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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.

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What must students do when solving problems
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
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
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
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 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
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
Solve the Problem

  • ESTIMATE your answer.

  • SHOW all work.


Check your solution
Check your Solution

  • RESTATE the question.

  • CHECK your answer to be sure it is reasonable.

  • ADD necessary units or labels.


Example problem
Example Problem

Middle School Student Populations

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


Other possible questions
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
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
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.