Mom has 7 cupcakes on a tray. Grandma's tray has 2 more cupcakes than Mom's has. How many cupcakes are on Grandma's tray?
1P-2) Dean had some beans. He then eats 5 beans. 2 beans are left. How many beans did Dean have to begin with?
1P-1) 6 cubes are in a pile. Jake takes some cubes. 2 cubes are left. How many cubes did Jake take?
Expectations of Core Processes from the 2008 Mathematics Standards Revision (draft) - Grade 1
Identify questions to be answered when solving a problem. Solve problems, choosing from a variety of problem-solving strategies such as drawing pictures, manipulating objects, using numbers, or acting out the situation. Tell what they did to solve a problem, using drawings or models if necessary. Identify what is known and unknown in a problem and recognize when information is missing. Determine whether a solution makes sense. Example:
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GUESS, CHECK, AND REVISE
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
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
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
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
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
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
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
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.