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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.

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What Must Students Do When Solving Problems?

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  1. 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

  2. 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.

  3. 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.

  4. Problem Solving Steps 1) READ and UNDERSTAND the problem. 2) PLAN a solution. 3) SOLVE the problem. 4) CHECK your solution.

  5. 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.

  6. 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

  7. Solve the Problem • ESTIMATE your answer. • SHOW all work.

  8. Check your Solution • RESTATE the question. • CHECK your answer to be sure it is reasonable. • ADD necessary units or labels.

  9. Example Problem Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

  10. 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?

  11. 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.

  12. 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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