Problem Solving Jan Sands KESAM 2006 Sources: Dr. Grayson Wheatley, AIMS, Connected Math

Problem solving is… In problem solving the answer is not apparent. Problem solving is what you do when you don’t know what to do. If you know how to get an answer, it is not problem solving.

Strategies Many and varied strategies Students develop strategies Try something !

Problem Solving #1 Use problem-solving approaches act out situations represent problems with drawings and lists, use concrete, pictorial, graphical, oral, written, and/or algebraic models understand a problem, devise a plan, carry out the plan, look back

Problem Solving #2 Formulate problems from everyday and mathematical situations how many forks are needed? how many students are absent? how can we share/divide these cookies? how many different ways can we find to compare these fractions?

Problem Solving #3 Develop, test, and apply strategies to solve a variety of routine and nonroutine problems look for patterns make a table make a problem simpler process of elimination trial and error

Problem Solving #4 Verify and interpret results with respect to the original problem students explain verbally why an answer makes sense explain in a written format why an answer makes sense verify the validity of each step taken to obtain a final result

Problem Solving #5 Distinguish between necessary and irrelevant information in solving problems play games and discuss “best” clues write riddles with sufficient information identify unnecessary information in written story problems

Three Coins I have some pennies, nickels, dimes and quarters in my pocket. If I pull out 3 coins, how much money could I have in my hand? List all possibilities.

Cats At the zoo Patty saw 21 lions and tigers. There were five more lions than tigers. How many were tigers?

Tables We have 12 square tables, each of which seats 1 person on a side. If we push them together to form one long table, how many people can be seated?

Chest The distance between the tips of my fingers is 65 inches. Each of my arms is 24 inches long. How far is it across my chest?

Think of a Number I am thinking of a number. If 23 is subtracted from the result of multiplying it by 7, the result is 89.

Cubes Which cubes share exactly four faces with other cubes?

Cube Layers How many cubes have no paint? How many cubes are painted on 1 side? 2 sides? 3 sides? 4 sides? More than 4 sides?

Painted Cubes Paint is poured down over this big cube. There is no paint on the bottom. How many small cubes will not have paint on them?

Mystery Numbers I am thinking of two numbers. When I add them I get 61. When I subtract them I get 13. What are the two numbers?

Mystery Numbers I am thinking of two numbers. When I add them I get 61. When I subtract them I get 13. What are the two numbers?

Mystery Numbers I am thinking of two numbers. When I add them I get 61. When I subtract them I get 13. What are the two numbers?