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"It isn't that they can't see the solution. It is that they can't see the problem." -- G.K. Chesterton Michelle Vaudreuil Kim VanSprange The Problem Solver 4 step method Makes competent and confident problem solvers Incorporates think-pair-share Integrates writing with math notebooking Metacognitive strategies Utilizes 10 different strategies Pre and post test results “Find Out” Read question Reread, pulling only important info. Restate in own words Turn and talk “Choose a Strategy” Choose a strategy card Be prepared to explain Think-pair-share Whole class holds up card Teacher leads to correct strategy through questioning “Solve It” Teacher guides whole group Students record in notebook Must show proof that strategy was used Reflect – Did the strategy help solve the problem? “Look Back” Reread problem and necessary info. Did you use all necessary info.? Did you answer the question? Does your answer make sense? Explain in writing Model, model, model! Let’s Practice! Every July 4th the Mahoneys get together for a picnic, each with a musical instrument. There is one grandmother and one grandfather. There are 4 mothers and 4 fathers. One half of the mothers have 3 daughters, one mother has 2 daughters, and one mother has one daughter. One half of the fathers have one son. There are 3 sons-in-law and no daughters-inlaw. What is the fewest number of instruments the Mahoneys will bring to the picnic? Think About the Following… What questions might you ask to guide students through each stage of the 4 step model? What are some common misconceptions students might have regarding the problem? What are some common errors you might see? What reading strategy might help solve this problem? Now You’re the Teacher! Recently, a census was taken on space station Gamma. Of the 100 residents interviewed, 75 traced their ancestry to planet Omicron, 85 traced their ancestry to planet Omega, and 60 residents traced their ancestry to both planets. How many residents have ancestors from ONLY Omicron, and how many residents had ancestors from ONLY Omega? Try Another Strategy “You’re kidding,” said Caleb to his friend Donna. “You want to be that when you grow up?” Alice, Barklay, Kayla, and Donna are talking about what they want to do when they grow up. Caleb enjoys helping his younger brother learn his math facts. Donna gets motion sickness. Both Donna and Barklay hate to go camping and hiking. Together they want to be a doctor, a pilot, a forest ranger, and a teacher. Can you match each person with each occupation? Questions? Do you have any questions for us? Websites to visit http://www.hawaii.edu/suremath/k4_12dir/k4_12men u.html (K-12 word problems) http://www.mystfx.ca/special/mathproblems/grade6. html (6th grade problems) http://www.mystfx.ca/special/mathproblems/grade7. html (7th grade problems) http://www.mystfx.ca/special/mathproblems/grade8. html (8th grade problems) References Problem Solving. (n.d.). Rock Valley College. Retrieved March 27, 2011, from http://www.rockvalleycollege.edu/StudentServices/TutoringLab/ProblemSolving.cfm Problem Solving Resources for Middle Grades Teachers. (n.d.). Appalachian State University :: Boone, North Carolina. Retrieved March 27, 2011, from http://www.appstate.edu/~salinastm/problemsolving.htm Instructional Strategies Online - Think, Pair, Share. (n.d.). Online Learning Centre. Retrieved March 27, 2011, from http://olc.spsd.sk.ca/DE/PD/instr/strats/think/ Tajika, H., Nakatsu, N., Nozaki, H., Neumann, E., & Maruno, S. (2007). Effects of self-explanation as a metacognitive strategy for solving mathematical word problems. Japanese Psychological Research, 49(3), 222-233. doi:10.1111/j.14685884.2007.00349.x