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The students will be able to draw a model to help them write expressions that can be use to solve one‐ and two‐step problems.
The skills and strategies needed for successful mathematical problem solving start developing in the preschool years, when children acquire a basic conceptual understanding of the base 10 numerical system Students in grades three, four, and five continue to apply and refine the skills and strategies necessary to solve real life mathematics problems However, many students, especially students with learning disabilities, have difficulty solving math word problems because they often cannot decide what to do to solve the problem. Most textbooks are not very helpful when it comes to teaching students how to solve math problems.
Teaching mathematical problem solving is a challenge for many teachers, many of whom rely almost exclusively on mathematics textbooks to guide instruction. Most mathematics textbooks simply instruct students to draw a picture or make a diagram
Students who have difficulty solving math word problems usually draw a picture of the problem without considering the relationship among the problem components and, as a result, still do not understand the problem and therefore cannot make a plan to solve it. So, it is not simply a matter of drawing a picture or making a diagram; rather, it is the type of picture or diagram that is important. Effective visual representations, whether with manipulatives, with paper and pencil, or in ones imagination, show the relationship among the problem parts.
For upper elementary students, math problem solving instruction should start with onestep problems involving only whole numbers. When students have mastered the problems at this level, they can progress to one‐step problems with decimals. They can then progress to two‐step problems with whole numbers, and so on.
(From Math Problem Solving for Upper Elementary Students with Disabilities; Marjorie Montague, Ph.D., University of Miami; see Resources.)
This lesson will explore a variety of strategies, methods, and classroom structures that can be used in helping students to become better problem solvers, but the main focus of the lesson will be on using a whole/part model that can be used as a tool to help students understand and solve one and two operation problems that are required by the fifth Grade Math Core. This whole/part model also relates to the fifth Grade Science Core, Standard 1, which deals with physical and chemical changes in matter. In this science standard students learn that matter cannot be created or destroyed, and that the sum of the parts is equal to the whole. Often this is a hard concept for students to understand, but, by using the whole/part model in math and science, it can help to deepen students understanding of this fundamental concept.
When students approach a math problem, they need to be armed with strategies that will allow them to be successful. Since students face a wide variety of problems, they need a variety of strategies. The whole/part approach is just one approach to problem solving and is not applicable to all types of problems. It works well for many one step choose an operation type problems and many multiple‐step problems.
Invitation to Learn:
Explain to the class that today they will be discussing problem solving, and to get everyone into the spirit of problem solving you are going to give them some problems to solve. Have students find the Problem Solving Quiz (this quiz has trick questions and riddles) and work the problems. Give participants time to complete the quiz. Discuss the answers to the questions and have students share strategies they used to find the answers.
Problem Solving Quiz Answers
12, they all have at least 28 days
He has 9; the rest died
None; you cannot take dirt out of a hole.
You have 2 apples
70 because 30 / ½ = 30 x 2/1 = 60; 60 + 10 = 70
A half‐dollar and a nickel. One's not a nickel; the other one is.
12 is always a dozen
They both have 4 quarters
At a yard sale
Only once; after that you no longer have 30
Lesson and Activity Time Schedule:
Activity Connected to Lesson:
Problem Writing Activity:
Assign the class a Problem of the Day. Have students work in pairs, teams or individually to solve the problem. Have students share their solutions with the class and discuss.
Encourage students to share or teach what they have learned about model drawing with parents and family members.
Use student problem solutions to determine their understanding of the process and what type of problems they need to be assigned to continue to progress.