What Must Students Do When Solving Problems?

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# What Must Students Do When Solving Problems - PowerPoint PPT Presentation

What Must Students Do When Solving Problems?. To solve even simple problems, students must: -understand the vocabulary and instructions contained within the problem -recall mathematical rules and formulas -recognize patterns -use sequential ordering to solve multi-step problems.

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Presentation Transcript
What Must Students Do When Solving Problems?
• To solve even simple problems, students must:

-understand the vocabulary and instructions

contained within the problem

-recall mathematical rules and formulas

-recognize patterns

-use sequential ordering to solve multi-step

problems

What Does NCTM Say About Problem Solving?
• The difference between successful and unsuccessful problem solvers lies in their beliefs about problem solving, themselves as problem solvers, and about ways to approach solving problems.
• When students who believe that math problems can be solved quickly and directly don’t immediately know how to solve a problem, they give up.
How Can We Help?
• Incorporate problem solving regularly in the classroom so students become comfortable with it.
• Teach problem solving steps and strategies.
• Use real-life data and integrate other content areas into the problems as much as possible.
• Use word problems, charts, and tables to introduce units of study not just at the end.
Problem Solving Steps

1) READ and UNDERSTAND the problem.

2) PLAN a solution.

3) SOLVE the problem.

• READ the problem carefully and RESTATE it in your own words.
• HIGHLIGHT important information and ignore what is not needed.
• DETERMINE the question to be solved.
Plan a Solution

-find a pattern -guess and check

-make an organized list -draw a diagram

-write an equation -work backward

-solve a simpler problem -read a table/chart

• DECIDE what mathematical operation(s) need to be used
Solve the Problem
• SHOW all work.
• RESTATE the question.
• ADD necessary units or labels.
Example Problem

Middle School Student Populations

How many more students are at Lincoln Middle School than at Washington Middle School?

Other Possible Questions
• How many more male students than female students are there?
• How many total students are there at all three schools?
• Which school has the largest or smallest population?
• What is the difference between the school with the largest population and the one with the smallest population?
• What is the mean of the female or male students?
Strategies
• When first presenting a table or chart, have students summarize what information is contained in the table before asking them to answer any questions.
• Have students create their own questions based on the information in the table or chart and have classmates answer them.
Strategies continued…
• Pose a question based on the table or chart and have students use the four problem solving steps to solve it.
• Have students reword the existing problem in such a way that essential information is the same, but it is worded differently.
• Alter important information in the problem and talk about how the problem has been changed.