Grade 2 Practice Problems: Reasoning, Problem Solving & Communication
Expectations from Standards Revision and Strategy Description
2P-13) Dawn wanted to earn some money to buy a bathing suit. She made ice tea to sell. Her friend Carl came to buy some. Carl paid 10 cents for his first glass of ice tea and 5 cents for each glass of ice tea after that. Carl drank a total of 15 glasses of ice tea. How much money did Carl pay Dawn for all of the iced tea he drank? Show your work.
2P-12) It is two miles from my house to Mike's. It is twice as far from Mike's house to Ben's. How far is it from my house to Ben's?
2P-11) There are 10 crayons in each box. We had 5 full boxes and 2 extra crayons. We gave away 38 crayons. How many crayons are left?
2P-10) In the circus there are 2 clowns. There are twice as many elephants as clowns. There are twice as many lions as elephants. There are 2 more bears than lions. There are half as many ponies as bears. How many elephants, bears, and ponies are there?
2P-9) There are 9 rungs on the ladder. Beth is on the third rung. Ellen is 3 rungs higher than Beth. What number rung is Ellen on?
2P-8) Some dogs are playing in a kennel. 5 dogs jumped out of the kennel. 3 dogs are left in the kennel. How many dogs are there to begin with?
2P-7) Mary traded trailers with Chet. She gave Chet 3 red trailers and 4 blue ones. She wants to get an equal number of trailers back. How many trailers must Chet give her?
2P-6) I see 3 wires with 8 birds on them. 5 birds sit on the first wire. 0 birds sit on the second wire. How many birds sit on the third wire?
2P-5) Every year Carol gets a new pearl for her necklace. 2 years ago Carol had 7 pearls in the necklace. How old is Carol now?
2P-4) My room is 6 yardsticks long. My sister's room is 2 yardsticks longer than my room. My brother's room is half as long as my sister's room. How long is my brother's room?
2P-3) These eagles eat 3 salmon at each meal. The eagles eat 3 meals a day. 18 eels were eaten at today's meal. How many eagles were there?
2P-2) We are saving pennies to buy a treat for the class. Sarah has 10 pennies. Kate has twice as many pennies as Sarah. Tim has half as many pennies as Sarah has. Mike has half as many pennies as Kate has. Lillian has twice as many pennies as Tim and Mike have together. How many pennies do we have?
2P-1) Rick and Mike went to an orchard to buy fruit trees. They came home with the same number of trees. Rick got 5 apple trees, 3 peach trees, and 4 plum trees. Mike got 6 apple trees and 2 peach trees. The rest of Mike's trees were pear trees. How many pear trees did Mike buy?
Expectations of Core Processes from the 2008 Mathematics Standards Revision (draft) - Grade 2
Identify questions to be answered when solving a problem. Recognize when information is missing from a problem. Identify what is known and unknown in a problem. Solve problems, choosing from a variety of problem-solving strategies such as drawing pictures, manipulating objects, using numbers, looking for a pattern, or making a list. Tell what they did to solve a problem, using drawings or models if necessary. Determine whether a solution makes sense. Example:
|
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.