When a child sits down to play a game of checkers, he must take things slowly, and weigh all of his options before making a move. Each new turn is a problem for him to solve, and checkers especially hones in on the consequences of a decision; if you make the wrong move, your opponent can jump your piece. Encourage your child to identify each possible move and weigh the outcomes of each move before making a final decision.
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The "Egg Drop" is a problem-solving game that has been used for decades to encourage children to solve the problem of how to protect an egg from cracking when it is dropped from a height of eight feet or higher. This activity works because when the problem has not been solved, the consequence is immediately evident -- a smashed egg. Explain the concept to your child, and have her brainstorm ideas. Provide her with the supplies she needs to create the structure, making sure to encourage her to keep going if the first (or first several) ideas don't work out.
See Reference 3
On a flat surface, draw two parallel lines as the "Start" and "Finish" lines. They should be at least two feet apart. Place a piece of crumpled paper at the "Start," and tell your child that he must get the paper to the "Finish" line without touching it. You have the option of allowing him to touch the paper with other materials such as a stick, or you can stick with the rule that nothing can touch the paper. His only option will be to blow the paper to the "Finish" line.
If you are working with a young child who is around preschool age, hone her problem-solving skills by placing her favorite toy just out of reach. You can put it on a shelf a foot above her head, or push it underneath the couch. Encourage her to try as many different ways as she can to get her toy, from standing on a stool to using a mixing spoon to knock the toy off of the counter, or to pull it from under the couch.