1. Problem Solving Strategies Kaitlynn Hoehne

2. Click each picture to explore each of the problem solving strategies Draw a diagramGuess and checkSolve an easier related problem Make a systematic listIdentifying sub-problemsCreating a physical representation Eliminate possibilitiesAnalyze the unitsVisualize spatial relationships Use matrix logicDraw Venn diagramsOrganize info in more ways Look for a patternWork backwardsConvert to algebra

3. Draw a Diagram 0 Do not hesitate to draw 0 You don’t have to be an artist to draw a useful diagram 0 If you can visualize it, draw a diagram!

4. Make a systematic list 0 Start with a messy list/lists you are willing to give up 0 Be sure you thoroughly understand system 0 Monitor your system, being especially careful at logical break points 0 If the system doesn’t seem to be working don’t be afraid to revise it or start over

5. Eliminate possibilities 0 Generate possibilities 0 Eliminate possibilities by finding contradictions 0 List the remaining possibilities 0 Check them against the evidence. There may be more than one solution 0 Think about possibilities you might have missed

6. Use matrix logic 0 Mark traits from clues 0 Combine clues, perhaps using adjunct lists 0 Eliminate possibilities and act on eliminated possibilities 0 Substitute 0 Cross-correlate 0 For other approaches or problems: study the introduction, and test assumptions

7. Look for a pattern 0 Write down the sequence, and extend it if you can 0 Make a chart 0 Calculate differences 0 Try other operations as needed 0 Describe the pattern with symbols

8. 0 Start a guess-and-check chart 0 Be ready to start over 0 Build from smaller to bigger numbers 0 Bracket to close in on an answer 0 Be careful to rate guesses correctly 0 Avoid arithmetic mistakes

9. Identifying sub-problems 0 Figure out what you need to know 0 Break problem up into small, doable sub-problems 0 Solve sub-problems 0 Use sub-problems to answer original problem

10. Analyze the units 0 Identify all the units in the problem and answer 0 Make manipulatives for the given information and reciprocals 0 Use one-n-oes for the conversion of units 0 Be flexible in organizing the manipulatives and one-n- oes so that the unwanted units will cancel

11. Solve an easier related problem 0 Use a number instead of a variable 0 Try smaller or easier numbers 0 Change, fix, or get rid of some conditions 0 Look for a pattern in easier examples 0 Find a process in an easier example

12. Creating a physical representation 0 Use manipulatives 0 Act it out 0 Allows you to “touch” the problem

13. Work backwards 0 Work from the end to the beginning 0 Draw diagrams as needed 0 Perhaps act it out 0 Use algebra or other tools to get from one step to the previous one 0 Check from the beginning to the end

14. Draw Venn diagrams 0 Draw overlapping loops for intersecting sets 0 Fill regions from the inside out 0 Subtract carefully 0 After regions are filled, see what number answers the question 0 Check the calculations

15. Convert to algebra 0 Analyze the problem to see if it can be solved algebraically 0 Create an equation or inequality based on the problem 0 Solve the equation 0 Check the solution

16. Organize info in more ways 0 Imagine special cases as needed 0 Draw an array or tree diagram 0 Carefully examine the branches of the tree 0 Think critically about your solution

17. 0 Use a graph or a scale drawing 0 Measure carefully 0 Apply other strategies, such as unit analysis 0 Interpret the results

18. Work Cited 0 This presentation and information brought to you by Cathy Banks course “Problem Solving in Secondary Education”