Students will

Explore different ways to find solutions to problems or situations.

Draw a picture that represents a problemsolving strategy.

ProblemSolving: Math, Episode 2 video

Drawing paper

Crayons

Pencils and crayons

Discuss problems students have had and the ways they solved them. Ask students these kinds of questions:

Have you ever forgotten your lunch? What did you do?

Have you ever been unable to do your homework because you didn't understand it? What did you do?

Have you ever been in a fight with somebody? How did you work it out?
Talk about the strategies scientists, engineers, and mathematicians use when solving problems. How are their strategies similar to those of the students? A good way to introduce the topic of problem solving is to watch ProblemSolving: Math, Episode 2 .

After watching the program, discuss the strategies featured. When does diagramming or drawing pictures come in handy? When do students or their parents make lists to help them solve problems? How does discussing a problem or situation help solve it? Why is it important to think clearly and be organized when solving a problem?

Brainstorm some schoolbased problems with the class, such as trash on the playground, noise in the hallways, limited handicapped access in some areas, too few bathrooms or dirty bathrooms, incorporating healthier foods in the cafeteria, the need for more computers). Choosing one, discuss with students how they might go about solving it. What are some possible solutions to this problem? How would you test the solutions? Who would you talk with to discuss possible solutions? Would a diagram or drawing help you solve this problem? Do you need math to solve this problem? What would you say to make people understand your solution?

Ask volunteers to share some small problems they have encountered and as a class, discuss some of the ways to go about solving them. Once you are confident that students understand problemsolving techniques and the importance of delivering a clear explanation of problems and solutions, tell them that they are going to draw pictures of a problem and how they solved it.

Demonstrate drawing a line down the center of a piece of paper. Draw an example of a problem on one side of the paper, such as a forgotten lunch or difficulty building a model airplane. On the other side of the divided paper, draw a solution to the problem, perhaps asking a friend to share their lunch, or a child drawing a diagram of the model airplane.

Make sure students understand what you are asking them to do. Then distribute the drawing paper and allow time to draw pictures. More advanced students can write a sentence or two describing their problem and solution.

Once students have completed their drawings, have volunteers share them with the class. Talk about the different problems and solutions.
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Use the following threepoint rubric to evaluate students' work during this lesson.

Three points: Students were highly engaged in class discussions; demonstrated a clear understanding of different problemsolving strategies; and drew colorful, unique pictures that clearly identified a problem and a solution.

Two points: Students participated in class discussions; demonstrated a general understanding of different problemsolving strategies; and drew somewhat colorful and unique pictures that mostly identified a problem and a possible solution.

One point: Students participated minimally in class discussions; were unable to demonstrate a basic understanding of different problemsolving strategies; and drew incomplete or inaccurate pictures that did not clearly identify a problem or drew a solution that did not fit the problem.
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diagram
Definition : A plan, sketch, drawing, or outline designed to demonstrate or explain how something works or to clarify the relationship between the parts of a whole
Context : Diagrams can be used to plan new structures and to find out how a damaged building looked originally.
explanation
Definition : The act or process of defining something or making it understood to others
Context : A good explanation of a solution can help us understand and solve similar problems.
problem
Definition : A question to be considered, solved, or answered
Context : Making a list is a way of organizing information to solve a problem.
strategy
Definition : To determine the dimensions, quantity, or capacity of something
Context : Discussing a problem is a good strategy to make sure a science team understands what each individual needs to solve the problem.
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Midcontinent Research for Education and Learning (McREL)
McREL's Content Knowledge: A Compendium of Standards and Benchmarks for K12 Education addresses 14 content areas. To view the standards and benchmarks, visithttp://www.mcrel.org/compendium/browse.asp
This lesson plan addresses the following national standards:

Life SkillsThinking and Reasoning: Understands and applies basic principles of logic and reasoning; Applies basic troubleshooting and problemsolving techniques

MathematicsUses a variety of strategies in the problemsolving process
National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics (NCTM) has developed national standards to provide guidelines for teaching mathematics. To view the standards online, go tohttp://standards.nctm.org/.
This lesson plan addresses the following national standards:

Problem Solving: Solve problems that arise in mathematics and other contexts; Apply and adapt a variety of appropriate strategies to solve problems
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