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What Must Students Do When Solving Problems?PowerPoint Presentation

What Must Students Do When Solving Problems?

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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.

4) CHECK your solution.

Read and Understand 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

- CHOOSE a strategy to help you solve the problem
-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

- ESTIMATE your answer.
- SHOW all work.

Check your Solution

- RESTATE the question.
- CHECK your answer to be sure it is reasonable.
- 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.

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